Example of Interactive Question
Question 1.1
The energy released by the complete combustion of gaseous methane to CO(g) and H2O(g) is 803 kJ.mol-1.
Given that:
- The O-O bond energy is 498 kJ.mol-1
- The C-O bond energy in CO2 is 805 kJ.mol-1
- The O-H bond energy in H2O is 497 kJ.mol-1
Estimate the C-H bond energy in methane.
Hint: Write a balanced chemical equation for the combustion of methane and then think about the number and type of bonds broken or made as the reaction proceed.
Answer
Reveal Step 1
The hint is a good one, because we won't be able to get anywhere without a balanced equation. This is it:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
Reveal Step 2
So, the number of bonds on each side of the equation are:
4 × C-H + 2 × O=O → 2 × C=O + 4 × O-H
Reveal Step 3
Energy cannot be created or destroyed (the first law of thermodynamics) so whatever energy we need to put in to break up all the bonds on the right hand side of this equation, we need to put the same amount of energy in to break up all the bonds on the left hand side of the equation. The 803 kJ.mol-1 released in the reaction is energy coming out, not energy we are putting in, so we have to give it the opposite sign in our equation to balance the energies.
4 × EC-H + 2 × 498 kJ.mol-1 = 2 × 805 kJ.mol-1 + 4 × 497 kJ.mol-1 - 803 kJ.mol-1
Reveal Step 4
Then we do a little algebra.
4 × EC-H = 1610 kJ.mol-1 + 1988 kJ.mol-1 - 803 kJ.mol-1 - 996 kJ.mol-1
4 × EC-H = 1799 kJ.mol-1
EC-H = 450 kJ.mol-1
Reveal Step 5
This is close to the bond enthalpy one can look up for a C-H bond, 421 kJ.mol-1, but not exactly the same - since the general C-H value is an average for a great number of different carbon compounds, and experimentally the strength of C-H bonds is greater the more hydrogens are attached to the carbon. (CH4 > CH3 > CH2 > CH)
