2C8H18(ℓ) + 17O2(g) ⇌ 16CO(g) + 18H2O(ℓ) ΔH < 0
What is the activation energy for the forward
reaction?(4)
Read about the Arrhenius equation and the data required to determine Ea.
To determine the activation energy for the forward reaction, we need to calculate the difference between the enthalpy of the products and the enthalpy of the reactants, which is represented by the symbol ΔH.
In the given reaction:
2C8H18(ℓ) + 17O2(g) ⇌ 16CO(g) + 18H2O(ℓ)
The stoichiometric coefficients give us the ratio of moles between the reactants and products. From the equation, we can see that for every 2 moles of C8H18, 16 moles of CO are formed.
Let's denote ΔH_f as the enthalpy of formation:
ΔH_f[CO] = ΔH_f[H2O] = 0 kJ/mol, since these substances are the most stable forms of carbon monoxide and water.
To calculate the enthalpy change for the reaction (ΔH), we need to consider the enthalpy of formation of each reactant and product.
Reactants:
ΔH_f[C8H18] = -250 kJ/mol (given information)
ΔH_f[O2] = 0 kJ/mol, as it is the most stable form of oxygen.
Products:
ΔH_f[CO] = 0 kJ/mol
ΔH_f[H2O] = 0 kJ/mol
Using Hess's law, we can sum up the enthalpies of formation for the reactants and subtract the sum of the enthalpies of formation for the products to find the overall enthalpy change (ΔH) for the reaction.
ΔH = 2 * ΔH_f[C8H18] + 17 * ΔH_f[O2] - 16 * ΔH_f[CO] - 18 * ΔH_f[H2O]
ΔH = 2 * (-250 kJ/mol) + 17 * 0 kJ/mol - 16 * 0 kJ/mol - 18 * 0 kJ/mol
ΔH = -500 kJ/mol
Since ΔH is negative, it indicates that the reaction is exothermic, meaning that it releases heat.
However, the activation energy (Ea) is not determined by the equation or given values. It is a separate quantity that represents the energy barrier that reactant molecules must overcome to form the products. The activation energy cannot be determined directly from the given information.
To determine the activation energy for the forward reaction, we need information about the activation energy. The reaction you provided is a combustion reaction between octane (C8H18) and oxygen (O2) to produce carbon monoxide (CO) and water (H2O).
To find the activation energy, we need the Arrhenius equation:
k = A * e^(-Ea/RT)
Where:
k = rate constant
A = pre-exponential factor
Ea = activation energy
R = gas constant (8.314 J/mol·K)
T = temperature in Kelvin
However, we don't have the rate constant (k) or the pre-exponential factor (A). Without these values, we cannot directly calculate the activation energy.
The activation energy can be experimentally determined by measuring the rate of the forward reaction at different temperatures and using the Arrhenius equation. The rate of the reaction can be determined by monitoring the concentration of products or reactants over time and fitting the data to a rate equation.
Once the rate constants at different temperatures are known, the activation energy can be calculated by plotting ln(k) against 1/T and determining the slope of the resulting line. The activation energy can be obtained from the slope using the equation:
Ea = -R * slope
Therefore, to find the activation energy for the forward reaction, you would need experimental data, such as rate constants at different temperatures, or additional information about the rate equation or Arrhenius parameters (A and k).