Question

question 7 of 17
a sample of gas occupies a volume of 59.2 ml. as it expands, it does 131.4 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, \(1\space L = 1000\space mL\), so \(V_1 = 59.2\space mL=59.2\times10^{- 3}\space L\).
The work formula for a gas at constant pressure is \(w=-P\Delta V=-P(V_2 - V_1)\). Given \(w=- 131.4\space J\). Since \(1\space L\cdot atm=101.325\space J\), then \(w=-131.4\space J\times\frac{1\space L\cdot atm}{101.325\space J}\approx - 1.297\space L\cdot atm\).

Step2: Solve for \(V_2\)

From \(w=-P(V_2 - V_1)\), we can rewrite it as \(V_2=V_1-\frac{w}{P}\).
Substitute the values: \(V_2 = 59.2\times10^{-3}\space L-\frac{-1.297\space L\cdot atm}{1.03\space atm}\).
First, calculate \(\frac{-1.297\space L\cdot atm}{1.03\space atm}\approx - 1.26\space L\) (the negative sign cancels out).
Then \(V_2=0.0592\space L + 1.26\space L=1.32\space L = 1320\space mL\).

Answer:

\(1320\space mL\)