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AQA GCSE · Question 08.3 · Energy changes

Figure 9 H H H H C C C H H H H + 5 O O 3 O C O + 4 H O H

Figure 9 shows the displayed formula equation for the reaction between propane and oxygen.
The overall energy change of this exothermic reaction is 2219 kJ/mol.
Table 4 shows the bond energies of the bonds in the reaction.
Calculate the bond energy of the C-H bond (X).

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<table border="1" cellpadding="10" cellspacing="0" style="border-collapse: collapse; font-family: Arial, sans-serif; font-size: 14px; border: 2px solid black;"> <caption style="font-weight: bold; font-size: 16px; margin-bottom: 10px;">Table 4</caption> <tr> <th style="border: 1px solid black; padding: 10px;"></th> <th style="border: 1px solid black; padding: 10px; text-align: center;">C — C</th> <th style="border: 1px solid black; padding: 10px; text-align: center;">C — H</th> <th style="border: 1px solid black; padding: 10px; text-align: center;">O = O</th> <th style="border: 1px solid black; padding: 10px; text-align: center;">C = O</th> <th style="border: 1px solid black; padding: 10px; text-align: center;">O — H</th> </tr> <tr> <td style="border: 1px solid black; padding: 10px; font-weight: bold;">Energy in kJ/mol</td> <td style="border: 1px solid black; padding: 10px; text-align: center;">347</td> <td style="border: 1px solid black; padding: 10px; text-align: center; font-weight: bold;">X</td> <td style="border: 1px solid black; padding: 10px; text-align: center;">498</td> <td style="border: 1px solid black; padding: 10px; text-align: center;">805</td> <td style="border: 1px solid black; padding: 10px; text-align: center;">464</td> </tr> </table> <br/><br/>

How to approach this question

1. **Set up the equation:** Overall Energy Change (ΔH) = Energy absorbed to break bonds - Energy released forming bonds. 2. **Calculate energy to break bonds (reactants):** - Carefully count the number of each type of bond in the reactants (1 molecule of C₃H₈ and 5 molecules of O₂). - C₃H₈ has two C-C bonds and eight C-H bonds. - 5O₂ has five O=O bonds. - Write an expression for the total energy absorbed, using 'X' for the C-H bond energy. 3. **Calculate energy released forming bonds (products):** - Count the bonds in the products (3 molecules of CO₂ and 4 molecules of H₂O). - 3CO₂ has 3 × 2 = six C=O bonds. - 4H₂O has 4 × 2 = eight O-H bonds. - Calculate the total energy released using the values from the table. 4. **Solve for X:** - Substitute the known values into the main equation. Remember that for an exothermic reaction, the overall energy change is negative (-2219 kJ/mol). - Rearrange the equation to solve for X.

Full Answer

**1. Energy absorbed to break bonds (reactants):** Propane (C₃H₈) has 2 C-C bonds and 8 C-H bonds. Oxygen (O₂) has 1 O=O bond. There are 5 O₂ molecules. Energy in = [ (2 × C-C) + (8 × C-H) ] + [ 5 × (O=O) ] Energy in = [ (2 × 347) + (8 × X) ] + [ 5 × 498 ] Energy in = [ 694 + 8X ] + [ 2490 ] Energy in = 3184 + 8X **2. Energy released forming bonds (products):** Carbon dioxide (CO₂) has 2 C=O bonds. There are 3 CO₂ molecules. Water (H₂O) has 2 O-H bonds. There are 4 H₂O molecules. Energy out = [ 3 × (2 × C=O) ] + [ 4 × (2 × O-H) ] Energy out = [ 6 × C=O ] + [ 8 × O-H ] Energy out = [ 6 × 805 ] + [ 8 × 464 ] Energy out = 4830 + 3712 = 8542 kJ **3. Overall energy change:** ΔH = Energy in - Energy out -2219 = (3184 + 8X) - 8542 -2219 = 8X - 5358 8X = 5358 - 2219 8X = 3139 X = 3139 / 8 X = 392.375 kJ/mol **X ≈ 392 kJ/mol**
The overall energy change (ΔH) is the difference between the energy required to break the bonds in the reactants and the energy released when forming the bonds in the products. ΔH = Σ(bonds broken) - Σ(bonds made) **Step 1: Calculate the energy of bonds broken (reactants)** Reactants are 1 × C₃H₈ and 5 × O₂. From the displayed formula for propane (C₃H₈), we count: - 2 × C-C bonds - 8 × C-H bonds From 5 × O₂, we have: - 5 × O=O bonds Energy IN = (2 × E(C-C)) + (8 × E(C-H)) + (5 × E(O=O)) Energy IN = (2 × 347) + (8 × X) + (5 × 498) Energy IN = 694 + 8X + 2490 Energy IN = 3184 + 8X **Step 2: Calculate the energy of bonds made (products)** Products are 3 × CO₂ and 4 × H₂O. In one CO₂ molecule (O=C=O), there are 2 × C=O bonds. So in 3 molecules, there are 3 × 2 = 6 C=O bonds. In one H₂O molecule (H-O-H), there are 2 × O-H bonds. So in 4 molecules, there are 4 × 2 = 8 O-H bonds. Energy OUT = (6 × E(C=O)) + (8 × E(O-H)) Energy OUT = (6 × 805) + (8 × 464) Energy OUT = 4830 + 3712 = 8542 kJ **Step 3: Use the overall energy change to find X** The reaction is exothermic, so ΔH = -2219 kJ/mol. ΔH = Energy IN - Energy OUT -2219 = (3184 + 8X) - 8542 -2219 = 8X - 5358 Now, rearrange to solve for 8X: 8X = 5358 - 2219 8X = 3139 Now, solve for X: X = 3139 / 8 X = 392.375 kJ/mol The bond energy of the C-H bond is **392 kJ/mol** (to 3 s.f.).

Common mistakes

✗ Miscounting the number of bonds in the molecules (especially C-H bonds in propane). ✗ Forgetting to multiply the bond energies by the number of molecules (e.g., 5 for O₂, 3 for CO₂, 4 for H₂O). ✗ Forgetting to use a negative sign for the overall energy change of an exothermic reaction. ✗ Errors in rearranging the final equation.
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