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Chapter 12: Problem 36

A 7.53 I. sample of \(\mathrm{N}_{2}(\mathrm{g})\) at \(742 \mathrm{mmHg}\) and \(45.0^{\circ} \mathrm{C}\) is bubbled through \(\mathrm{CCl}_{4}(1)\) at \(45.0^{\circ} \mathrm{C} .\) Assuming the gas becomes saturated with \(\mathrm{CCl}_{4}(\mathrm{g}),\) what is the volume of the resulting gaseous mixture, if the total pressure remains at \(742 \mathrm{mm} \mathrm{Hg}\) and the temperature remains at \(45^{\circ} \mathrm{C} ?\) The vapor pressure of \(\mathrm{CCl}_{4}\) at \(45^{\circ} \mathrm{C}\) is \(261 \mathrm{mmHg}\)

Short Answer

Expert verified
The volume of the resulting gaseous mixture is 62.8 L

Step by step solution

01

Evaluate the Partial Pressure of Nitrogen

First, compute the partial pressure of the nitrogen gas. Because \(N_{2}\) and \(CCl_{4}\) are in equilibrium, the partial pressure of \(N_{2(g)}\) is also 742 mmHg. This is obtained by subtracting the vapor pressure of the \(CCl_{4}(g)\) from the total pressure. \(P_{N2} = P_{total} - P_{CCl4} = 742 mmHg - 261 mmHg = 481 mmHg\)
02

Convert Temperatures to Kelvin

Now convert the temperature from Celsius to Kelvin. Kelvin is the SI unit for temperature and is necessary to use the ideal gas law equation. \(T = 45^{\circ}C + 273 = 318 K\)
03

Calculate the Volume of Nitrogen Gas

Utilize the ideal gas law to calculate the original volume of nitrogen gas. Rearrange the formula \(P_{N2}V=N_{N2}RT\) for volume: \(V_{N2} = (N_{N2}RT) / P_{N2}\). Using \(R = 0.0821 L·atm/mol·K\), convert the pressure of \(N_{2(g)}\) to atmospheres (1 atm = 760 mmHg), which gives us \(P_{N2} = 481 mmHg * (1 atm / 760 mmHg) = 0.633 atm\). The number of moles of nitrogen, \(N_{N2}\), is equal to 7.53I. So, volume of \(N_{2(g)}\) becomes \(V_{N2} = (7.53 mol * 0.0821 L·atm/mol·K * 318K) / 0.633 atm = 31.4 L\)
04

Calculate Volume of Carbon Tetrachloride Gas

The volume of \(CCl_{4}(g)\) is the same as that of \(N_{2(g)}\) because they share the same conditions of pressure and temperature. Hence, \(V_{CCl4} = V_{N2} = 31.4 L\)
05

Calculate Total Volume of the Resulting Mixture

The total volume of the mixture, \(V_{total}\), can be found by adding the individual volumes of the gases. \(V_{total} = V_{N2} + V_{CCl4} = 62.8 L\)

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