Question

a 5.00 l tank at 19.4 °c is filled with 18.5 g of carbon dioxide gas and 11.8 g of sulfur hexafluoride gas. you can assume both gases behave as ideal gases under these conditions. calculate the mole fraction of each gas. be sure each of your answer entries has the correct number of significant digits. gas mole fraction carbon dioxide sulfur hexafluoride

Explanation:

Step1: Calculate moles of each gas

• Molar mass of \(CO_2\): \(M_{CO_2}=(12.01 + 2\times16.00)\space g/mol = 44.01\space g/mol\)
• Moles of \(CO_2\): \(n_{CO_2}=\frac{m_{CO_2}}{M_{CO_2}}=\frac{18.5\space g}{44.01\space g/mol}\approx0.420\space mol\)
• Molar mass of \(SF_6\): \(M_{SF_6}=(32.07+6\times19.00)\space g/mol = 146.07\space g/mol\)
• Moles of \(SF_6\): \(n_{SF_6}=\frac{m_{SF_6}}{M_{SF_6}}=\frac{11.8\space g}{146.07\space g/mol}\approx0.0808\space mol\)

Step2: Calculate total moles

• Total moles: \(n_{total}=n_{CO_2}+n_{SF_6}=0.420 + 0.0808=0.5008\space mol\)

Step3: Calculate mole fractions

• Mole fraction of \(CO_2\): \(x_{CO_2}=\frac{n_{CO_2}}{n_{total}}=\frac{0.420}{0.5008}\approx0.839\)
• Mole fraction of \(SF_6\): \(x_{SF_6}=\frac{n_{SF_6}}{n_{total}}=\frac{0.0808}{0.5008}\approx0.161\)

Answer:

• Carbon dioxide: \(0.839\)
• Sulfur hexafluoride: \(0.161\)