Question

How much oxygen, both the moles and grams, is needed to burn all 5000 moles of methane

Answer 1

CH4+2 O2->CO2+2 H2O
If you need to burn 1mole of CH4 you need 2 moles of O2 so for 5000moles we need 10000moles=320000g=320 kg.

Answer 2

CH4 + 2O2-----------------> CO2 +2H2O
mole ratio CH4: O2 = 1: 2
moles of O2 required to burn 5000moles of CH4 = 5000*2 =10000moles
mass = moles * Rmm
= 10000 * 32
= 320000g