A quantity of N2 gas originally held at 5.25 atm 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 5.25 atm 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. <Step 1: Use the ideal gas law to find the number of moles of N2 gas.> \( PV = nRT \) where \( P = 5.25 \text{ atm}, V = 1.00 \text{ L}, R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}, T = 26°C = 299 \text{ K} \). Solve for \( n \).
2. <Step 2: Use the ideal gas law to find the number of moles of O2 gas.> \( PV = nRT \) where \( P = 5.25 \text{ atm}, V = 5.00 \text{ L}, R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}, T = 26°C = 299 \text{ K} \). Solve for \( n \).
3. <Step 3: Calculate the total number of moles of gas in the new container by adding the moles of N2 and O2.>
4. <Step 4: Use the ideal gas law to find the total pressure in the new container.> \( P_{\text{total}}V = n_{\text{total}}RT \) where \( V = 12.5 \text{ L}, R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}, T = 20°C = 293 \text{ K} \). Solve for \( P_{\text{total}} \).
5. <Step 5: Ensure all units are consistent and check calculations for accuracy.>

Key Concepts

Ideal Gas Law

The Ideal Gas Law, represented as PV = nRT, relates the pressure (P), volume (V), and temperature (T) of an ideal gas to the number of moles (n) and the ideal gas constant (R). This law is fundamental for calculating changes in gas conditions, allowing us to determine how pressure varies with volume and temperature.

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. This principle is crucial for calculating the total pressure in a container after transferring gases, as it allows us to consider the contributions of each gas separately.

Gas Behavior under Changing Conditions

Gases behave differently under varying conditions of temperature and volume. When a gas is transferred to a new container with a different volume and temperature, its pressure will change according to the Ideal Gas Law. Understanding how these variables interact is essential for predicting the final pressure in the new container.