Assume that you have a gas cylinder with a movable piston filled with oxygen. The initial conditions are T = 250 K, n = 0.140 mol O2, and P = 1.00 atm. If the initial volume is 1.0 L, what is the volume when the temperature is increased to 400 K and the pressure is decreased to 0.75 atm? (LO 10.3) (a) 2.1 L (b) 1.2 L (c) 0.83 L (d) 1.6 L

Verified step by step guidance

1. Identify the initial and final conditions of the gas: initial temperature (T1) = 250 K, initial pressure (P1) = 1.00 atm, initial volume (V1) = 1.0 L, final temperature (T2) = 400 K, final pressure (P2) = 0.75 atm.
2. Use the combined gas law, which is \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \), to relate the initial and final states of the gas.
3. Rearrange the combined gas law to solve for the final volume \( V_2 \): \( V_2 = \frac{P_1 V_1 T_2}{T_1 P_2} \).
4. Substitute the known values into the equation: \( V_2 = \frac{(1.00 \text{ atm})(1.0 \text{ L})(400 \text{ K})}{(250 \text{ K})(0.75 \text{ atm})} \).
5. Calculate the expression to find the final volume \( V_2 \).

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas. It is expressed as PV = nRT, where R is the ideal gas constant. This law allows us to predict how a gas will behave under different conditions, making it essential for solving problems involving gas properties.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. Mathematically, it can be expressed as V1/T1 = V2/T2. This concept is crucial for understanding how changes in temperature affect the volume of a gas, especially in scenarios where pressure varies.

Boyle's Law

Boyle's Law describes the inverse relationship between the pressure and volume of a gas when temperature is held constant. It can be represented as P1V1 = P2V2. This principle is important for analyzing how changes in pressure will influence the volume of a gas, particularly when temperature is not constant.