5) i have a balloon that can hold 100 liters of air. if i blow up this balloon with 3 moles of oxygen gas at…

Explanation:

Step1: Recall ideal - gas law

The ideal - gas law is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal - gas constant ($R=0.0821\ L\cdot atm/(mol\cdot K)$), and $T$ is temperature.

Step2: Rearrange the formula for temperature

We want to find $T$, so we can rewrite the ideal - gas law as $T=\frac{PV}{nR}$.

Step3: Substitute the given values

We know that $P = 1\ atm$, $V = 100\ L$, $n = 3\ mol$, and $R=0.0821\ L\cdot atm/(mol\cdot K)$. $T=\frac{1\ atm\times100\ L}{3\ mol\times0.0821\ L\cdot atm/(mol\cdot K)}$

Step4: Calculate the temperature

$T=\frac{100}{3\times0.0821}\ K\approx406\ K$

Answer:

$406\ K$