Gas volume calculation based on temperature and pressure variations

Understanding Gas Laws

Boyle's Law: states that the volume of a gas is inversely proportional to its pressure at a constant temperature. In simpler terms, when the pressure on a gas is increased, its volume decreases, and vice versa.

Charles's Law: states that the volume of a gas is directly proportional to its temperature at a constant pressure. This means that when the temperature of a gas increases, its volume also increases, and when the temperature decreases, the volume decreases.

Gas Volume Calculation

Given that at a temperature of 200° and a pressure of 500 mmHg, the volume of the gas is 240 cm³, we can apply the combined gas law to calculate the volume at 275° and 400 mmHg.

The combined gas law equation is (P1 * V1) / T1 = (P2 * V2) / T2, where initial conditions are represented by subscripts 1 and final conditions by subscripts 2.

Converting temperatures to Kelvin: T1 = 200° + 273.15 = 473.15 K, T2 = 275° + 273.15 = 548.15 K.

Plugging in the given values: (500 * 240) / 473.15 = (400 * V2) / 548.15. Solving for V2 gives us: V2 = (500 * 240 * 548.15) / (400 * 473.15) = 330 cm³.

Therefore, the volume of the gas at 275° and 400 mmHg is 330 cm³ as calculated using Boyle's law and Charles's law.