Consider two containers of gases at the same temperature. One has helium at a pressure of 1.00 atm. The other contains carbon dioxide with the same density as the helium gas. What is the pressure of the carbon dioxide gas sample?

• A. 0.063 atm
• B. 0.091 atm
• C. 0.133 atm
• D. 1.51 atm
• E. 2.71 atm

Answer: (B)

Verified step by step guidance

1. Start by using the ideal gas law equation: \( PV = nRT \). Since the temperature and volume are constant for both gases, we can relate the pressure and density using the molar mass.
2. Express the density \( \rho \) in terms of the ideal gas law: \( \rho = \frac{PM}{RT} \), where \( M \) is the molar mass of the gas.
3. Since the densities of helium and carbon dioxide are equal, set their density expressions equal: \( \frac{P_{\text{He}}M_{\text{He}}}{RT} = \frac{P_{\text{CO}_2}M_{\text{CO}_2}}{RT} \).
4. Cancel out the common terms \( RT \) from both sides of the equation, leading to: \( P_{\text{He}}M_{\text{He}} = P_{\text{CO}_2}M_{\text{CO}_2} \).
5. Solve for the pressure of carbon dioxide \( P_{\text{CO}_2} \) by rearranging the equation: \( P_{\text{CO}_2} = \frac{P_{\text{He}}M_{\text{He}}}{M_{\text{CO}_2}} \). Substitute the known values: \( P_{\text{He}} = 1.00 \text{ atm} \), \( M_{\text{He}} = 4.00 \text{ g/mol} \), and \( M_{\text{CO}_2} = 44.01 \text{ g/mol} \).