Question:
Find the pressure of a sample of CCl$_4$ if 1.0 mole occupies 35 L at 77$^\circ$C. Assume CCl$_4$ obeys the van der Waals equation of state. ($a = 20$, $b = 0.14$)
Find the pressure of a sample of CCl$_4$ if 1.0 mole occupies 35 L at 77$^\circ$C. Assume CCl$_4$ obeys the van der Waals equation of state. ($a = 20$, $b = 0.14$)
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Always convert temperature to Kelvin before using gas equations.
Updated On: Apr 23, 2026
- 0.56 atm
- 0.572 atm
- 0.82 atm
- 0.807 atm
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The Correct Option is D
Solution and Explanation
Concept:
Van der Waals equation:
\[
\left(P + \frac{a}{V^2}\right)(V - b) = RT
\]
Step 1: Convert temperature to Kelvin:
\[ T = 77 + 273 = 350K \]
Step 2: Substitute given values:
\[ \left(P + \frac{20}{35^2}\right)(35 - 0.14) = 0.0821 \times 350 \] \[ \left(P + \frac{20}{1225}\right)(34.86) = 28.735 \] \[ \left(P + 0.0163\right)(34.86) = 28.735 \]
Step 3: Solve for pressure:
\[ P + 0.0163 = \frac{28.735}{34.86} \approx 0.824 \] \[ P = 0.824 - 0.0163 \approx 0.807 \text{ atm} \] Conclusion:
Pressure = 0.807 atm
Step 1: Convert temperature to Kelvin:
\[ T = 77 + 273 = 350K \]
Step 2: Substitute given values:
\[ \left(P + \frac{20}{35^2}\right)(35 - 0.14) = 0.0821 \times 350 \] \[ \left(P + \frac{20}{1225}\right)(34.86) = 28.735 \] \[ \left(P + 0.0163\right)(34.86) = 28.735 \]
Step 3: Solve for pressure:
\[ P + 0.0163 = \frac{28.735}{34.86} \approx 0.824 \] \[ P = 0.824 - 0.0163 \approx 0.807 \text{ atm} \] Conclusion:
Pressure = 0.807 atm
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