Gas volume calculation based on temperature and pressure variations

What is the relationship between the volume of a gas, its temperature, and pressure according to the given data? The volume of a gas varies directly as the temperature and inversely as the pressure, based on the given data. This relationship is described by Boyle's law and Charles's law in gas physics.

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.

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