/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 44 Compounds like \(\mathrm{CCl}_{2... [FREE SOLUTION] | 91影视

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Chapter 11: Problem 44

Compounds like \(\mathrm{CCl}_{2} \mathrm{F}_{2}\) are known as chlorofluorocarbons, or CFCs. These compounds were once widely used as refrigerants but are now being replaced by compounds that are believed to be less harmful to the environment. The heat of vaporization of \(\mathrm{CCl}_{2} \mathrm{F}_{2}\) is 289 \(\mathrm{J} / \mathrm{g}\) . What mass of this substance must evaporate to freeze 200 \(\mathrm{g}\) of water initially at \(15^{\circ} \mathrm{C} ?\) (The heat of fusion of water is \(334 \mathrm{J} / \mathrm{g} ;\) the specific heat of water is \(4.18 \mathrm{J} / \mathrm{g}-\mathrm{K}\) .

Short Answer

Expert verified
To freeze 200g of water initially at 15掳C, 274.53 g of CCl鈧侳鈧� must evaporate.

Step by step solution

01

Calculate the heat required to cool water from 15掳C to 0掳C

Using the formula q = mc螖T, where m = 200g, c = 4.18 J/g-K, and 螖T = -15 K: q鈧� = (200g)(4.18 J/g-K)(-15 K) = -12540 J
02

Calculate the heat required to convert water to ice

Now we find the heat needed to convert water at 0掳C to ice using the formula q = mL, where m = 200g and L = 334 J/g: q鈧� = (200g)(334 J/g) = 66800 J
03

Calculate the total heat required

Add the absolute values of the heats q鈧� and q鈧� to get the total heat required: q_total = |q鈧亅 + q鈧� = 12540 J + 66800 J = 79340 J
04

Calculate the mass of CCl鈧侳鈧� required

Finally, we find the mass of CCl鈧侳鈧� that needs to evaporate. Since we know the heat of vaporization of CCl鈧侳鈧� (L鈧� = 289 J/g), we can use the formula q = mL鈧� and solve for m: m_CCl鈧侳鈧� = q_total / L鈧� = 79340 J / 289 J/g = 274.53 g So, we need 274.53 g of CCl鈧侳鈧� to evaporate to freeze 200 g of water initially at 15掳C.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Heat of Vaporization
The heat of vaporization is the energy required to change a substance from a liquid to a gas. This process occurs at the boiling point. For chlorofluorocarbons (CFCs) like CCl鈧侳鈧�, this energy is measured as 289 J/g.
To understand this concept, think about boiling water. When water boils, it absorbs energy to change into steam. This energy doesn't increase the temperature but instead changes the state from liquid to gas.
  • Energy is absorbed but temperature remains constant during vaporization.
  • Each substance has a specific heat of vaporization which depends on molecular structure.
This concept links directly to refrigerants since they often rely on cyclical vaporization and condensation to transfer heat.
Heat of Fusion
Heat of fusion refers to the energy needed to change a substance from solid to liquid at its melting point. For water, this is 334 J/g.
Consider ice melting in a glass. It absorbs energy from the surroundings without changing temperature until it completely melts.
  • Measures energy needed to overcome intermolecular forces in a solid.
  • Is crucial during phase changes where temperature stays stable.
In the context of freezing water from the original exercise, this energy must be removed to transform liquid water into solid ice.
Specific Heat Capacity
Specific heat capacity is the amount of heat required to raise the temperature of 1 gram of a substance by 1掳C. For water, it is 4.18 J/g-K.
This concept is vital in understanding how substances absorb and retain heat.
  • It determines how quickly a substance heats up or cools down.
  • Water has a high specific heat capacity, which helps regulate temperature in environments.
In the exercise, specific heat capacity is used to calculate the energy needed to lower the water's temperature before freezing.
Latent Heat
Latent heat is the energy absorbed or released during a phase change without changing temperature, common in vaporization and fusion.
This concept helps explain why substances require a lot of energy to change states.
  • Latent heat of vaporization involves going from liquid to gas.
  • Latent heat of fusion involves going from solid to liquid.
These hidden energies are essential in processes such as cooking, weather systems, and in our exercise, the role of CFCs in refrigerants.

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Most popular questions from this chapter

If 42.0 \(\mathrm{kJ}\) of heat is added to a \(32.0-\mathrm{g}\) sample of liquid methane under 1 \(\mathrm{atm}\) of pressure at a temperature of \(-170^{\circ} \mathrm{C}\) , what are the final state and temperature of the methane once the system equilibrates? Assume no heat is lost to the surroundings. The normal boiling point of methane is \(-161.5^{\circ} \mathrm{C}\) The specific heats of liquid and gaseous methane are 3.48 and \(2.22 \mathrm{J} / \mathrm{g}-\mathrm{K}\) , respectively. [ Section 11.4\(]\)

Suppose you have two colorless molecular liquids, one boiling at \(-84^{\circ} \mathrm{C},\) the other at \(34^{\circ} \mathrm{C},\) and both at atmospheric pressure. Which of the following statements is correct? For each statement that is not correct, modify the statement so that it is correct. (a) The higher-boiling liquid has greater total intermolecular forces than the lower- boiling liquid. (b) The lower-boiling liquid must consist of nonpolar molecules. (c) The lower- boiling liquid has a lower molecular weight than the higher-boiling liquid. (d) The two liquids have identical vapor pressures at their normal boiling points. (e) At \(-84^{\circ}\) both liquids have vapor pressures of 760 \(\mathrm{mm} \mathrm{Hg}\) .

Ethylene glycol \(\left(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)\) and pentane \(\left(\mathrm{C}_{5} \mathrm{H}_{12}\right)\) are both liquids at room temperature and room pressure, and have about the same molecular weight. (a) One of these liquids is much more viscous than the other. Which one do you predict is more viscous? (b) One of these liquids has a much lower normal boiling point \(\left(36.1^{\circ} \mathrm{C}\right)\) compared to the other one \(\left(198^{\circ} \mathrm{C}\right) .\) Which liquid has the lower normal boiling point? (c) One of these liquids is the major component in antifreeze in automobile engines. Which liquid would you expect to be used as antifreeze? (d) One of these liquids is used as a "blowing agent" in the manufacture of polystyrene foam because it is so volatile. Which liquid would you expect to be used as a blowing agent?

In terms of the arrangement and freedom of motion of the molecules, how are the nematic liquid crystalline phase and an ordinary liquid phase similar? How are they different?

(a) What is the relationship between surface tension and temperature? (b) What is the relationship between viscosity and temperature? (c) Why do substances with high surface tension also tend to have high viscosities?
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