Consider a gas cylinder containing 0.100 moles of an ideal gas in a volume of 1.30 L with a pressure of 1.00 atm. The cylinder is surrounded by a constant temperature bath at 298.0 K. With an external pressure of 5.00 atm, the cylinder is compressed to 0.500 L. Calculate the ΔS(gas) for this compression process, in J/K.
Added by Nicole M.
Step 1
100 \) moles, \( R = 8.314 \, \text{J/mol} \cdot \text{K} \), \( V_1 = 1.30 \, \text{L} \), and \( V_2 = 0.500 \, \text{L} \). Show more…
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Consider a gas cylinder containing 0.100 moles of an ideal gas in a volume of 1.00 L with a pressure of 1.00 atm. The cylinder is surrounded by a constant temperature bath at 298.0 K. With an external pressure of 5.00 atm, the cylinder is compressed to 0.500 L. Calculate the ∆S(universe) for this compression process, in J/K.
Ronald P.
Madhur L.
An ideal gas has a volume of exactly 1 liter at $1.00 \mathrm{~atm}$ and $-20{ }^{\circ} \mathrm{C}$. To how many atmospheres of pressure must it be subjected in order to be compressed to $0.500$ liter when the temperature is 40 ${ }^{\circ} \mathrm{C}$ ? $$ \begin{array}{c} \frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}} \quad \text { or } \quad P_{2}=P_{1}\left(\frac{V_{1}}{V_{2}}\right)\left(\frac{T_{2}}{T_{1}}\right) \\ \text { from which } \quad P_{2}=(1.00 \mathrm{~atm})\left(\frac{1.00 \mathrm{~L}}{0.500 \mathrm{~L}}\right)\left(\frac{273 \mathrm{~K}+40 \mathrm{~K}}{273 \mathrm{~K}-20 \mathrm{~K}}\right)=2.47 \mathrm{~atm} \end{array} $$
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