A quantity of N2 gas originally held at 531.96 kPa pressure in a 1.00-L container at 26 °C is transferred to a 12.5-L container at 20 °C. A quantity of O2 gas originally at 531.96 kPa and 26 °C in a 5.00-L container is transferred to this same container. What is the total pressure in the new container?

Verified step by step guidance

1. Identify the initial conditions for each gas: \(N_2\) and \(O_2\). For \(N_2\), initial pressure \(P_1 = 531.96\, \text{kPa}\), volume \(V_1 = 1.00\, \text{L}\), and temperature \(T_1 = 26\, ^\circ\text{C}\). For \(O_2\), initial pressure \(P_2 = 531.96\, \text{kPa}\), volume \(V_2 = 5.00\, \text{L}\), and temperature \(T_2 = 26\, ^\circ\text{C}\).
2. Convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature. \(T_1 = 26 + 273.15 = 299.15\, \text{K}\) and \(T_2 = 26 + 273.15 = 299.15\, \text{K}\). The final temperature \(T_f = 20 + 273.15 = 293.15\, \text{K}\).
3. Use the ideal gas law to find the final pressure of each gas in the new container. For \(N_2\), use \(P_1 V_1 / T_1 = P_f V_f / T_f\) to solve for \(P_f\). Substitute \(P_1 = 531.96\, \text{kPa}\), \(V_1 = 1.00\, \text{L}\), \(T_1 = 299.15\, \text{K}\), \(V_f = 12.5\, \text{L}\), and \(T_f = 293.15\, \text{K}\).
4. Repeat the calculation for \(O_2\) using the same formula: \(P_2 V_2 / T_2 = P_f V_f / T_f\). Substitute \(P_2 = 531.96\, \text{kPa}\), \(V_2 = 5.00\, \text{L}\), \(T_2 = 299.15\, \text{K}\), \(V_f = 12.5\, \text{L}\), and \(T_f = 293.15\, \text{K}\).
5. Add the partial pressures of \(N_2\) and \(O_2\) obtained from the previous steps to find the total pressure in the new container.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under varying conditions and allows for the calculation of pressure changes when gases are transferred between containers.

Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas. This concept is crucial for determining the total pressure in the new container after combining the nitrogen and oxygen gases, as it allows for the addition of their respective pressures.

Gas Volume and Temperature Relationships

The behavior of gases is influenced by changes in volume and temperature, as described by Charles's Law and Boyle's Law. Understanding how these factors affect gas pressure is vital for calculating the new pressure after transferring gases to a larger container and adjusting for temperature differences.