To calculate the total energy of the reactants in the reaction \( C_2H_4 + H_2 \rightarrow C_2H_6 \), we need to consider the bond energies of the bonds that are broken in the reactants.
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Identify the bonds in the reactants:
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Ethylene (\( C_2H_4 \)) has:
- 1 double bond between the two carbon atoms (C=C)
- 4 single bonds between carbon and hydrogen atoms (C-H)
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Hydrogen (\( H_2 \)) has:
- 1 single bond between the two hydrogen atoms (H-H)
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Break down the energy values:
- \( C=C \) bond energy is typically around 612 kJ/mol (average).
- Each C-H bond energy is about 413 kJ/mol. There are 4 C-H bonds in ethylene.
- The \( H-H \) bond energy is about 436 kJ/mol.
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Calculate the total energy of the reactants: \[ \text{Total energy for } C_2H_4 = \text{energy of } C=C + 4 \times \text{energy of } C-H \] \[ = 612 \text{ kJ/mol} + 4 \times 413 \text{ kJ/mol} = 612 + 1652 = 2264 \text{ kJ/mol} \] \[ \text{Total energy for } H_2 = \text{energy of } H-H = 436 \text{ kJ/mol} \]
Now, combine the total energy for both reactants: \[ \text{Total energy of reactants} = 2264 \text{ kJ/mol} + 436 \text{ kJ/mol} = 2700 \text{ kJ/mol} \]
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Conclusion: Therefore, the total energy of the reactants \( C_2H_4 + H_2 \) is approximately 2700 kJ/mol using the given bond energies. This value may not match exactly with the provided options, but based on the calculation using standard bond energies, that is the result. If any specific values were provided, they would have been utilized in the calculation.