Compounds like CCl2F2 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 CCl2F2 is 289 J/g. What mass of this substance must evaporate to freeze 200 g of water initially at 15 °C? (The heat of fusion of water is 334 J/g; the specific heat of water is 4.18 J/g-K.)

Verified step by step guidance

Calculate the amount of heat that must be removed from the water to lower its temperature from 15 °C to 0 °C using the formula: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of water, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Calculate the amount of heat that must be removed to freeze the water at 0 °C using the formula: \( q = m \cdot \Delta H_{fusion} \), where \( m \) is the mass of water and \( \Delta H_{fusion} \) is the heat of fusion.

Add the heat calculated in the first two steps to find the total heat that must be removed from the water.

Use the heat of vaporization of CCl2F2 to determine the mass of CCl2F2 that must evaporate to remove the total heat calculated in the previous step. Use the formula: \( q = m \cdot \Delta H_{vaporization} \), where \( q \) is the total heat to be removed and \( \Delta H_{vaporization} \) is the heat of vaporization.

Solve for the mass of CCl2F2 by rearranging the formula from the previous step: \( m = \frac{q}{\Delta H_{vaporization}} \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert a unit mass of a liquid into vapor without a change in temperature. In this context, the heat of vaporization of CCl2F2 is 289 J/g, meaning that for every gram of CCl2F2 that evaporates, 289 joules of energy are absorbed from the surroundings. This concept is crucial for calculating how much CCl2F2 is needed to absorb enough heat to freeze water.

Heat of Fusion

The heat of fusion is the amount of energy required to change a substance from solid to liquid at its melting point. For water, the heat of fusion is 334 J/g, indicating that 334 joules are needed to convert 1 gram of ice at 0 °C to liquid water at the same temperature. This concept is essential for determining how much energy must be removed from water to freeze it, which directly relates to the mass of CCl2F2 needed.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. For water, this value is 4.18 J/g-K, which means it takes 4.18 joules to raise the temperature of 1 gram of water by 1 °C. Understanding specific heat is important for calculating the energy changes involved when cooling water from 15 °C to 0 °C before it can freeze.

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Heat Capacity

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Textbook Question

Ethyl chloride (C₂H₅Cl) boils at 12 °C. When liquid C₂H₅Cl under pressure is sprayed on a room-temperature (25 °C) surface in air, the surface is cooled considerably. (a) What does this observation tell us about the specific heat of C₂H₅Cl(g) as compared with that of C₂H₅Cl(l)?

Ethyl chloride (C₂H₅Cl) boils at 12 °C. When liquid C₂H₅Cl under pressure is sprayed on a room-temperature (25 °C) surface in air, the surface is cooled considerably. (b) Assume that the heat lost by the surface is gained by ethyl chloride. What enthalpies must you consider if you were to calculate the final temperature of the surface?

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Textbook Question

For many years drinking water has been cooled in hot climates by evaporating it from the surfaces of canvas bags or porous clay pots. How many grams of water can be cooled from 35 to 20 °C by the evaporation of 60 g of water? (The heat of vaporization of water in this temperature range is 2.4 kJ/g. The specific heat of water is 4.18 J/g-K).

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Open Question

Ethanol (C2H5OH) melts at -114 °C and boils at 78 °C. The enthalpy of fusion of ethanol is 5.02 kJ/mol, and its enthalpy of vaporization is 38.56 kJ/mol. The specific heats of solid and liquid ethanol are 0.97 and 2.3 J/g-K, respectively. (a) How much heat is required to convert 42.0 g of ethanol at 35 °C to the vapor phase at 78 °C? (b) How much heat is required to convert the same amount of ethanol at -155 °C to the vapor phase at 78 °C?

Open Question

The fluorocarbon compound C2Cl3F3 has a normal boiling point of 47.6 °C. The specific heats of C2Cl3F3(l) and C2Cl3F3(g) are 0.91 and 0.67 J/g-K, respectively. The heat of vaporization for the compound is 27.49 kJ/mol. Calculate the heat required to convert 35.0 g of C2Cl3F3 from a liquid at 10.00 °C to a gas at 105.00 °C.

Open Question

Indicate whether each statement is true or false: (a) The critical pressure of a substance is the pressure at which it turns into a solid at room temperature. (b) The critical temperature of a substance is the highest temperature at which the liquid phase can form. (c) Generally speaking, the higher the critical temperature of a substance, the lower its critical pressure. (d) In general, the more intermolecular forces there are in a substance, the higher its critical temperature and pressure.