Ideal Gas Law: Estimating the Number of Moles of Air in an Evacuated Chamber

How can we estimate the number of moles of air in an evacuated chamber using the ideal gas law?

Given the dimensions of the chamber and the temperature and pressure of the air inside, how can we calculate the approximate number of moles of air in the chamber? What is the equation we should use?

Estimating the Number of Moles of Air

To estimate the number of moles of air in the evacuated chamber, we can utilize the ideal gas law equation PV = nRT. In this equation, P represents pressure, V stands for volume, n signifies the number of moles, R is the gas constant, and T denotes the temperature in Kelvin.

First, let's calculate the volume of the chamber by multiplying its height, width, and length: V = 8.2 m * 6.6 m * 12.4 m = 646.848 m^3.

Next, we can rearrange the ideal gas law equation to solve for n: n = PV / RT. By substituting the given values of P = 1.00×10^3 Pa, R = 8.314 J/(mol.K), and T = 306 K into the equation, we can calculate the approximate number of moles of air in the chamber.

After performing the calculations, we find that the approximate number of moles of air in the evacuated chamber is 2,828 moles. Therefore, utilizing the ideal gas law, we can estimate the number of moles of air in a specified volume under known pressure and temperature conditions.