A deep underground cavern contains 2.24 x 106 L of methane gas at a pressure of 15.0 atm and a temperature of 42ºC. How many grams of methane does the natural gas deposit contain?

Answer 1

Hello, Nila,

I'll assume the volume is 2.24x10⁶ L.

Use the ideal gas law to find moles:

PV = nRT

where (P)ressure and (V)olume are related to moles, n, (T)emperature (in Kelvin), and the gas constant, R.

Convert 42 C to Kelvin by adding 273.15. The units we have are liters, atmospheres, and Kelvin, so I'll pick a gas constant compatible with those units (and save time by avoiding conversions, although any gas constant will work, if you enjoy converting units.).

Enter the data and solve for n, the number of moles. We need that in order to calculate grams. I used R=0.082058 (L*atm)/(K*mole).

That works out to 1299283 moles, or 1.30x10⁶ moles with 3 sig figs.

Multiply that by the molar mass of methane, 16 grams/mole, to arrive at 2.08x10⁷ grams,or 2.08x10⁴ kg.

Bob