The Division Property of Equality states that if you have an equation, you can divide both sides by the same nonzero number without changing the equality.
In the equation \( PV = nRT \), if you want to solve for one of the variables by using the Division Property of Equality, you can divide both sides of the equation by a specific variable.
For example, if you want to solve for \( n \), you can rearrange the equation as follows:
-
Start with the original equation: \[ PV = nRT \]
-
Divide both sides by \( RT \): \[ \frac{PV}{RT} = n \]
This shows that you used the Division Property of Equality to rearrange the equation \( PV = nRT \) to isolate \( n \).
Similarly, if you wanted to solve for \( P \), you could divide both sides by \( V \): \[ P = \frac{nRT}{V} \]
Both are examples of using the Division Property of Equality to rearrange the original equation.