Determine ΔH° for the production of coal gas using Hess’ Law.

Question

Determine ΔH° for the production of coal gas using Hess’ Law. (HINT, the answer is given in the next line and using the next 3 individual questions to get the answer, it’s a puzzle.)

2C (s) + 2H₂O (g) --> CH₄ (g) + CO₂ (g)

Using:

C(s) + H₂O(g) --> CO(g) + H₂(g) ΔH°= 131.3 KJ

CO(g) + H₂O(g) --> CO₂(g) + H_2(g) ΔH°= -41.2 KJ

CH₄(g) + H₂O(g) --> CO(g) + 3H₂(g) ΔH°= 206.1 KJ

Answer 1

Since I'm limiting in characters, may have to answer this using the "comments" section as well.

Target equation:

2C(s) + 2H2O(g) --> CH4(g) + CO2(g)

Eq 1: C(s) + H₂O(g) --> CO(g) + H₂(g) ΔH°= 131.3 KJ

Eq 2: CO(g) + H₂O(g) --> CO₂(g) + H_2(g) ΔH°= -41.2 KJ

Eq 3: CH₄(g) + H₂O(g) --> CO(g) + 3H₂(g) ΔH°= 206.1 KJ

Copy Eq 1 and multiply by 2: 2C(s) + 2H₂O(g) --> 2CO(g) + 2H₂(g) ΔH°= 262.6 KJ

Copy Eq 2 as it is.................. CO(g) + H₂O(g) --> CO₂(g) + H_2(g) ΔH°= -41.2 KJ

Reverse Eq 3 & change sign. CO(g) + 3H₂(g) --> CH₄(g) + H₂O(g) ∆Hº = -206.1 kJ

Next, we will add these up (see comments sections below)