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$\ce{CH2CH2(g) + H2(g) -> CH3CH3(g)}$

Using this table, source: http://www.kentchemistry.com/images/links/Kinetics/TB08_003.GIF http://www.kentchemistry.com/images/links/Kinetics/TB08_003.GIF

C-C enthalpy = 348 kJ/mol
C-H enthalpy = 413 kJ/mol
H-H enthalpy = 436 kJ/mol

The way I see it, H-H has to break, C-C has to break, and then two C-H bonds have to form.

(Units omitted) Therefore, should the answer be: $413 \cdot 2 - 348 - 436 = 42 \, \text{kJ/mol}$

So then it has to be an endothermic reaction. Is this correct, or am I wrong?

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Your reasoning is correct, but your numbers are wrong.

You are not breaking a C-C bond, but changing a C=C bond to C-C. So you will also need the energy for C=C which is 614 kJ/mol.

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