b) A 25 mol% mixture of A in B is to be separated by distillation at an average pressure of 130 kPa into a distillate containing 95 mol% of A and a bottom containing 98 mol% of B. Determine the ratio

Answers

Answer 1

The ratio of the molar flow rate of the distillate to the molar flow rate of the bottom in the distillation of a 25 mol% mixture of A in B, at an average pressure of 130 kPa, to obtain a distillate containing 95 mol% of A and a bottom containing 98 mol% of B, is 1.33.

In distillation, the ratio of molar flow rates of the distillate to the bottom, known as the reflux ratio, plays a crucial role in achieving the desired separation. The reflux ratio determines the amount of liquid returned to the distillation column as reflux.

To calculate the reflux ratio, we need to consider the mole fractions of A and B in the feed, distillate, and bottom. Let's assume the total molar flow rate of the feed is 1 (mol/s) for simplicity.

Feed composition: 25 mol% A and 75 mol% B

Distillate composition: 95 mol% A and 5 mol% B

Bottom composition: 98 mol% B and 2 mol% A

Using the overall material balance equation:

Feed flow rate = Distillate flow rate + Bottom flow rate

1 = Distillate flow rate + Bottom flow rate

To achieve a separation, we need to choose a reflux ratio that provides the desired product compositions. In this case, the distillate should contain 95 mol% A, which means 0.95 of the distillate flow rate is A. Similarly, the bottom should contain 98 mol% B, which means 0.98 of the bottom flow rate is B.

Using the component material balance equations:

0.25 (feed flow rate) = 0.95 (distillate flow rate) + 0.02 (bottom flow rate)

0.75 (feed flow rate) = 0.05 (distillate flow rate) + 0.98 (bottom flow rate)

Solving these equations, we find that the distillate flow rate is 0.2 and the bottom flow rate is 0.8.

The reflux ratio is given by:

Reflux ratio = Distillate flow rate / Bottom flow rate

Reflux ratio = 0.2 / 0.8

Reflux ratio = 1.33

To achieve the desired separation of a 25 mol% mixture of A in B, with a distillate containing 95 mol% of A and a bottom containing 98 mol% of B, a reflux ratio of 1.33 is required. This reflux ratio ensures that the appropriate amounts of liquid are recycled back to the distillation column, facilitating the separation of the components according to their volatility.

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Related Questions

how many grams of naoh are needed to give a ph of 11.5 in a 14.5 l tank of water?

Answers

1.84 x 10^(-9) g (or 1.84 ng) of NaOH to give a pH of 11.5 in a 14.5 L tank of water.

What mass of NaOH is required to achieve a pH of 11.5 in a 14.5 L water tank?

To find the mass of NaOH needed to give a pH of 11.5 in 14.5 L of water, we first need to calculate the concentration of hydroxide ions (OH-) required to achieve that pH.

The pH of a solution is defined as the negative logarithm of the hydrogen ion (H+) concentration, so we can write:

\(pH = -log[H+]\)

We can rearrange this equation to solve for [H+]:

\([H+] = 10^(-pH)For a pH of 11.5, we have:[H+] = 10^(-11.5) = 3.16* 10^(-12) M\)

Since NaOH is a strong base that completely dissociates in water, we know that the concentration of hydroxide ions will be the same as the concentration of NaOH we add.

Therefore, we can calculate the amount of NaOH needed using the following equation:

\(moles of NaOH = volume of water (in L) * desired [OH-] concentration (in M)moles of NaOH = 14.5 L * 3.16 * 10^(-12) M = 4.59 * 10^(-11) mol\)

Finally, we can convert moles of NaOH to grams using the molar mass of NaOH:

\(mass of NaOH = moles of NaOH * molar mass of NaOHmass of NaOH = 4.59 x 10^(-11) mol* 40 g/mol = 1.84 * 10^(-9) g\)

Therefore, we need 1.84 x 10^(-9) g (or 1.84 ng) of NaOH to give a pH of 11.5 in a 14.5 L tank of water.

