Question

1. a container holds three gases: oxygen, carbon dioxide, and helium. the partial pressures of the three gases are 2.00 atm, 3.00 atm, and 4.00 atm, respectively. what is the total pressure inside the container?
2. 80.0 liters of oxygen is collected over water at 50 °c. ($p_{h2o}$ @ 50 c = 12.334 kpa). the atmospheric pressure in the room is 96.00 kpa. what is the partial pressure of the oxygen?
3. if 60.0 l of nitrogen is collected over water at 40.0 °c when the atmospheric pressure is 760.0 mm hg, what is the partial pressure of the nitrogen? ($p_{h2o}$ @ 40 c = 7.38 kpa)
4. a mixture of 40.0 g of oxygen and 40.0 g of helium has a total pressure of 0.900 atm. what is the partial pressure of each gas?
5. a mixture of 66% nitrogen and 33% neon gases has a total mass of 15.0 g. what is the density of this gas mixture at 350 k and 7.0 atm? assume ideal gas behavior.
6. a mixture of gases contains 2.14 g of $n_2$, 5.85 g of $h_2$, and 4.18 g of $nh_3$. if the total pressure of the mixture is 4.58 atm, what is the partial pressure of each component?
7. three gases (8.00 g of methane, $ch_4$, 18.0 g of ethane, $c_2h_6$, and an unknown amount of propane, $c_3h_8$) were added to the same 10.0 l container. at 23.0 °c, the total pressure in the container was measured to be 4.43 atm. calculate the partial pressure of each gas in the container.

Explanation:

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Problem 9

Step1: Sum partial pressures

$P_{total} = P_{O_2} + P_{CO_2} + P_{He}$

Step2: Substitute given values

$P_{total} = 2.00\ \text{atm} + 3.00\ \text{atm} + 4.00\ \text{atm}$
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Problem 10

Step1: Subtract water vapor pressure

$P_{O_2} = P_{atm} - P_{H_2O}$

Step2: Substitute given values

$P_{O_2} = 96.00\ \text{kPa} - 12.334\ \text{kPa}$
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Problem 11

Step1: Convert atm to kPa

$760.0\ \text{mm Hg} = 101.325\ \text{kPa}$

Step2: Subtract water vapor pressure

$P_{N_2} = 101.325\ \text{kPa} - 7.38\ \text{kPa}$
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Problem 12

Step1: Calculate moles of each gas

$n_{O_2} = \frac{40.0\ \text{g}}{32.00\ \text{g/mol}} = 1.25\ \text{mol}$, $n_{He} = \frac{40.0\ \text{g}}{4.003\ \text{g/mol}} \approx 9.99\ \text{mol}$

Step2: Find mole fractions

$\chi_{O_2} = \frac{1.25}{1.25+9.99} \approx 0.111$, $\chi_{He} = 1 - 0.111 = 0.889$

Step3: Calculate partial pressures

$P_{O_2} = \chi_{O_2}P_{total}$, $P_{He} = \chi_{He}P_{total}$
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Problem 13

Step1: Find masses of each gas

$m_{N_2} = 0.66 \times 15.0\ \text{g} = 9.9\ \text{g}$, $m_{Ne} = 0.33 \times 15.0\ \text{g} = 4.95\ \text{g}$

Step2: Calculate total moles

$n_{N_2} = \frac{9.9\ \text{g}}{28.02\ \text{g/mol}} \approx 0.353\ \text{mol}$, $n_{Ne} = \frac{4.95\ \text{g}}{20.18\ \text{g/mol}} \approx 0.245\ \text{mol}$
$n_{total} = 0.353 + 0.245 = 0.598\ \text{mol}$

Step3: Use ideal gas law for volume

$V = \frac{n_{total}RT}{P} = \frac{0.598\ \text{mol} \times 0.0821\ \text{L·atm/(mol·K)} \times 350\ \text{K}}{7.0\ \text{atm}} \approx 2.47\ \text{L}$

Step4: Calculate density

$
ho = \frac{m_{total}}{V}$
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Problem 14

Step1: Calculate moles of each gas

$n_{N_2} = \frac{2.14\ \text{g}}{28.02\ \text{g/mol}} \approx 0.0764\ \text{mol}$, $n_{H_2} = \frac{5.85\ \text{g}}{2.016\ \text{g/mol}} \approx 2.90\ \text{mol}$, $n_{NH_3} = \frac{4.18\ \text{g}}{17.03\ \text{g/mol}} \approx 0.245\ \text{mol}$

Step2: Find total moles

$n_{total} = 0.0764 + 2.90 + 0.245 \approx 3.221\ \text{mol}$

Step3: Calculate mole fractions and partial pressures

$\chi_i = \frac{n_i}{n_{total}}$, $P_i = \chi_i P_{total}$
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Problem 15

Step1: Calculate moles of known gases

$n_{CH_4} = \frac{8.00\ \text{g}}{16.04\ \text{g/mol}} = 0.499\ \text{mol}$, $n_{C_2H_6} = \frac{18.0\ \text{g}}{30.07\ \text{g/mol}} \approx 0.599\ \text{mol}$

Step2: Find total moles via ideal gas law

$n_{total} = \frac{P_{total}V}{RT} = \frac{4.43\ \text{atm} \times 10.0\ \text{L}}{0.0821\ \text{L·atm/(mol·K)} \times 296.15\ \text{K}} \approx 1.82\ \text{mol}$

Step3: Find moles of propane

$n_{C_3H_8} = 1.82 - 0.499 - 0.599 = 0.722\ \text{mol}$

Step4: Calculate partial pressures

$P_i = \frac{n_i}{n_{total}}P_{total}$
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Answer:

1. $9.00\ \text{atm}$
2. $83.67\ \text{kPa}$
3. $93.95\ \text{kPa}$
4. $P_{O_2} = 0.0999\ \text{atm}$, $P_{He} = 0.800\ \text{atm}$
5. $\approx 6.07\ \text{g/L}$
6. $P_{N_2} = 0.111\ \text{atm}$, $P_{H_2} = 4.17\ \text{atm}$, $P_{NH_3} = 0.298\ \text{atm}$
7. $P_{CH_4} = 1.21\ \text{atm}$, $P_{C_2H_6} = 1.45\ \text{atm}$, $P_{C_3H_8} = 1.77\ \text{atm}$