Three moles of an ideal gas are in a rigid cubical box with...

Three moles of an ideal gas are in a rigid cubical box with sides of length $0.170 \mathrm{~m} .$ (a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is $16.0^{\circ} \mathrm{C} ?$ (b) What is the force when the temperature of the gas is increased to $107.0^{\circ} \mathrm{C} ?$

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Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is fundamental in relating pressure, volume, temperature, and amount of substance for an ideal gas. It allows one to determine any of these properties when the others are known, making it essential for calculations involving gases in confined spaces.

Pressure and Force Relationship

Pressure is defined as the force per unit area (P = F/A). Understanding this relationship allows one to calculate the force that a gas exerts on a container’s walls, once the pressure and surface area are known.

Temperature Conversion to Kelvin

Since the ideal gas law requires the temperature to be in Kelvin, converting from Celsius to Kelvin (by adding 273.15) is an essential step in ensuring that the calculations are correct and consistent with the law.

Volume Calculation of a Cube

Determining the volume of a gas confined in a cubical container involves calculating the cube's volume using the formula V = L^3, where L is the length of one side. This is a vital step in the application of the ideal gas law for finding pressure.

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