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The Ideal Gas Law is a concept in chemistry that describes how a gas behaves in given conditions. The law states that
\[ PV = nRT \] where $P$ is the pressure (in atmospheres), $V$ is the volume of the gas (in liters), $T$ is the temperature of the gas (in Kelvin), $n$ is the amount of gas (in moles) and $R$ is a constant equal to $0.0821 \frac{L\cdot atm}{mol \cdot K}$. This can be used to describe a variety of situations.
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    \item There was a story on the news about someone's can of dry shampoo that exploded when it was left in a hot car. Assume that the volume of the canister was $0.5 L$ and $n = 0.2$. If the temperature was changing at a rate of $2 K/min$ when it reached $380 K$, how fast was the pressure increasing at that moment?
    \item Now, consider an entirely different scenario. You blow up a balloon to a volume of $1 L$ at a pressure of $1$ atm and a temperature of $300 K$. Then, you take the balloon into a diving pool and take it underwater. As the pressure increases, the volume of the balloon will decrease. If the pressure is increasing at a rate of $0.5$ $atm/min$, how fast is the volume decreasing when the pressure reaches $1.2$ atm?
    \textbf{Hint:} You'll need to use the gas law to solve for both the initial value of $n$, as well as the volume when the pressure is 1.2 atm.
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