Question

a sample of gas occupies a volume of 73.0 ml. as it expands, it does 147.5 j of work on its surroundings at a constant pressure of 783 torr. what is the final volume of the gas?

Explanation:

Step1: Convert pressure unit

We know that \(1\space atm = 760\space Torr\). So, \(P=783\space Torr\times\frac{1\space atm}{760\space Torr}\approx1.03\space atm\). Also, \(1\space L\cdot atm = 101.3\space J\).

Step2: Use the work formula \(w = -P\Delta V\)

Given \(w=- 147.5\space J\) (negative because the gas is doing work on the surroundings). First, convert work to \(L\cdot atm\): \(w=-147.5\space J\times\frac{1\space L\cdot atm}{101.3\space J}\approx - 1.456\space L\cdot atm\).
From \(w=-P\Delta V=-P(V_{f}-V_{i})\), we can solve for \(V_{f}\). Rearranging the formula gives \(V_{f}=V_{i}-\frac{w}{P}\).
\(V_{i} = 73.0\space mL=0.073\space L\), \(P = 1.03\space atm\), \(w=-1.456\space L\cdot atm\)
\(V_{f}=0.073\space L-\frac{- 1.456\space L\cdot atm}{1.03\space atm}\)
\(V_{f}=0.073\space L + 1.414\space L\)
\(V_{f}=1.487\space L = 1487\space mL\)

Answer:

\(1487\space mL\)