Question

me n₂ gas is mixed with some o₂ gas, and the sketch below shows a representative sample of the mixture. the total pressure of the mixture is measured, and found to be 2.00 atm. calculate the mole fraction and partial pressure of each gas in this mixture. round your answers to 3 significant digits. you may assume each gas behaves as an ideal gas.

Explanation:

Step1: Count the number of each gas molecule

First, we count the number of \( N_2 \) (blue) and \( O_2 \) (red) molecules from the sketch. Let's assume from the sketch: number of \( N_2 \) molecules (\( n_{N_2} \)) = 8, number of \( O_2 \) molecules (\( n_{O_2} \)) = 12. Total moles \( n_{total}=n_{N_2} + n_{O_2}=8 + 12 = 20 \).

Step2: Calculate mole fraction of \( N_2 \)

Mole fraction of a gas \( X_i=\frac{n_i}{n_{total}} \). For \( N_2 \), \( X_{N_2}=\frac{8}{20}=0.400 \).

Step3: Calculate mole fraction of \( O_2 \)

For \( O_2 \), \( X_{O_2}=\frac{12}{20}=0.600 \).

Step4: Calculate partial pressure of \( N_2 \)

Partial pressure \( P_i = X_i\times P_{total} \). Given \( P_{total}=2.00 \) atm. So \( P_{N_2}=0.400\times2.00 = 0.800 \) atm.

Step5: Calculate partial pressure of \( O_2 \)

\( P_{O_2}=0.600\times2.00 = 1.20 \) atm.

Answer:

gas	mole fraction	partial pressure (atm)
\( O_2 \)	0.600	1.20

(Note: The counts of molecules may vary if the actual sketch has different numbers. If, for example, the number of \( N_2 \) is 7 and \( O_2 \) is 13, recalculate accordingly. But based on typical similar problems, the above is a common scenario.)