Several properties of gases can be experimentally measured: temperature, pressure, volume, and the amount of the gas (i.e., the number of moles). The ideal gas law states that the relationship between these properties, or variables, in a mathematical formula.
The ideal gas law is PV = nRT.
P is the pressure in atmospheres (atm), V is the volume in liters (L), n is the number of moles, R is the gas constant (0.0821 L∙atm/(mol∙K)), and T is the temperature in Kelvins (K).
Consider the following conditions: a 3,500 mL tank was filled with 27 moles of argon gas under a pressure of 12 atm.
Assume you are going to use the ideal gas law to solve for the unknown variable.
What variable are you solving for?
Are all of variables in the correct units? If not, which variable needs to be converted to the correct units?
In this scenario, we are solving for the temperature (T) of the gas in Kelvins.
The volume is given in milliliters (mL), but it needs to be converted to liters (L) for the ideal gas law formula to work correctly. So, the volume variable needs to be converted to the correct units.
Given:
Volume = 3,500 mL = 3.5 L
Pressure (P) = 12 atm
Number of moles (n) = 27 moles
Gas constant (R) = 0.0821 L∙atm/(mol∙K)
Using the ideal gas law formula, PV = nRT, we can rearrange it to solve for the temperature (T):
T = PV / nR
Plugging in the values:
T = (12 atm) x (3.5 L) / (27 moles) x (0.0821 L∙atm/(mol∙K))
T = 1.59 K
Therefore, the temperature of the argon gas in the tank is approximately 1.59 Kelvins.