Calculate the value of ΔHo for the reaction

2 CH4 (g) -> C2H6 (g) + H2 (g)
given the following thermochemical equations:

C2H2 (g) + H2 (g) -> C2H4 (g) ΔHo = – 175.1 kJ

C2H6 (g) -> C2H4 (g) + H2 (g) ΔHo = + 136.4 kJ

C2H2 (g) + 3 H2 (g) -> 2 CH4 (g) ΔHo = – 376.8 kJ

a) + 65.3 kJ
b) + 338.1 kJ
c) – 415.5 kJ
d) + 688.3 kJ

Reverse equation 2 and equation 3 and add them to equation 1. See if that isn't the equation you want. When you reverse an equation you change the sign for delta H for that reaction. Then add all of the DH values.

To calculate the value of ΔHo for the given reaction, we need to use a combination of the given thermochemical equations.

First, we can see that the reactions involving C2H6 (g) and C2H4 (g) have ΔHo values given in the problem. Let's rearrange the second equation to match the desired reaction:

C2H6 (g) - C2H4 (g) - H2 (g) ΔHo = +136.4 kJ

Next, we can see that the reaction involving C2H4 (g) and H2 (g) is the reverse of the first equation given in the problem. Therefore, we need to reverse its sign to match the desired reaction:

C2H2 (g) + H2 (g) - C2H4 (g) ΔHo = +175.1 kJ

Finally, we can see that the reaction involving 2 CH4 (g) is the reverse of the third equation given in the problem. Therefore, we need to reverse its sign to match the desired reaction:

2 CH4 (g) - C2H2 (g) - 3 H2 (g) ΔHo = +376.8 kJ

Now, we can add up these three equations to obtain the desired reaction:

2 CH4 (g) - C2H6 (g) - H2 (g) ΔHo = +136.4 kJ + 175.1 kJ - 376.8 kJ

ΔHo = -65.3 kJ

Therefore, the value of ΔHo for the given reaction is -65.3 kJ.

Option a) +65.3 kJ