Question

If you know the temperature, volume and pressure of a gas, how would you rearrange the ideal gas equation to find the number of moles?
(A) Divide PV by T only
(B) Multiply PV by R only
(C) Divide PV by both T and R
(D) Divide PV by n
(E) Multiply PV by both T and R

Answer 1

Hint: The ideal gas equation can be given as under where n is the number of moles, R is the universal gas constant, T is temperature, P is pressure and V is volume.
PV = nRT

Complete step by step solution:
We need to find the equation of finding the number of moles of a gas in the ideal gas equation in order to give the answer of this question.
- Ideal gas equation is also called general gas equation. This equation is the equation state of a hypothetical gas whose behavior is ideal. This equation is a good approximation of the behavior of many gases under certain conditions. It also has several limitations.
- This equation was first stated by Clapeyron who combined Boyle’s, Charles’ Gay-Lussac and Avogardo’s law.
The ideal gas equation can be written as below.
PV = nRT …..(1)
Where, P = Pressure of the system (in atm)
V = Volume of the system (in ${m^{ - 3}}$)
n = amount of the substance or gas in moles
R = Ideal gas constant
T = Temperature (in K)
Now, we are given that we need to find the number of moles of the gas. So, we can write the equation (1) as
$n{\text{ = }}\dfrac{{PV}}{{RT}}$
Thus, we can say that we can find the number of moles by dividing PV by both R and T.

Therefore, the correct answer is (C).

Note: Remember that we need to put the SI units of every quantity given in the ideal gas equation. So, pressure needs to be in the atm unit, volume in ${m^{ - 3}}$ unit and temperature in K. If any other units are there, then we need to convert them to SI units.