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HELP MEE
What kind of materials do you think would be best to use to build different parts of the playhouse? Explain your reasoning.

Answers

Answer:

Cedar, mahogany, red wood or something else is fine, but the only downside is that it will cost you more. However, a project that is partially or fully exposed to the elements, something more than normal lumber is a must. The most cost effective method is to use pressure treated lumber.

Explanation:

You can use bricks or asbestos sheet to build a playhouse or high quality clothes or wood can also make a playhouse parts better.

What are building materials?

Some materials are good  enough in construction field and which can be used to build houses and other buildings. Mainly metals, woods and bricks are used as building materials.

Metals are very shiny and hard and they will not perish easily. Metals are malleable and ductile. Hence they can be changed to any shape or size as we wish.

Bricks are made of soil cubes which are harder and have to be strong to use in builds. However, the most available material to build a playhouse in our surroundings. There are various hard wood that can be shaped and sized to desired look.

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1/ Hydra, a type of cnidarian, have equal survival rates through life because they are equally fit at all stages. Hydra are an example of an organism with a type ______ survivorship curve. Select one: a. 0 b. I c. II d. III e. IV 2/ What is different about how energy moves through an ecosystem compared to how chemicals move through the ecosystem? 3/ Tropical rain forest soils are usually Select one: a. nutrient-rich. b. low in organic matter. c. nutrient-poor and low in organic matter. d. nutrient-rich and low in organic matter. e. nutrient-poor.

Answers

Hydra, a type of cnidarian, have equal survival rates through life because they are equally fit at all stages. Hydra are an example of an organism with a type I survivorship curve. Thus, the correct option is b. II.

Differences between how energy moves through an ecosystem compared to how chemicals move through the ecosystem. The fundamental difference between how energy moves through an ecosystem compared to how chemicals move through the ecosystem is that energy can not be recycled. Energy is obtained from the sun and is stored in organic molecules, and it flows through an ecosystem through metabolic processes. However, the number of chemicals like carbon, oxygen, nitrogen, water, and phosphorus remains constant in an ecosystem.

Tropical rainforest soils are usually nutrient-poor and low in organic matter. Therefore, option c. nutrient-poor and low in organic matter is the correct answer. The soil in the tropical rainforest is nutrient-poor because heavy rainfall washes away the nutrients, and the soil contains a high level of aluminum and iron, which are toxic to plants. Due to these reasons, there is slow decomposition of organic matter that makes the soil low in organic matter.

Thus, the correct option is b.

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How many molecules are there in 24 grams of FeF_3?

Answers

1.2 × 10²³ molecules are there in 24 grams of  FeF₃ molecule. 1 mole is equal to 6.023 × 10²³ particles.

What do you mean by mole ?

A mole is a important unit of measurement that chemists use in calculation. 1 mole is exactly equal to the 6.023 × 10²³ particles.

The term mole is defined as the amount of substance containing 6.023 × 10²³ molecules.

First multiply the number of moles supplied by Avogadro's Number to detect how many molecules there are.

Moles are determined from the molecular weight.

For FeF₃ molecule,

55.8 + 3⋅19 = 116g/mole

24 gram /  116g/mole

= 0.207 moles of  FeF₃

= 0.207 moles × 6.023 × 10²³

= 1.2 × 10²³ molecules

Thus, in 24 grams of FeF₃ molecule 1.2 × 10²³ molecules are present.

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Using standard formation enthalpies, calculate the standard reaction enthalpy for this reaction. 6CO2(g) + 6H2O(l)C6H12O6 + 6O2(g) ANSWER: kJ/mol

Answers

Answer:

2802.5 KJ/mol

Explanation:

Calculate standard enthalpy of the Reaction :

6CO2(g) + 6H2O(l)C6H12O6 + 6O2(g)

using standard formation enthalpies . hence the standard enthalpy of the reaction = 2802.5 KJ/mol

attached below is the detailed solution

Using standard formation enthalpies, calculate the standard reaction enthalpy for this reaction. 6CO2(g)

What are good life notes about science

Answers

Answer:

science is pointless and you will never need it so just get thru the class and let it go.

