Question

In the equation pv = nrt, how would you solve for v?

Answer 1

Hint pv = nrt is an ideal gas equation. Means ideal gas is going to obey the equation pv = nrt at all temperatures and pressures. Real gas does not obey the principle of pv = nrt.
Here p = pressure of the gas
v = volume of the gas
n = number of moles of the gas
r = gas constant
t = temperature of the gas

Complete step by step answer:
- In the question it is asked in the equation pv = nrt, how we can solve for v.
- It is very easy to calculate the value of v form the equation pv = nrt and it is as follows.
- Just divide the equation on both sides with p and check we will get the value of v from the equation pv = nrt and it is as follows.
\[\begin{align}
& \Rightarrow pv=nrt \\
& \Rightarrow \dfrac{pv}{p}=\dfrac{nrt}{p} \\
& \Rightarrow v=\dfrac{nrt}{p} \\
\end{align}\]
- Now we can cross check if the above equation is correct or not by using principles of gas laws.

Note: The gas laws are Boyle's laws, Charles law and Avogadro’s law.
Boyle's law : $P=\dfrac{1}{V}$ where nRT is constant.
Charles law: V = T, where $\dfrac{nR}{P}$ is constant.
Avogadro’s law : V = n where $\dfrac{RT}{P}$ is constant.
In the all the above formulas P = pressure of the gas
V = volume of the gas
N = number of moles of the gas
R = gas constant
T = temperature of the gas