Question

dalton’s law of partial pressures scenarios
directions: solve the problems below using dalton’s law or mole fractions and information on your preap chemistry reference materials. the answers for each problem are given, so the only way to earn credit is to show all of your work. you must follow this checklist while solving for the scenarios:

• identify the unknown value in the scenario. what is the question asking you to find and in what unit?
• write all quantitative data given in the scenario and given on your reference sheet.
• determine which formula you need to use by comparing knowns and your unknown to the equations given.
• convert all units for the same property of gas given to you in the problem to match each other.
• rearrange the equation for the unknown value you are solving for.
• plug in values with units and solve.
• show how units cancel and leave only the desired units, as needed.
• convert answer to desired units, if necessary.

$p_{tot} = p_1 + p_2 + p_3 + \dots$ $x_i = \frac{p_i}{p_{tot}} = \frac{n_i}{n_{tot}} = \frac{v_i}{v_{tot}}$

part a: dalton’s law introductory scenarios

1. a mixture of oxygen, hydrogen and nitrogen gases exerts a total pressure of 278 kpa. if the partial pressures of the oxygen and the hydrogen are 112 kpa and 101 kpa respectively, what would be the partial pressure exerted by the nitrogen?

1. a mixture of neon and argon gases exerts a total pressure of 2.39 atm. the partial pressure of the neon alone is 1.84 atm, what is the partial pressure of the argon gas in kpa?

1. a 5.0-liter container at 20.0°c has 4 gases pumped in. the total pressure of the gases is 4.80 atm. if the pressure of the first gas is 1.20 atm, and the pressure of the second gas is 0.490 atm, the pressure of the third gas is 0.780...

Explanation:

Step1: Identify knowns and unknown for Q1

Known: \( P_{\text{tot}} = 278 \, \text{kPa} \), \( P_{\text{O}_2} = 112 \, \text{kPa} \), \( P_{\text{H}_2} = 101 \, \text{kPa} \). Unknown: \( P_{\text{N}_2} \).

Step2: Use Dalton’s Law formula

Dalton’s Law: \( P_{\text{tot}} = P_{\text{O}_2} + P_{\text{H}_2} + P_{\text{N}_2} \). Rearrange for \( P_{\text{N}_2} \): \( P_{\text{N}_2} = P_{\text{tot}} - P_{\text{O}_2} - P_{\text{H}_2} \).

Step3: Substitute values

\( P_{\text{N}_2} = 278 \, \text{kPa} - 112 \, \text{kPa} - 101 \, \text{kPa} \).

Step4: Calculate

\( 278 - 112 - 101 = 65 \). So \( P_{\text{N}_2} = 65 \, \text{kPa} \).

(For Q2:

Step1: Identify knowns and unknown

Known: \( P_{\text{tot}} = 2.39 \, \text{atm} \), \( P_{\text{Ne}} = 1.84 \, \text{atm} \). Unknown: \( P_{\text{Ar}} \) (then convert to kPa).

Step2: Use Dalton’s Law

\( P_{\text{Ar}} = P_{\text{tot}} - P_{\text{Ne}} = 2.39 \, \text{atm} - 1.84 \, \text{atm} = 0.55 \, \text{atm} \).

Step3: Convert atm to kPa

1 atm = 101.325 kPa, so \( 0.55 \, \text{atm} \times 101.325 \, \text{kPa/atm} \approx 55.73 \, \text{kPa} \) (or 56 kPa with rounding).)

Answer:

(for Q1):
The partial pressure of nitrogen is \(\boldsymbol{65 \, \text{kPa}}\) (for Q2: ~55.7 kPa or 56 kPa).