Explanation:

have a good day in need to get rid of the adds so I'm answering as many questions ap

magnesium has three stable isotopes, 24mg (23.985042 amu), 25mg (24.985837 amu), and 26mg (25.982593 amu). the relative abundance of 24mg is 79%. what is the percent relative abundance of 25mg?

Answers

The stable magnesium isotope has a nuclear spin of 5/2, a 10.0 atom percent natural abundance, and a relative atomic mass of 24.985837 amu.

Isotopes are atoms with the same number of protons but differing numbers of neutrons. The quantity of a substance is determined by mass. It is expressed as a kilogram or gram. The mass of an element's isotopes is known as the average mass. It can be computed by multiplying an isotope's mass by its natural abundance.

The mass that is in relation to a substance that is regarded as standard is called the relative mass. Relative mass in chemistry is equivalent to one-twelfth the mass of the C-12 isotope].

Average atomic mass is equal to (mass of the first isotope times its percent abundance) plus (mass of the second isotope times its percent abundance).

replacing the specified values

Average atomic mass is equal to 0.7899 x 23.985 x 0.10 x 24.985 x 0.101 x 25.9825, or 24.305 amu.

Consequently, magnesium has an average atomic mass of 24.305 amu.

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Which atom (magnesium or chlorine) is larger? _______________________(you should also be prepared to answer the question if asked for the smaller atom)3a. Explain why the atom is larger. Include the following terms in your answer: protons, electrons, shells or layers, columbic attractions

Answers

Answer:

The magnesium atom is larger.

Explanation:

The magnesium atom is larger because it is on the left side of the Periodic Table (period 3 and group 2) where the atomic radius is larger.

Atomic radius is the distance from the center of the nucleus of an atom to the most external electron shell.

The greater the columbic attractions, the closer the protons in the nucleus are to the electrons in the outer layers, making the size of the atom smaller.

help pls before I end it all

help pls before I end it all

Answers

Answer:

We might just have to end it together

Explanation:

I tried to answer it now I'm stuck in the same hole -_-

Ok so for every 8 miles of NHO3 you can make 4 moles of water

So 70 moles of NHO3 can give you 70/8*4=35 moles of water

2Ag(s) + S(s) -> Ag2S(s)

If we used 0.7 moles Ag and 0.312 moles S, would Ag be the limiting reactant?

Answers

Answer:

Sulphur

Explanation:

Sulphur because we been 2 ag for 1 s therefore 0.312 S will need 0.624 of Ag

Ag is not the limiting reactant in this case. The limiting reactant is determined by the reactant that is completely consumed first, and in this case, it is S.

To determine the limiting reactant, we need to compare the moles of each reactant to the stoichiometric ratio of the balanced equation. The balanced equation for the reaction is:

2Ag(s) + S(s) →Ag₂S(s)

According to the balanced equation, the stoichiometric ratio between Ag and S is 2:1. This means that 2 moles of Ag react with 1 mole of S to produce 1 mole of Ag₂S.

Given:

Moles of Ag = 0.7 moles

Moles of S = 0.312 moles

To determine if Ag is the limiting reactant, we need to compare the moles of Ag to the stoichiometric ratio.

Moles of Ag / Stoichiometric coefficient of Ag = 0.7 moles / 2 = 0.35 moles

Comparing this value to the moles of S, we can see that 0.35 moles of Ag is less than 0.312 moles of S. Therefore, Ag is not the limiting reactant in this case. The limiting reactant is determined by the reactant that is completely consumed first, and in this case, it is S.

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A car traveling 60 km/h can brake to a stop within a distance d of 20 m. If the car is going twice as fast, 120 km/h, what is its stopping distance

Answers

The stopping distance for a car traveling at 120 km/h is **80 meters**.

To calculate the stopping distance, we can use the formula: stopping distance = k × (initial speed)², where k is a constant that depends on factors like braking power and road conditions. In this case, we know that a car traveling 60 km/h can stop within 20 meters, so we can find the constant k as follows: k = stopping distance / (initial speed)² = 20 / (60)². Now, let's double the initial speed to 120 km/h and find the new stopping distance: stopping distance = k × (initial speed)² = k × (120)². Since we already know the value of k, we can plug it in and find the stopping distance, which turns out to be 80 meters. This demonstrates that the stopping distance increases with the square of the initial speed.

