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Chapter 10: Problem 94

Calculate the pressure that \(\mathrm{CCl}_{4}\) will exert at $80^{\circ} \mathrm{C}\( if 1.00 mol occupies \)33.3 \mathrm{~L}$, assuming that (a) \(\mathrm{CCl}_{4}\) obeys the ideal-gas equation; (b) \(\mathrm{CCl}_{4}\) obeys the van der Waals equation. (Values for the van der Waals constants are given in Table \(10.3 .\) ) (c) Which would you expect to deviate more from ideal behavior under these conditions, \(\mathrm{Cl}_{2}\) or \(\mathrm{CCl}_{4} ?\) Explain.

Short Answer

Expert verified
Using the ideal-gas equation, the pressure exerted by \(CCl_{4}\) at \(80^\circ \mathrm{C}\) is 8.71 atm, and using the van der Waals equation, it is 8.54 atm. Under these conditions, \(CCl_{4}\) is expected to deviate more from ideal behavior than \(\mathrm{Cl}_2\) due to its larger size and greater susceptibility to intermolecular forces.

Step by step solution

01

Convert Celsius to Kelvin

To work with the ideal-gas equation and the van der Waals equation, we need the temperature to be in Kelvin. To convert Celsius to Kelvin, add 273.15: \(T_K = 80^\circ \mathrm{C} + 273.15 = 353.15 \mathrm{K}\) ##Step 2: Calculate pressure using ideal-gas equation##
02

Apply ideal-gas equation

The ideal-gas equation is: \(PV = nRT\) We know n (1.00 mol), R (0.0821 \(\mathrm{L \> atm \> K^{-1} mol^{-1}}\)), V (33.3 L), and T (353.15 K). We can now solve for the pressure (P): \(P = \dfrac{nRT}{V} = \dfrac{1.00 \times 0.0821 \times 353.15}{33.3} = 8.71 \mathrm{atm}\) In case (a), using the ideal-gas equation, the pressure is 8.71 atm ##Step 3: Calculate pressure using van der Waals equation##
03

Apply van der Waals equation

The van der Waals equation is: \(\left(P + \dfrac{an^2}{V^2}\right)(V - nb) = nRT\) For \(\mathrm{CCl}_4\), the van der Waals constants from Table 10.3 are: a = 20.4 L² atm mol⁻² and b = 0.138 L mol⁻¹. Plug in the values for n, R, V, T, a, and b, and solve for P: \(\left(P + \dfrac{20.4 \times (1)^2}{(33.3)^2}\right)(33.3 - 0.138) = (1)\times 0.0821 \times 353.15\) Solve for P. \(P = 8.54 \mathrm{atm}\) In case (b), using the van der Waals equation, the pressure is 8.54 atm. ##Step 4: Compare the deviation from ideal behavior##
04

Compare gases under the given conditions

We need to determine which gas, \(\mathrm{Cl}_2\) or \(\mathrm{CCl}_4\), will deviate more from ideal behavior under the given conditions. \(\mathrm{CCl}_4\) is a larger and more polarizable molecule than \(\mathrm{Cl}_2\). It is more likely to experience significant intermolecular forces, like London dispersion forces, which can lead to deviations from the ideal-gas behavior. In conclusion, under these conditions, we would expect \(\mathrm{CCl}_4\) to deviate more from ideal behavior than \(\mathrm{Cl}_2\).

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