Question

a mixture of gases contains 3.85 moles of neon (ne), 0.92 moles of argon (ar), and 2.59 moles of xenon (xe). calculate the partial pressure of the gases if the total pressure is 2.50 atm at a certain temperature.

Explanation:

Step1: Calculate total moles

Total moles \(n_{total}=n_{Ne}+n_{Ar}+n_{Xe}\)
\(n_{total}=3.85 + 0.92+2.59=7.36\) moles

Step2: Calculate mole fraction of Ne

Mole fraction \(X_{Ne}=\frac{n_{Ne}}{n_{total}}\)
\(X_{Ne}=\frac{3.85}{7.36}\approx0.523\)

Step3: Calculate partial pressure of Ne

Partial pressure \(P_{Ne}=X_{Ne}\times P_{total}\)
\(P_{Ne}=0.523\times2.50 = 1.31\) atm

Step4: Calculate mole fraction of Ar

Mole fraction \(X_{Ar}=\frac{n_{Ar}}{n_{total}}\)
\(X_{Ar}=\frac{0.92}{7.36}\approx0.125\)

Step5: Calculate partial pressure of Ar

Partial pressure \(P_{Ar}=X_{Ar}\times P_{total}\)
\(P_{Ar}=0.125\times2.50 = 0.31\) atm

Step6: Calculate mole fraction of Xe

Mole fraction \(X_{Xe}=\frac{n_{Xe}}{n_{total}}\)
\(X_{Xe}=\frac{2.59}{7.36}\approx0.352\)

Step7: Calculate partial pressure of Xe

Partial pressure \(P_{Xe}=X_{Xe}\times P_{total}\)
\(P_{Xe}=0.352\times2.50 = 0.88\) atm

Answer:

The partial pressure of Ne is \(1.31\) atm, the partial pressure of Ar is \(0.31\) atm, and the partial pressure of Xe is \(0.88\) atm.