The following reaction is done at STP:

C (s) + 2H2 (g) = CH4 (g)

If the reaction produces 145 liters of CH4, how many liters of H2 were consumed?

290.0 L.

Explanation:

From the balanced equation: C + 2H₂ → CH₄,

it is clear that 1.0 mole of C reacts with 2.0 moles of H₂ to produce 1.0 mole of CH₄.

We should convert the liters of CH₄ (145.0 L) to moles using the relation:

PV = nRT,

where, P is the pressure of the CH₄ gas produced in atm (P = 1.0 atm at STP).

V is the volume of the CH₄ gas produced in L (V = 145.0 L).

n is the no. of moles of the CH₄ gas produced in mol.

R is the general gas constant (R = 0.082 L. atm/mol. K).

T is the temperature of the CH₄ gas produced in K (T = 273.15 K at STP).

∴ n = PV/RT = (1.0 atm) (145.0 L) / (0.082 L. atm/mol. K) (273.15 K) = 6.47 mol.

Using cross multiplication:

2.0 moles of H₂ produce → 1.0 mole of CH₄, from the stichiometry.

? mole of H₂ produce → 6.47 mole of CH₄.

∴ The no. of moles of H₂ consumed to produce 145.0 L CH₄ = (2.0) (6.47) / (1.0) = 12.94 mol.

Now, we can get the liters of H₂ consumed to produce 145.0 L CH₄:

∴ V = nRT/P = (12.94 mol) (0.082 L. atm/mol. K) (273.15 K) / (1.0 atm) = 290.0 L.