Please help me with this Chemistry question

Question

A deep underground cavern contains 3.05 x 10⁶ L of methane gas (CH₄) at a pressure of 1.6 x 10³ kPa, and a temperature of 312 K. How many kilograms of methane does the cavern contain? Please show your work so I will understand better.

Answer 1

Use the Ideal Gas Law: PV = nRT and solve for n (moles), then convert moles to grams and kilograms

P = pressure = 1.6x10³ kPa x 1 atm /101.325 kPa = 15.79 atm

V = volume in liters = 3.05x10⁶ L

n = moles = ?

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 312K

Solving for n..

n = PV/RT = (15.79)(3.05x10⁶) / (0.0821)(312)

n = 1.88x10⁶ moles CH₄

mass in kg = 1.88x10⁶ moles x 16 g/mol x 1 kg/1x10³ g = 3.0x10⁴ kg CH₄ (2 sig.figs.)