Calculate the respective vapour pressure contribution for methylbenzene at this concentration
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here are the calculations for the vapor pressure contribution of methylbenzene.
Assumption: The vapor pressure of pure methylbenzene ($P_{\text{methylbenzene}}^\circ$) is not provided. Therefore, the vapor pressure contributions of methylbenzene will be expressed in terms of $P_{\text{methylbenzene}}^\circ$.
Step 1: Use the mole fractions of methylbenzene ($X_{\text{methylbenzene}}$) calculated previously.
Step 2: Calculate the vapor pressure contribution of methylbenzene ($P_{\text{methylbenzene}}$).
According to Raoult's Law for an ideal solution:
$$P_{\text{methylbenzene}} = X_{\text{methylbenzene}} P_{\text{methylbenzene}}^\circ$$
where $P_{\text{methylbenzene}}^\circ$ is the vapor pressure of pure methylbenzene.
Here are the results for the given concentrations:
| $X_{\text{benzene}}$ | $X_{\text{methylbenzene}}$ | $P_{\text{methylbenzene}}$ (Vapor Pressure Contribution) |
| :------------------- | :------------------------- | :------------------------------------------------------- |
| 0 | 1 | $1 \cdot P_{\text{methylbenzene}}^\circ = P_{\text{methylbenzene}}^\circ$ |
| 0.25 | 0.75 | $0.75 \cdot P_{\text{methylbenzene}}^\circ$ |
| 0.5 | 0.5 | $0.5 \cdot P_{\text{methylbenzene}}^\circ$ |
| 0.75 | 0.25 | $0.25 \cdot P_{\text{methylbenzene}}^\circ$ |
| 1 | 0 | $0 \cdot P_{\text{methylbenzene}}^\circ = 0$ |
The respective vapor pressure contributions of methylbenzene are $P_{\text{methylbenzene}}^\circ$, $0.75 P_{\text{methylbenzene}}^\circ$, $0.5 P_{\text{methylbenzene}}^\circ$, $0.25 P_{\text{methylbenzene}}^\circ$, 0.
