Question

How would you solve for n in $PV=nRT$?

Answer 1

Hint The given equation in the question is the ideal gas equation $PV=nRT$ having n number of moles. When three values in the given equation are given then the fourth value can be calculated because the value of R is constant and it is called a gas constant. By keeping all the given values to one side and keeping the value that is to be calculated on the other side the equation can be solved.

Complete step by step answer:
The given equation in the question is the ideal gas equation $PV=nRT$ having n number of moles. It is solved by combining three laws called Boyle’s law, Charles law, and Avogadro law. When the volume is kept constant, the pressure of the gas is directly proportional to the temperature.
$P\propto T$
When the pressure is kept constant, the volume of the gas is directly proportional to the temperature.
$V\propto T$
When the temperature is kept constant, the pressure of the gas is inversely proportional to the volume.
$P\propto {\displaystyle \frac{1}{V}}$
So, by combining all these and removing the proportionality sign, we got the formula:
$PV=nRT$
In which n is the number of moles of the gas.
When three values in the given equation are given then the fourth value can be calculated because the value of R is constant and it is called a gas constant. By keeping all the given values to one side and keeping the value that is to be calculated on the other side the equation can be solved.
The value of n can be calculated by:
$n={\displaystyle \frac{PV}{RT}}$

Note: If we want to calculate the pressure of the gas then the equation will become:
$P={\displaystyle \frac{nRT}{V}}$
If we want to calculate the volume of the gas then the equation will become:
$V={\displaystyle \frac{nRT}{P}}$
If we want to calculate the temperature of the gas then the equation will become:
$T={\displaystyle \frac{PV}{nR}}$