Step 1: Use the pressure-volume unit shortcut:
1 bar $\times$ 1 mL = $10^5$ Pa $\times 10^{-6}$ m$^3$ = 0.1 J.
Step 2: Find the net contraction:
HCl is the limiting reagent, so 150 mL each of $\text{C}_2\text{H}_4$ and HCl turn into 150 mL of $\text{C}_2\text{H}_5\text{Cl}$. The mixture shrinks by 300 - 150 = 150 mL.
Step 3: Compute the work:
Because the system is compressed, work is done on the system and is positive: $w = 150 \times 0.1 = 15$ J.
Step 4: Check the sign:
Gas volume decreased, so the surroundings do work on the system, so $w > 0$. The magnitude 15 J matches option A.
Final Answer:
Using 0.1 J per mL at 1 bar, the 150 mL contraction gives 15 J.
\[ \boxed{\text{(A) }15\ \text{J}} \]