After a chemical reaction, there are two containers with gas collected. Both containers hold a constant volume of 5 L at a constant pressure of 1 atm. In the first container, 2 mole of gas A are collected. In the second container, 1 mole of gas B are collected.

Question

Use the ideal gas law to determine if the temperature of the two collected gases will be the same. Explain your reasoning

Answer 1

According to the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

In this case, both containers have the same volume (5 L) and pressure (1 atm). We can rearrange the ideal gas law equation to solve for temperature:

T = (PV) / (nR)

Let's calculate the temperature for each container:

For container 1 (gas A):
n = 2 moles
T1 = (1 atm * 5 L) / (2 moles * R)

For container 2 (gas B):
n = 1 mole
T2 = (1 atm * 5 L) / (1 mole * R)

Given that both containers have the same pressure, volume, and gas constant R, the only difference between the two equations is the number of moles. Since the temperature calculation is proportional to the number of moles, we can conclude that the temperature of both collected gases will be the same.

Therefore, the temperature of the two collected gases will be the same.