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According to the article, The Future of Energy Use, the Earth's average surface temperature increased in the last century is about ___°C

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According to the article, 'The Future of Energy Use', the Earth's average surface temperature increased in the last century by about 2.5 °C.

What is global warming?

The expression global warming refers to the sudden increase in temperatures around the Earth during the last decades.

It has been shown that global warming is directly associated with the burning of fossil fuels.

Global warming is caused by the increase of greenhouses gases (for example, carbon dioxide) in the atmosphere.

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How do volcanoes cause changes in the Earth's surface?

Answers

Answer: If lava hit water it forms rock that helps make islands and moutains

Explanation:

Answer: When volcanoes erupt, hot lava is released from inside the Earth.

Explanation: allowing molten rock, or magma, to escape the earth and create rock formations or mountains.

1. The modern periodic table organizes the elements based on?

Answers

Answer:

By element with the lowest atomic number to the highest atomic number.

Explanation:

ten moles of helium gas and one mole of solid argon are in thermal equilibrium with each other at 10 k. both helium and argon are monatomic, and argon is ten times as massive as helium. how do the average speeds of the atoms in these two substances compare under the conditions specified? explain/justify your answer using appropriate components of the particle model of thermal energy and/or previous models we have used

Answers

Helium moves more quickly on average than argon.

How much thermal energy does helium have compared to argon?

Helium has a lower thermal energy than argon does.

Explanation:

Due to the smaller mass of helium atoms in comparison to argon atoms, their average speed is higher under the given conditions. An atom's average speed is inversely related to its mass. While the average speed of an atom reduces as the mass of the atom grows, the opposite is true if the mass of the atom decreases.

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what is the name for a change in the environment that causes an organism to change it's activity

Answers

Answer:

the answer is stimilus!

Explanation:

The name of this is called stimulus hope this helps a lot

Discuss the regulation of citrate synthase and explain why the effectors NADH, ATP and succinyl CoA make sense.The rate of flow is limited by the availability of the citrate synthase substrates, oxaloacetate and acetyl- CoA, or of NAD+, which is depleted by its conversion to NADH.• The enzyme is inhibited by high ratios of [ATP]/[ADP] and [NADH]/[NAD], as high concentrations of ATP and NADH show that the energy supply is high for the cell. This is to make sure not more NADH is produced that is converted into ATP. Similarly, when enough ATP is around, the introduction of acetyl-CoA into the pathway is inhibited.

Answers

The regulation of citrate synthase is important for maintaining cellular energy balance. The enzyme is inhibited by effectors such as NADH, ATP, and succinyl CoA, which makes sense due to their roles in cellular energy metabolism.

Citrate synthase catalyzes the reaction between oxaloacetate and acetyl-CoA to form citrate, a key step in the citric acid cycle. The rate of this reaction is limited by the availability of substrates oxaloacetate, acetyl-CoA, and NAD+, which gets converted to NADH during the cycle.

High concentrations of NADH and ATP indicate that the cell has sufficient energy supply. In such cases, citrate synthase is inhibited to prevent excessive production of NADH, which would ultimately lead to more ATP generation. This ensures that the cell does not produce more energy than needed.

Similarly, when there is an abundance of ATP, the enzyme is inhibited to prevent the introduction of acetyl-CoA into the citric acid cycle. This allows the cell to maintain an optimal energy balance by preventing unnecessary energy production.

In conclusion, the regulation of citrate synthase by effectors such as NADH, ATP, and succinyl CoA is crucial for maintaining cellular energy homeostasis. By responding to the concentrations of these molecules, citrate synthase helps to ensure that the cell produces the appropriate amount of energy for its needs.

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Which fluid is expected to have lowest viscosity?

Answers

Among common fluids, gases generally have the lowest viscosity compared to liquids.

