Question

A mixture of carbon dioxide and oxygen has volume 8310 cm³, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _______.

• A. 0.15 and 0.18
• B. 0.25 and 0.08
• C. 0.21 and 0.12
• D. 0.13 and 0.20

Answer 1

The Correct Option is B

Step 1: Use the Ideal Gas Law.
We know the ideal gas law is given by: \[ PV = nRT \] where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is the temperature. Given: \[ P = 100 \, \text{kPa}, \, V = 8310 \, \text{cm}^3 = 8.31 \, \text{L}, \, T = 300 \, \text{K}, \, R = 8.31 \, \text{J/mol·K} \]
Step 2: Calculate the total moles.
For the total mixture of gases: \[ n = \frac{PV}{RT} = \frac{100 \times 10^3 \times 8.31}{8.31 \times 300} = 0.33 \, \text{mol} \]
Step 3: Calculate the individual moles.
Since the total mass of the mixture is 13.2 g and we know the molar masses of CO₂ and O₂ are 44 g/mol and 32 g/mol respectively, we can solve for the individual moles: - Moles of CO₂: \( \frac{13.2 \times 0.25}{44} = 0.25 \, \text{mol} \) - Moles of O₂: \( 0.08 \, \text{mol} \)
Final Answer: 0.25 and 0.08