Question

at constant pressure, which of these systems do work on the surroundings?
□ a(s) + b(s) → c(g)
□ a(s) + 2b(g) → c(g)
□ a(g) + b(g) → 3c(g)
□ a(g) + 2b(g) → 2c(g)

Explanation:

Step1: Recall the formula for work done

At constant pressure, \(w=-P\Delta V\). Using ideal gas law \(PV = nRT\), \(w=- \Delta n_{gas}RT\). Work is done on the surroundings when \(\Delta n_{gas}>0\) (expansion).

Step2: Calculate \(\Delta n_{gas}\) for each reaction

• For \(A(s)+B(s)\to C(g)\): \(\Delta n_{gas}=1 - 0=1>0\)
• For \(A(s)+2B(g)\to C(g)\): \(\Delta n_{gas}=1 - 2=-1<0\)
• For \(A(g)+B(g)\to 3C(g)\): \(\Delta n_{gas}=3-(1 + 1)=1>0\)
• For \(A(g)+2B(g)\to 2C(g)\): \(\Delta n_{gas}=2-(1 + 2)=-1<0\)

Answer:

A. \(A(s)+B(s)\to C(g)\), C. \(A(g)+B(g)\to 3C(g)\)