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A sample of air contains only N(2), O(2)...

A sample of air contains only `N_(2), O_(2)` and `H_(2)O`. It is saturated with water vapours and the total pressure is 640 torr. The vapurs of water is 40 torr and the molar ratio of `N_(2) : O_(2)` is `3 : 1`. The partial pressure of `N_(2)` in the sample is

A

480 torr

B

600 torr

C

525 torr

D

450 torr

Text Solution

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The correct Answer is:
To find the partial pressure of \( N_2 \) in the given sample of air, we can follow these steps: ### Step 1: Understand the given data - Total pressure \( P_{total} = 640 \, \text{torr} \) - Vapor pressure of water \( P_{H_2O} = 40 \, \text{torr} \) - Molar ratio of \( N_2 : O_2 = 3 : 1 \) ### Step 2: Calculate the pressure of the gas mixture (without water vapor) The pressure of the gas mixture (which includes \( N_2 \) and \( O_2 \)) can be calculated by subtracting the vapor pressure of water from the total pressure: \[ P_{N_2} + P_{O_2} = P_{total} - P_{H_2O} \] Substituting the known values: \[ P_{N_2} + P_{O_2} = 640 \, \text{torr} - 40 \, \text{torr} = 600 \, \text{torr} \] ### Step 3: Determine the moles of \( N_2 \) and \( O_2 \) Let the number of moles of \( O_2 \) be \( x \). Then, the number of moles of \( N_2 \) will be \( 3x \) based on the molar ratio \( 3:1 \). ### Step 4: Calculate the total moles of the gas mixture The total number of moles of the gas mixture is: \[ \text{Total moles} = N_{2} + O_{2} = 3x + x = 4x \] ### Step 5: Calculate the mole fractions The mole fraction of \( N_2 \) can be calculated as follows: \[ \text{Mole fraction of } N_2 = \frac{N_{2}}{N_{2} + O_{2}} = \frac{3x}{4x} = \frac{3}{4} \] ### Step 6: Calculate the partial pressure of \( N_2 \) Using Dalton's Law of Partial Pressures, the partial pressure of \( N_2 \) can be calculated as: \[ P_{N_2} = P_{total \, (N_2 + O_2)} \times \text{Mole fraction of } N_2 \] Substituting the known values: \[ P_{N_2} = 600 \, \text{torr} \times \frac{3}{4} \] Calculating this gives: \[ P_{N_2} = 600 \times 0.75 = 450 \, \text{torr} \] ### Final Answer The partial pressure of \( N_2 \) in the sample is **450 torr**. ---
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