To solve this problem, we can use the following equation:
\[
\frac{P_o - P_t}{P_o} = \frac{n_s}{n_s + n_w}
\]
where:
\(P_o\) is the vapor pressure of the pure solvent,
\(P_t\) is the vapor pressure of the solution,
\(n_s\) is the number of moles of solute,
\(n_w\) is the number of moles of water.
We know that the vapor pressure of the solution is 2% lower than the vapor pressure of the pure solvent, so we can substitute the following values into the equation:
\[
\frac{P_o - P_t}{P_o} = 0.02
\]
We also know that the solution is 10% by mass, so we can calculate the number of moles of solute and water in the solution using the following equations:
\[
n_s = \frac{10}{100} \times \frac{1}{M_s}
\]
\[
n_w = \frac{90}{100} \times \frac{1}{18}
\]
where \(M_s\) is the molar mass of the solute.
Substituting these values into the equation, we get:
\[
0.02 = \frac{\frac{10}{100} \times \frac{1}{M_s}}{\frac{10}{100} \times \frac{1}{M_s} + \frac{90}{100} \times \frac{1}{18}}
\]
Solving for \(M_s\), we get:
\[
M_s = 90 \, \text{g/mol}
\]
Therefore, the correct answer is (3) 90. |