Viscosity is a measure of a fluid's resistance to flow or its internal friction. In gases, the molecules have greater separation and move more freely, resulting in lower intermolecular forces and thus lower viscosity.

Among gases, lighter gases with smaller molecular sizes tend to have lower viscosities. For example, helium (He) is one of the lightest gases and has a very low viscosity. Other gases like hydrogen (H2) and neon (Ne) also exhibit low viscosities.

It's important to note that the viscosity of a fluid can be influenced by various factors, such as temperature and pressure. However, in general, gases have lower viscosities compared to liquids.

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7. convert 22.7g to μg

Answers

The 22.7 g  in μg ( micro gram )  is 22.7 × \(10^{-6}\) .

We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation.

For example , we do not measure a pencil's length in kilometers . In this situation , one must convert from kilometers  ( km ) to centimeters ( cm ) . In most cases, multiplicative conversion factors are used to convert one unit to another of the same quantity .

Sometimes the units of measurement used may not correspond to the standards required for a particular process or application, as well as the measuring choice and convenience. The mass of object in micro gram unit is less than gram .

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PLEASE HELP ASAP!!!!!!!!

PLEASE HELP ASAP!!!!!!!!

Answers

Answer:

ouch......it's kinda a practical question..

Answer: ?

Explanation: what was the answer?

what happens when light hits something white? why does it happen?

Answers

Answer: White objects look white because they reflect back all the visible wavelengths of light that shine on them - so the light still looks white to us. Colored objects, on the other hand, reflect back only some of the wavelengths; the rest they absorb.

Explanation:

Baking soda is sodium bicarbonate, NaHCO3, and vinegar is primarily acetic acid, HC2H3O2. When baking soda is added to vinegar, the resulting reaction produces a tremendous amount of gas, as shown in this video. NaHCO3(s) + HC2H3O2(aq) rightarrow Complete this equation for the reaction of NaHCO3(s) with HC2H3O2(aq). Include phase symbols. NaHCO3(s)+ HC2H3O2(aq) rightarrow

Answers

NaHCO3(s) + HC2H3O2(aq) → CO2(g) + H2O(l) + NaC2H3O2(aq)

This equation represents the reaction of baking soda (sodium bicarbonate) with vinegar (acetic acid) to generate carbon dioxide gas, water, and sodium acetate.

The balanced equation for the reaction of NaHCO3(s) with HC2H3O2(aq) including phase symbols is

NaHCO3(s) + HC2H3O2(aq) → CO2(g) + H2O(l) + NaC2H3O2(aq)

Baking soda, also known as sodium bicarbonate, is a white, crystalline powder with the chemical formula NaHCO3. It is an alkaline substance that neutralizes acids.

Vinegar is mostly composed of acetic acid, HC2H3O2, which is a weak acid. Vinegar has a sour flavor and a strong smell due to the presence of acetic acid.

NaHCO3(s) + HC2H3O2(aq) → CO2(g) + H2O(l) + NaC2H3O2(aq)  This equation represents the reaction of baking soda (sodium bicarbonate) with vinegar (acetic acid) to generate carbon dioxide gas, water, and sodium acetate. When the baking soda and vinegar are combined, a chemical reaction occurs, causing carbon dioxide gas bubbles to form. This is due to the reaction between the acid and base in the mixture, which generates carbon dioxide gas as a byproduct. This reaction is commonly used in baking as a leavening agent to make cakes, muffins, and other baked goods rise.

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A diabetic is recommended to use 1 ml of insulin for every 10 g of carbohydrates consumed. the recommended daily intake of carboydrates is 300 g. a diabetic has eaten a slice of toast and has consumed 5% of their daily value of carbohydrates. how many ml of insulin should the diabetic use to maintain a proper blood sugar level after eating the piece of toast?

Answers

The diabetic should use 1.5 ml of insulin to maintain a proper blood sugar level after eating the piece of toast.

Insulin is a hormone that plays a crucial role in regulating blood sugar levels in the body, particularly in individuals with diabetes. In a person with diabetes, the body either doesn't produce enough insulin or is unable to effectively use the insulin it produces.

