Use bond energies to determine the enthalpy for the following reaction
HCN(g) + H2(g) → CH3NH2(g)
To determine the enthalpy change (∆H) for the given reaction using bond energies, you need to calculate the energy required to break the bonds of the reactants and the energy released when forming the bonds of the products.
First, you need to know the bond energies for the respective bonds involved in the reaction. Using experimental data, the bond energies are as follows:
C-H: 413 kJ/mol
N-H: 391 kJ/mol
C≡N: 891 kJ/mol
H-H: 436 kJ/mol
C-N: 305 kJ/mol
Now, let's calculate the energy required to break all the bonds in the reactants:
For HCN:
- One C-H bond: (1 mol) * (413 kJ/mol) = 413 kJ/mol
- One N≡C bond: (1 mol) * (891 kJ/mol) = 891 kJ/mol
For H2:
- Two H-H bonds: (2 mol) * (436 kJ/mol) = 872 kJ/mol
Now, let's calculate the energy released when forming all the bonds in the products:
For CH3NH2:
- Nine C-H bonds: (9 mol) * (413 kJ/mol) = 3,717 kJ/mol
- One C-N bond: (1 mol) * (305 kJ/mol) = 305 kJ/mol
- Six N-H bonds: (6 mol) * (391 kJ/mol) = 2,346 kJ/mol
Next, calculate the overall energy change:
Energy required to break bonds in reactants: (413 kJ/mol) + (891 kJ/mol) + (872 kJ/mol) = 2,176 kJ/mol
Energy released when forming bonds in products: (3,717 kJ/mol) + (305 kJ/mol) + (2,346 kJ/mol) = 6,368 kJ/mol
Finally, calculate the enthalpy change (∆H) using the equation:
∆H = (energy of bonds broken) - (energy of bonds formed)
∆H = 2,176 kJ/mol - 6,368 kJ/mol = -4,192 kJ/mol
Therefore, the enthalpy change (∆H) for the given reaction is -4,192 kJ/mol.
To determine the enthalpy change for a reaction using bond energies, you need to follow these steps:
Step 1: Understand and write the balanced chemical equation for the reaction.
The given balanced chemical equation is:
HCN(g) + H2(g) → CH3NH2(g)
Step 2: Identify the bonds that are broken and formed in the reaction.
In this reaction, the following bonds are broken:
1. C-H bond in HCN
2. H-H bond in H2
The following bond is formed:
1. C-N bond in CH3NH2
Step 3: Look up the average bond energies for the bonds involved.
The average bond energies (in kilojoules per mole) are as follows:
C-H bond: 413 kJ/mol
H-H bond: 436 kJ/mol
C-N bond: 305 kJ/mol
Step 4: Calculate the total energy required to break the bonds.
To calculate the energy required to break the bonds, multiply the number of moles of each bond by its respective bond energy.
For the C-H bond in HCN:
1 mole of C-H bonds × 413 kJ/mol = 413 kJ/mol
For the H-H bond in H2:
1 mole of H-H bonds × 436 kJ/mol = 436 kJ/mol
Step 5: Calculate the total energy released when new bonds are formed.
To calculate the energy released when new bonds are formed, multiply the number of moles of the newly formed bond by its respective bond energy.
For the C-N bond in CH3NH2:
1 mole of C-N bond × 305 kJ/mol = 305 kJ/mol
Step 6: Calculate the overall energy change.
The overall energy change (ΔH) for the reaction can be calculated by subtracting the energy required to break the bonds from the energy released when new bonds are formed.
ΔH = energy required to break bonds - energy released from forming bonds
ΔH = (413 kJ/mol + 436 kJ/mol) - 305 kJ/mol
ΔH = 849 kJ/mol - 305 kJ/mol
ΔH = 544 kJ/mol
Therefore, the enthalpy change (ΔH) for the reaction is 544 kJ/mol.
dHrxn = (bond energy reactants) - (bond energy products)
Post your work if you get stuck.