© All Rights reserved @ LearnWithDash
Step-by-Step Solution
Step 1: Identify the given data
• Vapour pressure of liquid P, $P_P = 80\,\text{torr}$.
• Vapour pressure of liquid Q, $P_Q = 60\,\text{torr}$.
• Number of moles of P, $n_P = 3$.
• Number of moles of Q, $n_Q = 2$.
Step 2: Calculate the total number of moles
Total moles, $n_{\text{total}} = n_P + n_Q = 3 + 2 = 5$.
Step 3: Determine the mole fractions of P and Q
Mole fraction of P, $X_P = \dfrac{n_P}{n_{\text{total}}} = \dfrac{3}{5}$.
Mole fraction of Q, $X_Q = \dfrac{n_Q}{n_{\text{total}}} = \dfrac{2}{5}$.
Step 4: Apply Raoult's law for total vapour pressure
According to Raoult's law for an ideal solution, the total vapour pressure $P_{\text{total}}$ is given by:
$P_{\text{total}} = X_P \times P_P + X_Q \times P_Q$.
Step 5: Substitute the values and calculate
$P_{\text{total}} = \left(\dfrac{3}{5}\right) \times 80 + \left(\dfrac{2}{5}\right) \times 60 \\
= 48 + 24 \\
= 72\,\text{torr}.$
Step 6: State the final answer
Therefore, the total vapour pressure of the solution is $72\,\text{torr}.$