Insulin helps facilitate the absorption of glucose (sugar) from the bloodstream into cells, where it is used for energy or stored for later use. It acts as a "key" that unlocks cells, allowing glucose to enter.

The goal of insulin therapy in diabetes management is to keep blood sugar levels within a target range to prevent complications associated with high or low blood sugar. The dosage and timing of insulin administration are determined based on factors such as individual needs, carbohydrate intake, activity level, and blood sugar monitoring.

If the recommended daily intake of carbohydrates is 300 g, and the slice of toast represents 5% of that,

Carbohydrates in the slice = 5% of 300 g = (5/100) * 300 g = 15 g

It is recommended that the ratio of 1 ml of insulin for every 10 g of carbohydrates,

Insulin needed = (Carbohydrates in the slice) / 10 = 15 g / 10 = 1.5 ml

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Which statement best describes the sun earth moon system during a spring tide

The moon the sun and earth form a right angle

The sun the moon and earth are in a straight line

The sun is between moon and earth

The moon is in the first quarter face

Which statement best describes the sun earth moon system during a spring tideThe moon the sun and earth

Answers

Answer:

yung una po

Explanation:

kasi meron yan sa grade 6

Answer:

The Answer Is B The Sun,The Moon,And Earth Are In A Straight Line

Explanation:

Hope This Helps!

Balance the chemical reaction
using an atom inventory.
What is the correct whole
number coefficient for iron(III)
bromide?
[?] FeBr3+ [ ]Na₂S →
]Fe₂S3 + [ ]NaBr

Please help!!

Answers

Answer:

Explanation:Balance equation:

2 FeBr3 + 3 Na2S → Fe2S3 + 6 NaBr

What are the three 3 factors affecting the performance of a chemical sanitiser?

Answers

Several physical and chemical factors also influence disinfectant procedures: temperature, pH, relative humidity, and water hardness.

What has an impact on the chemical sanitizer mixture?

Sanitizers can usually function properly in temperatures between 75°F and 120°F. Some metal objects may corrode when exposed to chlorine compounds at higher temperatures. Higher temperatures may also cause chlorine and iodine chemicals to evaporate from the solutions.

What aspects of sanitizing effectiveness are there?

Number of microbes: If the microbial load is large, a stronger concentration of disinfectant or a longer exposure period is required to reach a specific level of disinfection.

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4) The substance CuCl₂ 2H₂O is an ionic solid with 2 water molecules trapped in

the crystal for every molecule of CuCl₂. What is the molar mass for this

compound?

O63.55 g/mol

O134.55 g/mol

152.57 g/mol

O170.48 g/mol

O269.10 g/mol

305.13 g/mol

Answers

The molar mass of the compound: CuCl₂·2H₂O = (1 × 63.55) + (2 × 35.45) + (2 × 2 × 1.01) + (2 × 16.00) CuCl₂·2H₂O = 63.55 + 70.90 + 4.04 + 32.00 CuCl₂·2H₂O = 170.49 g/mol So, the molar mass of the compound CuCl₂·2H₂O is approximately 170.48 g/mol (as per the given options).

To determine the molar mass of CuCl₂ 2H₂O, we need to calculate the total mass of all the molecules present in one mole of the compound. The molecular weight of CuCl₂ is 134.45 g/mol (63.55 g/mol for Cu and 70.90 g/mol for Cl₂). Since there are two water molecules in the compound, we need to add their molecular weight as well, which is 2(18.015 g/mol) = 36.03 g/mol. Therefore, the molar mass of CuCl₂ 2H₂O is:

molar mass = 134.45 g/mol + 36.03 g/mol = 170.48 g/mol

Thus, option D is the correct answer.

In summary, to calculate the molar mass of a compound, we need to add up the masses of all the molecules present in one mole of the compound, which is expressed in grams per mole. Knowing the molar mass of a compound is useful for many purposes, including determining the amount of a substance needed for a chemical reaction, calculating the concentration of a solution, and converting between the mass and moles of a substance.

