A special gas mixture used in bacterial growth chambers contains 1.00% by weight CO2 and 99.0% O2. What is the partial pressure in atmospheres of each gas at a total pressure of 0.977 atm?

Verified step by step guidance

1. Determine the mass percentage of each gas in the mixture. For CO2, it is 1.00% and for O2, it is 99.0%.
2. Calculate the mole fraction of each gas. Assume a total mass of 100 g for simplicity, which means you have 1.00 g of CO2 and 99.0 g of O2. Convert these masses to moles using the molar mass of CO2 (44.01 g/mol) and O2 (32.00 g/mol).
3. Find the total moles of the gas mixture by adding the moles of CO2 and O2 together.
4. Calculate the mole fraction of each gas by dividing the moles of each gas by the total moles of the mixture.
5. Use Dalton's Law of Partial Pressures to find the partial pressure of each gas. Multiply the mole fraction of each gas by the total pressure of the mixture (0.977 atm).

Key Concepts

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. Each gas in the mixture behaves independently, and its partial pressure can be calculated by multiplying the total pressure by the mole fraction of that gas in the mixture.

Weight Percent and Mole Fraction

Weight percent is a way of expressing the concentration of a component in a mixture, calculated as the mass of the component divided by the total mass of the mixture, multiplied by 100. To find the mole fraction, which is necessary for calculating partial pressures, the weight percent must be converted to moles using the molar mass of each gas.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. While this question primarily focuses on partial pressures, understanding the Ideal Gas Law provides context for how gases behave under varying conditions and reinforces the concept of pressure in gas mixtures.