Let's solve the problem step by step:
1. Convert Volumes from mL to L:
The initial volume is 122 mL, which can be converted to liters as follows:
[tex]\[
\text{Initial Volume} = 122 \, \text{mL} = 0.122 \, \text{L}
\][/tex]
The final volume is 175 mL, which can be converted to liters as follows:
[tex]\[
\text{Final Volume} = 175 \, \text{mL} = 0.175 \, \text{L}
\][/tex]
2. Convert Pressure from mmHg to atm:
The external pressure is 858 mmHg. To convert this to atmospheres:
[tex]\[
\text{Pressure} = \frac{858 \, \text{mmHg}}{760 \, \text{mmHg/atm}} = 1.129 \, \text{atm}
\][/tex]
3. Determine the Change in Volume:
The change in volume ([tex]\( \Delta V \)[/tex]) is given by the final volume minus the initial volume:
[tex]\[
\Delta V = 0.175 \, \text{L} - 0.122 \, \text{L} = 0.053 \, \text{L}
\][/tex]
4. Calculate the Work Done (W = -PΔV):
The work done by the gas is given by the formula [tex]\( W = -P \Delta V \)[/tex]:
[tex]\[
W = -1.129 \, \text{atm} \times 0.053 \, \text{L} = -0.0598 \, \text{Lâ‹…atm}
\][/tex]
5. Convert Work from Lâ‹…atm to Joules:
To convert the work from Lâ‹…atm to Joules, we use the conversion factor (1 Lâ‹…atm = 101.325 J):
[tex]\[
W = -0.0598 \, \text{Lâ‹…atm} \times 101.325 \, \text{J/Lâ‹…atm} = -6.06 \, \text{J}
\][/tex]
Final Answer:
The work done when the gas expands is:
[tex]\[
W = -6.06 \, \text{J}
\][/tex]
