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Chapter 13: Problem 64

(a) What is an ideal solution? (b) The vapor pressure of pure water at \(60^{\circ} \mathrm{C}\) is 149 torr. The vapor pressure of water over a solution at \(60^{\circ} \mathrm{C}\) containing equal numbers of moles of water and ethylene glycol (a nonvolatile solute) is 67 torr. Is the solution ideal according to Raoult's law? Explain.

Short Answer

Expert verified
An ideal solution is a mixture of two or more substances that follows Raoult's law at all concentrations. The given solution contains equal mole fractions of water and ethylene glycol. According to Raoult's law, the expected vapor pressure of water over the ideal solution would be 74.5 torr. However, the measured vapor pressure is 67 torr, which significantly deviates from the expected value. Therefore, the solution is not ideal according to Raoult's law.

Step by step solution

01

(1) Definition of an Ideal Solution

An ideal solution is a mixture of two or more substances that follows Raoult's law at all concentrations. Raoult's law states that the partial vapor pressure of each component in an ideal solution is proportional to the mole fraction of that component. In mathematical terms, for component A in an ideal solution: \[\ P_A = \chi_A P_A^* \] Here, \(P_A\) is the partial vapor pressure of component A, \(\chi_A\) is the mole fraction of A in the solution, and \(P_A^*\) is the vapor pressure of the pure component A.
02

(2) Calculate the mole fraction

We are given that the solution contains equal numbers of moles of water and ethylene glycol. Therefore, the mole fractions of each component are: \[\chi_{H_2O} = \frac{1}{1 + 1} = 0.5\] \[\chi_{C_2H_6O_2} = \frac{1}{1 + 1} = 0.5\]
03

(3) Calculate vapor pressure according to Raoult's law

Now, we can use Raoult's law to calculate the vapor pressure of water over an ideal solution: \[P_{H_2O} = \chi_{H_2O} * P_{H_2O}^*\] \[P_{H_2O} = 0.5 * 149\,\text{torr} = 74.5\,\text{torr}\]
04

(4) Compare measured and calculated vapor pressures

The measured vapor pressure over the solution containing water and ethylene glycol is 67 torr, while the expected vapor pressure of water over an ideal solution according to Raoult's law is 74.5 torr. Since the measured vapor pressure is significantly lower than the expected vapor pressure, the solution is not ideal according to Raoult's law.
05

(5) Conclusion

An ideal solution is one that follows Raoult's law. In the given problem, the solution containing water and ethylene glycol does not show vapor pressures consistent with Raoult's law, indicating that the solution is not ideal.

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Most popular questions from this chapter

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