1. Given data

• Total pressure of vapour mixture: $P = 0.8\,\text{atm}$
• Mole fraction of $A$ in vapour phase: $y_A = 0.5$
• Mole fraction of $A$ in liquid phase: $x_A = 0.2$
• The liquid solution is ideal

We need to find vapour pressure of pure liquid $A$, i.e. $P_A^0$.

2. Use Dalton’s law to find partial pressure of $A$ in vapour

For the vapour phase, $p_A = y_A P$

So, $p_A = 0.5 \times 0.8 = 0.4\,\text{atm}$

3. Use Raoult’s law for an ideal solution

For component $A$, $p_A = x_A P_A^0$

Substitute the values: $0.4 = 0.2 \times P_A^0$

Therefore, $P_A^0 = \frac{0.4}{0.2} = 2\,\text{atm}$

4. Nearest integer

$P_A^0 = 2\,\text{atm}$

So the required integer answer is: $\boxed{2}$

5. Comparison with stored answer

Stored correct answer = $2$

Our derived answer also = $2$

Hence, the answer agrees with the stored correct answer.