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Chapter 11: Problem 105

At \(25^{\circ} \mathrm{C},\) the vapor in equilibrium with a solution containing carbon disulfide and acetonitrile has a total pressure of 263 torr and is 85.5 mole percent carbon disulfide. What is the mole fraction of carbon disulfide in the solution? At \(25^{\circ} \mathrm{C}\) , the vapor pressure of carbon disulfide is 375 torr. Assume the solution and vapor exhibit ideal behavior.

Short Answer

Expert verified
The mole fraction of carbon disulfide in the solution is approximately 0.6.

Step by step solution

01

Determine the partial pressure of carbon disulfide in the vapor

Given the total pressure (P_total) and the mole percentage of carbon disulfide in the vapor (85.5%), we can determine the partial pressure of carbon disulfide (P_CS2) using the following relationship: P_CS2 = P_total * (mole_percentage / 100) Where P_total = 263 torr and mole_percentage = 85.5%. Plugging in the values, we get: P_CS2 = 263 torr * (85.5 / 100) = 224.825 torr
02

Use Raoult's Law to determine the mole fraction of carbon disulfide in the solution

Raoult's Law states that the partial pressure of a component in the vapor phase is equal to the mole fraction of that component in the solution (x_CS2) times its vapor pressure (P*_CS2): P_CS2 = x_CS2 * P*_CS2 We know P_CS2 = 224.825 torr and P*_CS2 = 375 torr (given vapor pressure of carbon disulfide at 25°C). We can solve for x_CS2: x_CS2 = P_CS2 / P*_CS2 = 224.825 torr / 375 torr = 0.5994 Thus, the mole fraction of carbon disulfide in the solution is 0.5994, or approximately 0.6.

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Most popular questions from this chapter

Liquid A has vapor pressure \(x\) , and liquid \(\mathrm{B}\) has vapor pressure \(y .\) What is the mole fraction of the liquid mixture if the vapor above the solution is \(30 . \% \mathrm{A}\) by moles? $50 . \% \mathrm{A} ? 80 . \% \mathrm{A}\( ? (Calculate in terms of \)x\( and \)y . )$ Liquid A has vapor pressure \(x,\) liquid \(\mathrm{B}\) has vapor pressure y. What is the mole fraction of the vapor above the solution if the liquid mixture is \(30 . \% \mathrm{A}\) by moles? $50 . \% \mathrm{A} ? 80 . \% \mathrm{A}\( ? (Calculate in terms of \)x\( and \)y . )$

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For an acid or a base, when is the normality of a solution equal to the molarity of the solution and when are the two concentration units different?

An aqueous solution containing 0.250 mole of \(\mathrm{Q},\) a strong electrolyte, in \(5.00 \times 10^{2} \mathrm{g}\) water freezes at \(-2.79^{\circ} \mathrm{C} .\) What is the van't Hoff factor for \(\mathrm{Q} ?\) The molal freezing-point depression constant for water is $1.86^{\circ} \mathrm{C} \cdot \mathrm{kg} / \mathrm{mol}$ . What is the formula of \(\mathrm{Q}\) if it is 38.68\(\%\) chlorine by mass and there are twice as many anions as cations in one formula unit of \(\mathrm{Q} ?\)

Consider the following solutions: 0.010\(m \mathrm{Na}_{3} \mathrm{PO}_{4}\) in water 0.020 \(m \mathrm{CaBr}_{2}\) in water 0.020 \(m \mathrm{KCl}\) in water 0.020 \(m \mathrm{HF}\) in water \((\mathrm{HF} \text { is a weak acid.) }\) a. Assuming complete dissociation of the soluble salts, which solution(s) would have the same boiling point as 0.040 $\mathrm{m} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\( in water? \)\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ is a nonelectrolyte. b. Which solution would have the highest vapor pressure at $28^{\circ} \mathrm{C} ?$ c. Which solution would have the largest freezing-point depression?
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