# Oxygen gas is at STP when it occupies a volume 5.5 liters. To what temperature should it be raised to occupy a volume of 9.0 liters?

May 26, 2018

Well...for a given quantity of gas (such as we gots here)….

$V \propto T$

#### Explanation:

And this is old $\text{Charles' Law...}$

Now $\text{STP}$ specifies (depending on your syllabus) $298 \cdot K$ and (near to) $1 \cdot a t m$...

Given $V \propto T$, $V = k T$...solving for $k$, $k = \frac{V}{T}$...but this should apply at all temperatures for a given quantity of gas...and so...

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$...and we solve for ${T}_{2} = \frac{{V}_{2} \times {T}_{1}}{V} _ 1$

$\equiv \frac{9.0 \cdot L \times 273.15 \cdot K}{5.5 \cdot L} = 447.0 \cdot K \equiv 173.8$ ""^@C