A rigid container holds 2.0 mol of gas at a pressure of 1.0...

A rigid container holds $2.0 \mathrm{mol}$ of gas at a pressure of $1.0 \mathrm{atm}$ and a temperature of $30^{\circ} \mathrm{C}$.
a. What is the container's volume?
b. What is the pressure if the temperature is raised to $130^{\circ} \mathrm{C} ?$

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Key Concepts

Constant-Volume Process (Gay-Lussac's Law)

In a constant-volume process, such as in a rigid container, the volume of the gas remains unchanged even if the temperature or pressure varies. This leads to a direct proportionality between the temperature and pressure of the gas (Gay-Lussac's Law), meaning that as the absolute temperature increases, the pressure also increases proportionally, assuming the number of moles stays constant.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental principle that relates the pressure, volume, temperature, and number of moles of an ideal gas. This equation is crucial for solving problems involving gases, as it provides a direct relationship among these variables when one or more of them changes.

Temperature Conversion

Temperature conversion, particularly from degrees Celsius to Kelvin, is essential when using the ideal gas law. Since the gas constant R and the law itself require absolute temperature measurements, converting to Kelvin (by adding 273.15 to the Celsius temperature) ensures that the calculations are accurate and consistent.

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