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what is a mixture of elements and compounds

what is a mixture of elements and compounds

Answers

The substance in the image above would be classified as a mixture of elements (option E).

What is a compound and mixture?

A compound is a substance formed by chemical bonding of two or more elements in definite proportions by weight.

On the other hand, a mixture is made when two or more substances are combined, but they are not combined chemically.

According to this question, an image is shown with two different substances or elements as distinguished by coloration (white and purple). These elements are combined but not chemically bonded, hence, is a mixture.

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Consider an element Z that has two naturally occuring isotopes with the following percent abundances: the isotope with a mass number 22.0 is 65.0% abundant; the isotope with a mass number 24.0 is 35.0% abundant. What is the average atomic mass for element Z? Round your answer to the hundredth.

Answers

Answer:

Z=22.70

Explanation:

It is given that,

An element Z that has two naturally occurring isotopes with the following percent abundances as follows :

The isotope with a mass number 22 is 65.0% abundant; the isotope with a mass number 24 is 35.0% abundant.

The average atomic mass for element Z is given by :

\(Z=\dfrac{22\times 65+24\times 35}{100}\\\\Z=22.7\)

So, the average atomic mass for element Z is 22.70.

HD​:pSun ​=rhoMan ​=pTue ​=pWed ​=pThu ​=pFri ​=pSat ​=71​ Ha​ : Not all proportions are equal. HD​: Not all proportions are equal. Ha​:pSun ​=pMon ​=pTue ​=rhoWed ​=pThu ​=rhoFri ​=rhoSat ​=71​ HD​: Not all proportions are equal. Ha​:pSun ​=pMon ​=pTue ​=pWed ​=pThu ​=rhoFri ​=pSat ​=71​ HD​:pSun ​=pMon ​=pTue ​=pWod ​=pThu ​=pFri ​=pSat ​=71​ Ha​ : All proportions are equal. Find the value of the test statistic. (Round your answer to three d: Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Do not reject H0−​. We conclude that the proportion of traffic Reject HD​. We conclude that the proportion of traffic acciden Reject HD​. We conclude that the proportion of traffic acciden Do not reject H0−​We conclude that the proportion of traffic Compute the percentaqe of traffic accidents occurring on each day What day has the highest percentage of traffic accidents? Sunday Monday Tuesday Wednesday Thursday Friday Saturday Based on 2017 sales, the six top-selling compact showed the following number of vehicles sold. Use a goodness of fit test to determine if the sample data indicate that the market shares for compact cars in the city are different than the market shares suggested by nationwide 2017 sales. Use a 0.05 level of significance. State the null and alternative hypothesis. Ha​ : The market shares for the compact cars in the city are different for at least one of the nationwide market shares listed. o: The market shares for the compact cars in the city do not differ from market shares nationwide. : The market shares for the compact cars in the city are different from at least one of the nationwide market shares listed. Ha​ : The market shares for the compact cars in the city are not different from any of the natione Ha​ : The market shares for the compact cars in the city do not differ from market shares nationwide. "the test statistic.(Round your answer to two decimal places.) d the rho-value. (Round your answer to four decimal places.) Reject H0​. We cannot conclude that market shares for the compact cars in the city differ from the nationwide market shares. Do not reject H0​. We conclude that market shares for the compact cars in the city differ from the nationwide market shares. Do not reject H0​. We cannot conclude that market shares for the compact cars in the city differ from the nationwide market shares.

Answers

The p-value is greater than the significance level of 0.05, we do not reject the null hypothesis and conclude that all proportions are equal.

Firstly, let us conduct a Chi-square test of independence of categorical variables based on the information given above. We have three different cases of hypothesis testing that we have to solve one by one.


Case 1: HD​:pSun ​=rhoMan ​=pTue ​=pWed ​=pThu ​=pFri ​=pSat ​=71​
Ha​ : Not all proportions are equal.


