The main component of natural gas used for home heating and cooking is methane, CH4. Calculate the volume that 2.00 kg of methane gas will occupy...

This problem can be solved using the ideal gas law, PV=nRT. STP is standard temperature and pressure.  The information you are given is:

P = standard pressure = 1.00 atm

T = standard temperature = 273 K

mass of methane = 2.00 kg = 2000 g

The number of moles, n, can be calculated from the mass. The molar mass of CH4 is 16.0 grams/mole.

moles CH4 = (2000)*(1 mol/16.0 g) = 125 moles

R is the ideal gas constant, 0.0821 L-atm/mol-K

Rearrange PV=nRT to solve for volume:

V = nRT/P

V = (125 mol)(0.0821 L-atm/mol-K)(273 K)/1.00 atm = 2800 L

Another way to solve this problem, since the conditions are STP, is to use the molar volume. The volume of one mole of any gas at STP is 22.4 liters. Knowing this, you can multiply the number of moles by the molar volume:

(125 mol)(22.4 L/1. mole) = 2800 L