Question

Use division property of equality to rearrange “PV = nRT”

Answer 1

To rearrange the equation \( PV = nRT \) using the division property of equality, we can solve for any variable of interest by dividing both sides of the equation by the same value.

For example, if we want to solve for \( P \), we would divide both sides by \( V \):

\[
P = \frac{nRT}{V}
\]

If we want to solve for \( V \), we would divide both sides by \( P \):

\[
V = \frac{nRT}{P}
\]

If we want to solve for \( n \), we would divide both sides by \( RT \):

\[
n = \frac{PV}{RT}
\]

If we want to solve for \( R \), we divide both sides by \( nT \):

\[
R = \frac{PV}{nT}
\]

And if we want to solve for \( T \), we divide both sides by \( nR \):

\[
T = \frac{PV}{nR}
\]

These rearrangements allow you to express any variable in terms of the others using the division property of equality.