Test Statistic
For this hypothesis, we need to compute the test statistic that is given as:
\($$\chi^2=\sum_{i=1}^{k}\frac{(O_i-E_i)^2}{E_i}$$\)  where k is the number of groups/categories. Since we have 7 days of the week, \(k = 7. $O_i$ and $E_i$\) are the observed and expected frequencies respectively.  
Here, we have equal proportions of 71 for each day of the week.
Therefore, the expected frequencies are also equal to 71.
\($$E_i = 71, i=1,2,3,4,5,6,7.$$\)

We also have to use the given information to compute the observed frequencies,
\($O_i$.$$O_1 = 90, O_2 = 99, O_3 = 122, O_4 = 123, O_5 = 130, O_6 = 160, O_7 = 126$$\)

Therefore, the test statistic can be computed as \($$\chi^2=\frac{(90-71)^2}{71} + \frac{(99-71)^2}{71} + \frac{(122-71)^2}{71} + \frac{(123-71)^2}{71} + \frac{(130-71)^2}{71} + \frac{(160-71)^2}{71} + \frac{(126-71)^2}{71}$$$$\chi^2=180.14\)

Now we have to find the p-value of this test. Since the number of degrees of freedom is k - 1 = 7 - 1 = 6, the p-value can be found using the chi-square distribution table with 6 degrees of freedom at the 0.05 significance level. The p-value is 0.000014. ConclusionSince the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that not all proportions are equal.

The total number of accidents is \($$90+99+122+123+130+160+126=850$$\)

The percentage of accidents occurring on each day of the week can be found as follows:
\($$Sunday: $$\frac{90}{850}\times 100 = 10.59\%$$Monday: $$\frac{99}{850}\times 100 = 11.65\%$$Tuesday: $$\frac{122}{850}\times 100 = 14.35\%$$Wednesday: $$\frac{123}{850}\times 100 = 14.47\%$$Thursday: $$\frac{130}{850}\times 100 = 15.29\%$$Friday: $$\frac{160}{850}\times 100 = 18.82\%$$Saturday: $$\frac{126}{850}\times 100 = 14.82\%$$\)

From the above percentages, we can see that Friday has the highest percentage of traffic accidents.


Case 2:
HD​: Not all proportions are equal.

Ha​:pSun ​=pMon ​=pTue ​=rhoWed ​=pThu ​=rhoFri ​=rhoSat ​=71


Test Statistic

\($$E_1 = 78.57, E_2 = 86.57, E_3 = 106.86, E_4 = 107.43, E_5 = 113.57, E_6 = 139.43, E_7 = 109.14$$\)

We already know the observed frequencies,
\($$O_1 = 90, O_2 = 99, O_3 = 122, O_4 = 123, O_5 = 130, O_6 = 160, O_7 = 126.$$\)

The test statistic can be computed as:


\($$\chi^2=\frac{(90-78.57)^2}{78.57} + \frac{(99-86.57)^2}{86.57} + \frac{(122-106.86)^2}{106.86}+ \frac{(123-107.43)^2}{107.43} + \frac{(130-113.57)^2}{113.57} + \frac{(160-139.43)^2}{139.43} + \frac{(126-109.14)^2}{109.14} $$$$ \implies \chi^2=34.98$$\)
The p-value is 0.000001.
Conclusion- Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that not all proportions are equal.

Case 3:

All proportions are equal.
Test Statistic
The expected frequency for each group is
\(E = \frac{850}{7} = 121.43\)
We already know the observed frequencies,
\($$O_1 = 90, O_2 = 99, O_3 = 122, O_4 = 123, O_5 = 130, O_6 = 160, O_7 = 126.$$\)


The test statistic is,


\($$\chi^2=\frac{(90-121.43)^2}{121.43} + \frac{(99-121.43)^2}{121.43} + \frac{(122-121.43)^2}{121.43} + \frac{(123-121.43)^2}{121.43} + \frac{(130-121.43)^2}{121.43} + \frac{(160-121.43)^2}{121.43} + \frac{(126-121.43)^2}{121.43}} \\\implies \chi^2=9.17$$\)

The p-value is 0.1664.

Since the p-value is greater than the significance level of 0.05, we do not reject the null hypothesis and conclude that all proportions are equal.

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