# Question a9717

Jun 5, 2017

$1.29 \times {10}^{7}$ $\text{L}$

#### Explanation:

Any time you're given three of the four primary characteristics of gases (pressure, volume, quantity, and temperature), you'll be using the ideal-gas equation to find the fourth quantity:

$P V = n R T$

When using the ideal-gas equation,

• the pressure $P$ must be in atmospheres ($\text{atm}$)

• the volume $L$ must be in liters ($\text{L}$)

• the quantity $n$ must be in moles ($\text{mol}$)

• the temperature $T$ must be the absolute temperature; i.e. in Kelvin ($\text{K}$)

And $R$ is the universal gas constant, $0.08206 \left(\text{L" · "atm")/("mol" · "K}\right)$.

(I'll assume the given quantity $0.600$ $\text{million}$ is the number of moles. This is equal to $600 , 000$ $\text{mol}$)

We need to calculate the Kelvin temperature, which we can do using the equation

"K" = ""^"o""C" + 273 = 15.0^"o""C" + 273 = color(red)(288 color(red)("K"

Now that we have all our necessary variables, we can plug them in to the ideal-gas equation, and rearrange the equation to solve for the volume, $V$:

V = (nRT)/P = ((600000cancel("mol"))(0.08206("L" · cancel("atm"))/(cancel("mol") · cancel("K")))(288cancel("K")))/(1.10cancel("atm"))

= color(blue)(1.29 xx 10^7 color(blue)("L"#