A tank contains 115 moles of neon gas. It has a pressure of 57 atm at a temperature of 45 C. How do you calculate the volume of the tank?

Question

Caleb Adams · Accepted Answer

The volume of the tank is 53 L.

We can use the Ideal Gas Law to calculate the volume. The Ideal Gas Law is: #color(blue)(bar(ul(|color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "# where We can rearrange the Ideal Gas Law to get #V = (nRT)/P# #n = "115 mol"# #R = "0.082 06 L·atm·K"^"-1""mol"^"-1"# #T = "(45 + 273.15) K" = "318.15 K"# #P = "57 atm"# #V = (nRT)/P = (115 color(red)(cancel(color(black)("mol"))) × "0.082 06 L"· color(red)(cancel(color(black)("atm·K"^"-1""mol"^"-1"))) × 318.15 color(red)(cancel(color(black)("K"))))/(57 color(red)(cancel(color(black)("atm")))) = "53 L"#

Wyatt Adkins · Answer

undefined Using the ideal gas law equation, you can calculate the volume of the tank:

$V = \frac{{nRT}}{{P}}$

Where:
$V$ = Volume of the tank
$n$ = Number of moles of gas (115 moles)
$R$ = Ideal gas constant (0.0821 L.atm/mol.K)
$T$ = Temperature in Kelvin (45°C + 273.15 = 318.15 K)
$P$ = Pressure of the gas (57 atm)

Substituting the values:

$V = \frac{{115 \times 0.0821 \times 318.15}}{{57}}$

$V \approx 515.57 \, \text{liters}$

So, the volume of the tank is approximately 515.57 liters.