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Chapter 11: Problem 97

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 \(0.5999\).

Step by step solution

01

Calculate the partial pressure of carbon disulfide in the vapor using mole percent information

We are given that the vapor is \(85.5 \%\) mole percent carbon disulfide. This means that \(85.5\%\) of the total pressure in the vapor is due to carbon disulfide. We can calculate the partial pressure of carbon disulfide as follows: \(P_{CS_2} = 0.855 * P_{total}\) Where: - \(P_{CS_2}\) is the partial pressure of carbon disulfide, - \(P_{total}\) is the total pressure of the vapor (given as 263 torr). Now, we can calculate \(P_{CS_2}\): \(P_{CS_2} = 0.855 * 263 torr = 224.955 torr\)
02

Apply Raoult's Law to calculate the mole fraction of carbon disulfide in the solution

Now we apply Raoult's Law to calculate the mole fraction of carbon disulfide in the solution. Using the formula, we have: \(P_{CS_2}^* x_{CS_2} = P_{CS_2}\) Where: - \(P_{CS_2}^*\) is the vapor pressure of carbon disulfide in the pure state (given as 375 torr), - \(x_{CS_2}\) is the mole fraction of carbon disulfide in the solution, - \(P_{CS_2}\) is the partial pressure of carbon disulfide calculated in step 1 (224.955 torr). We can rearrange the formula to solve for the mole fraction of carbon disulfide in the solution: \(x_{CS_2} = \frac{P_{CS_2}}{P_{CS_2}^*}\) Now we can calculate \(x_{CS_2}\): \(x_{CS_2} = \frac{224.955 torr}{375 torr} = 0.59988\)
03

Express the mole fraction in the final form

We have calculated the mole fraction of carbon disulfide in the solution as 0.59988. We can express this value in the desired form. The mole fraction of carbon disulfide in the solution is approximately \(0.5999\).

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Most popular questions from this chapter

In flushing and cleaning columns used in liquid chromatography to remove adsorbed contaminants, a series of solvents is used. Hexane \(\left(\mathrm{C}_{6} \mathrm{H}_{14}\right)\), chloroform \(\left(\mathrm{CHCl}_{3}\right)\), methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\), and water are passed through the column in that order. Rationalize the order in terms of intermolecular forces and the mutual solubility (miscibility) of the solvents.

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

At a certain temperature, the vapor pressure of pure benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) is \(0.930\) atm. A solution was prepared by dissolving \(10.0 \mathrm{~g}\) of a nondissociating, nonvolatile solute in \(78.11 \mathrm{~g}\) of benzene at that temperature. The vapor pressure of the solution was found to be \(0.900\) atm. Assuming the solution behaves ideally, determine the molar mass of the solute.
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