To calculate the enthalpy change (ΔH) of the reaction using Hess's Law, we need to manipulate the given equations by multiplying them with appropriate coefficients, if necessary, so that the reactants and products match the desired reaction equation.
Given equations:
1) N2 + O2 → 2NO ΔH = +180 kJ/mol
2) 2NO + O2 → 2NO2 ΔH = -112 kJ/mol
We need to combine these equations to obtain the desired equation:
N2 + 2O2 → 2NO2
Let's manipulate equation 1) by reversing it and multiplying it by 2:
2NO → N2 + 2O2 ΔH = -2 * (+180 kJ/mol) = -360 kJ/mol
Now, equation 2) doesn't have the desired number of NO2 molecules, but notice that the coefficient of NO in equation 2) is half of the desired equation. So, let's multiply equation 2) by 2 to match it with the desired equation:
4NO + 2O2 → 4NO2 ΔH = 2 * (-112 kJ/mol) = -224 kJ/mol
Now, when we sum up the manipulated equations, we obtain the desired equation:
(N2 + 2O2) + (4NO + 2O2) → (2NO2) + (4NO2)
N2 + 6O2 + 4NO → 6NO2
To determine the overall enthalpy change of the reaction, we simply add up the ΔH values of the manipulated equations:
ΔH = (-360 kJ/mol) + (-224 kJ/mol)
ΔH = -584 kJ/mol
Therefore, the enthalpy change (ΔH) of the reaction N2(g) + 2O2(g) → 2NO2(g) using Hess's Law is -584 kJ/mol.