Pressure of 1 g of an ideal gas A at 27^∘ C is found to be 2 bar. When 2 g of another ideal gas

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Pressure of 1 g of an ideal gas A at 27^∘ C is found to be 2...

Pressure of 1 g of an ideal gas $A$ at $27^{\circ} \mathrm{C}$ is found to be 2 bar. When $2 \mathrm{~g}$ of another ideal gas $\mathrm{B}$ is introduced in the same flask at same temperature the pressure becomes 3 bar. Find a relationship between their molecular masses.

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental principle in thermodynamics that relates the pressure, volume, temperature, and number of moles of an ideal gas. It explains that for a fixed temperature and volume, the pressure of a gas is directly proportional to its number of moles, providing a basis for comparing different gases under the same experimental conditions.

Direct Proportionality of Pressure to Number of Moles

When the temperature and volume of a gas system are held constant, the pressure is directly proportional to the number of gas particles (or moles) present in the container. This concept allows us to infer changes in pressure as the amount of gas changes, which is crucial when analyzing mixtures of gases or when additional gas is introduced into a sealed system.

Mole Concept and Molar Mass

The mole concept is a central idea in chemistry that relates the mass of a substance to the number of particles it contains, through its molar mass. By dividing the mass of a gas by its molecular (or molar) mass, one can determine the number of moles present. This relationship is essential when comparing the contributions of different gases to the total pressure in a container.

Additivity of Gas Pressures

In a mixture of ideal gases, each gas contributes to the total pressure independently of the others. This principle, often related to Dalton’s law of partial pressures, states that the total pressure is the sum of the pressures that each gas would exert if it occupied the entire volume alone, provided the conditions of temperature and volume remain constant.

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