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Chapter 10: Problem 70

A sample of \(5.00 \mathrm{~mL}\) of diethylether \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OC}_{2} \mathrm{H}_{5},\right.\) density \(=\) \(0.7134 \mathrm{~g} / \mathrm{mL}\) ) is introduced into a 6.00 - \(\mathrm{L}\) vessel that already contains a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\), whose partial pressures are \(P_{\mathrm{N}_{2}}=0.751 \mathrm{~atm}\) and \(P_{\mathrm{O}_{2}}=0.208 \mathrm{~atm} .\) The temperature is held at \(35.0^{\circ} \mathrm{C}\), and the diethylether totally evaporates. (a) Calculate the partial pressure of the diethylether. (b) Calculate the total pressure in the container.

Short Answer

Expert verified
Short answer: (a) To calculate the partial pressure of diethylether, first determine the mass of diethylether using the volume and density (\(m_{diethylether} = V_{diethylether} \times \rho_{diethylether}\)). Convert the mass to moles using the molar mass (\(n_{diethylether} = \frac{m_{diethylether}}{molar\ mass_{diethylether}}\)). Then, use the Ideal Gas Law to calculate the partial pressure (\(P_{diethylether} = \frac{n_{diethylether}RT}{V}\)). (b) To calculate the total pressure in the container, sum up the partial pressures of N2, O2, and diethylether (\(P_{total} = P_{\mathrm{N}_{2}} + P_{\mathrm{O}_{2}} + P_{diethylether}\)).

Step by step solution

01

Calculate the mass of diethylether

First, let's calculate the mass of diethylether using its volume and density: \(m_{diethylether} = V_{diethylether} \times \rho_{diethylether}\) where \(m_{diethylether}\) is the mass of diethylether (in grams), \(V_{diethylether}\) is the volume of the diethylether (5.00 mL), and \(\rho_{diethylether}\) is the density of the diethylether (0.7134 g/mL).
02

Convert the mass of diethylether to moles

To convert the mass of diethylether to moles, we need to use the molar mass of diethylether: Molecular formula of diethylether is \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OC}_{2} \mathrm{H}_{5}\), which gives us a molar mass of \(4 * 12.01 + 10 * 1.01 + 1 * 16 = 74.12 \mathrm{g/mol}\). Now we can calculate the moles of diethylether: \(n_{diethylether} = \frac{m_{diethylether}}{molar\ mass_{diethylether}}\)
03

Calculate the partial pressure of diethylether

Now that we have the moles of diethylether, we can use the Ideal Gas Law to calculate the partial pressure of diethylether: \(P_{diethylether}V = n_{diethylether}RT\) where \(P_{diethylether}\) is the partial pressure of diethylether, V is the volume of the container (6.00 L), \(n_{diethylether}\) is the moles of diethylether calculated in Step 2, R is the ideal gas constant (\(0.08206 \mathrm{L~atm/mol~K}\)), and T is the temperature in Kelvin (35.0°C = 308.15 K). Now we can solve for \(P_{diethylether}\): \(P_{diethylether} = \frac{n_{diethylether}RT}{V}\)
04

Calculate the total pressure in the container

Finally, we can calculate the total pressure in the container by summing up the partial pressures of N2, O2, and diethylether: \(P_{total} = P_{\mathrm{N}_{2}} + P_{\mathrm{O}_{2}} + P_{diethylether}\) With this step by step solution, you should now have all the necessary information to solve for the partial pressure of diethylether (a) and the total pressure in the container (b).

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