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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°C, 274.53 g of CCl₂F₂ must evaporate.

Step by step solution

01

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

Using the formula q = mcΔT, where m = 200g, c = 4.18 J/g-K, and ΔT = -15 K: q₁ = (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°C to ice using the formula q = mL, where m = 200g and L = 334 J/g: q₂ = (200g)(334 J/g) = 66800 J
03

Calculate the total heat required

Add the absolute values of the heats q₁ and q₂ to get the total heat required: q_total = |q₁| + q₂ = 12540 J + 66800 J = 79340 J
04

Calculate the mass of CCl₂F₂ required

Finally, we find the mass of CCl₂F₂ that needs to evaporate. Since we know the heat of vaporization of CCl₂F₂ (L₀ = 289 J/g), we can use the formula q = mL₀ and solve for m: m_CCl₂F₂ = q_total / L₀ = 79340 J / 289 J/g = 274.53 g So, we need 274.53 g of CCl₂F₂ to evaporate to freeze 200 g of water initially at 15°C.

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Most popular questions from this chapter

You are high up in the mountains and boil water to make some tea. However, when you drink your tea, it is not as hot as it should be. You try again and again, but the water is just not hot enough to make a hot cup of tea. Which is the best explanation for this result? (a) High in the mountains, it is probably very dry, and so the water is rapidly evaporating from your cup and cooling it. (b) High in the mountains, it is probably very windy, and so the water is rapidly evaporating from your cup and cooling it. (c) High in the mountains, the air pressure is significantly less than 1 atm, so the boiling point of water is much lower than at sea level. (d) High in the mountains, the air pressure is significantly less than 1 atm, so the boiling point of water is much higher than at sea level.

(a) List the following molecules in order of increasing polar-izability: GeCl_ \(_{4}, \mathrm{CH}_{4}, \mathrm{SiCl}_{4}, \mathrm{SiH}_{4},\) and \(\mathrm{GeBr}_{4}\) . (b) Predict the order of boiling points of the substances in part (a).

The smectic liquid crystalline phase can be said to be more highly ordered than the nematic phase. In what sense is this true?

Which member in each pair has the greater dispersion forces? (a) \(\mathrm{H}_{2} \mathrm{O}\) or \(\mathrm{H}_{2} \mathrm{S},(\mathbf{b}) \mathrm{CO}_{2}\) or \(\mathrm{CO},(\mathbf{c}) \operatorname{siH}_{4}\) or \(\mathrm{GeH}_{4}\) .

Carbon tetrachloride, \(\mathrm{CCl}_{4},\) and chloroform, \(\mathrm{CHCl}_{3},\) are common organic liquids. Carbon tetrachloride's normal boiling point is \(77^{\circ} \mathrm{C} ;\) chloroform's normal boiling point is \(61^{\circ} \mathrm{C} .\) Which statement is the best explanation of these data? (a) Chloroform can hydrogen-bond, but carbon tetrachloride cannot. (b) Carbon tetrachloride has a larger dipole moment than chloroform. (c) Carbon tetrachloride is more polarizable than chloroform.
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