# Question d00ec

Mar 8, 2017

$\text{0.514 atm}$

#### Explanation:

The idea here is that you need to assume that the temperature of the balloon remains constant because this will allow you to use Boyle's law to calculate the pressure of the balloon at its new volume.

So, Boyle's Law states that when the temperature and number of moles of gas, i.e. the amount of gas, are being kept constant, the pressure and the volume of the gas have an inverse relationship

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{{P}_{1} {V}_{1} = {P}_{2} {V}_{2}}}}$

Here

• ${P}_{1}$ and ${V}_{1}$ represent the pressure and volume of the gas at an initial state
• ${P}_{2}$ and ${V}_{2}$ represent the pressure and volume of the gas at a final state

Now, the volume of the gas increases at it moves away from sea level, which implies that its pressure decreases.

Rearrange the equation to solve for ${P}_{2}$

${P}_{1} {V}_{1} = {P}_{2} {V}_{2} \implies {P}_{2} = {V}_{1} / {V}_{2} \cdot {P}_{1}$

The pressure at sea level is defined as $\text{1 atm}$, which means that the pressure of the gas when it has a volume of $\text{175.0 L}$ will be equal to

P_2 = (90.0 color(red)(cancel(color(black)("L"))))/(175.0color(red)(cancel(color(black)("L")))) * "1 atm" = color(darkgreen)(ul(color(black)("0.514 atm")))#

The answer is rounded to three sig figs, the number of sig figs you have for the initial volume of the gas.

As predicted, the volume of the gas increased because the pressure decreased.