Calculate the quantity of work associated with a \(3.5 \mathrm{L}\) expansion of a gas \((\Delta V)\) against a pressure of \(748 \space\mathrm{mmHg}\) in the units (a) atm \(\mathrm{L} ;\) (b) joules (J); (c) calories (cal).

Short Answer

Expert verified
Based on the step-by-step solution, the calculated work done by the gas against the pressure is \( -2.614 \) atm L, \( -264.3 \) J and \( -63.19 \) cal.

Step by step solution

01

Convert pressure to atm

To calculate work in atm L, first convert pressure from mmHg to atm. Use the conversion factor 1 atm = 760 mmHg.
02

Calculate Work (atm L)

Calculate work by plugging the values of pressure (in atm) and the volume change (in L) into the formula for work, \( W = -P \Delta V \).
03

Convert Work to Joules

To calculate work in joules (J), convert the result from Step 2, which is in atm L, to J. Use the conversion factor 1 atm L = 101.3 J.
04

Convert Work to Calories

To calculate work in calories (cal), convert the result from Step 2, which is in atm L, to J first (using the conversion factor from Step 3) and then convert J to cal, using the conversion factor 1 cal = 4.184 J.

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