# Question aa424

Jan 22, 2016

You rearrange the equation to isolate the missing variable and solve. You do not cross multiply.

#### Explanation:

Example
You are given the following information about a gas: ${V}_{1} = \text{25 L}$; ${T}_{1} = \text{350 K}$; ${T}_{2} = \text{270 K}$. What is the new volume $\left({V}_{2}\right)$?

Equation
${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

Solution
Rearrange the equation to isolate ${V}_{2}$, substitute the given values, and solve.

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

Multiply both sides by ${T}_{2}$ in order to isolate ${V}_{2}$.

${V}_{1} / {T}_{1} \left({T}_{2}\right) = {V}_{2} / {\cancel{T}}_{2} \left({\cancel{T}}_{2}\right)$

${V}_{2} = \frac{{V}_{1} {T}_{2}}{T} _ 1$

V_2=((25"L")xx(270cancel"K"))/(350cancel"K")#

${V}_{2} = \text{19 L}$

Notice that there was no cross multiplying. Instead, both sides of the equation were multiplied times ${T}_{2}$, which cancelled it out on the ${V}_{2}$ side and multiplied it times ${V}_{1}$ on the other side.