This picture represents a sample of gas at a pressure of 1 atm, a volume of 1 L, and a temperature of 25 °C. Draw a similar picture showing what would happen to the sample if the volume were reduced to 0.5 L and the temperature were increased to 250 °C. What would happen to the pressure?

Verified step by step guidance

1. Step 1: Identify the initial conditions of the gas sample: pressure (P1) = 1 atm, volume (V1) = 1 L, and temperature (T1) = 25 °C (which is 298 K).
2. Step 2: Convert the final temperature to Kelvin: T2 = 250 °C + 273 = 523 K.
3. Step 3: Use the combined gas law to relate the initial and final states of the gas: (P1 * V1) / T1 = (P2 * V2) / T2.
4. Step 4: Substitute the known values into the combined gas law equation: (1 atm * 1 L) / 298 K = (P2 * 0.5 L) / 523 K.
5. Step 5: Solve for the final pressure (P2) by isolating P2 in the equation.

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 helps predict how changing one of these variables affects the others, making it essential for understanding gas behavior under different conditions.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This means that if the temperature increases, the volume must also increase, and vice versa. In the context of the question, reducing the volume while increasing the temperature will significantly affect the pressure of the gas.

Boyle's Law

Boyle's Law describes the inverse relationship between the pressure and volume of a gas at constant temperature. According to this law, if the volume of a gas decreases, the pressure increases, provided the temperature remains constant. This principle is crucial for understanding how the pressure of the gas sample will change when its volume is halved.