Reaction coordinate theory is a way to calculate the rate of a chemical reaction based on the movements of particles during the reaction. The theory uses parameters like diffusion, velocity, and acceleration to calculate these rates.
Reaction coordinate theory was developed in part by Dr. Jan Kasprzak at The Chemical Institute of Canada. He has done extensive research on how to apply reaction coordinate theory in practical settings, and his website contains many resources for how to do so.
Calculating the rate of a chemical reaction via Reaction Coordinate Theory is a three-step process. The first step is calculating the No¨rsted-Poisson Diagram (NPD) for the reaction. The second step is calculating Δs∘rxn, or the difference in spatial variables between the reactants and the products. The third step is calculating ∆t∘rxn, or the difference in time between reactants and products. These two steps are then used in solving for ∆t∘rxn via Nernst Equation (NE).
Calculate the standard enthalpy of reaction
The final step in determining the overall reaction energy change is to calculate the standard enthalpy of reaction. The standard enthalpy of reaction is the sum of the standard enthalpies of formation of the products minus the sum of the standard enthalpies of formation of the reactants.
The calculation for the standard enthalpy of reaction is:
\[\Delta H^{\circ}_{reaction} = \Delta H^{\circ}_{products} + \Delta H^{\circ}_{reactants}\]
In this case, you would calculate: ΔHrxn = ΔHproducts + ΔHreactants. Then, you would calculate each term for each species. Once you have all your numbers, you can add them up to get your total ΔHrxn.
Calculate the standard entropy of reaction
When calculating the standard entropy of reaction, you must first calculate the enthalpy of reaction. The enthalpy of reaction is the total amount of energy lost or gained in a chemical reaction.
Calculating the enthalpy of reaction requires measuring the masses of each substance before and after the reaction, and calculating the temperature change for each substance. These measurements are used to find the heat transferred during the reaction via mathematics.
The difference in mass before and after the reaction, multiplied by the average molecular weight of each substance, is then divided by the temperature change to get joules. This value is then multiplied by a constant (usually 1 kilogram per joule) to get kilojoules per kilogram-kelvin.
The standard entropy of a chemical compound is measured in joules per kelvin per mole. Once you have calculated the standard enthalpy of reaction, you can calculate its entropy.
Calculate ΔHr and ΔSr
Once you have calculated ΔGs, you can calculate the enthalpy and entropy changes for the reaction. These are called residual properties, as they are left over after calculating the overall Gibbs free energy change.
Enthalpy (H) is a measure of the heat absorbed or released during a reaction. When a reaction produces products that are more highly concentrated in energy, then more enthalpy is absorbed.
Entropy (S) is a measure of disorder within a system. When a reaction produces products that are more disordered, then more entropy is produced.
Residual properties can be difficult to calculate due to having to account for all possible phases of the reactants and products. Most software uses default values for these quantities to account for this difficulty.
Use the following equations to calculate Δs∘rxn
In order to calculate Δs∘rxn, you need to know the standard enthalpy of reaction (ΔH), the temperature (T) of the reaction, and the species present in the reaction. You can find all of these values in the literature or online!
The equation to use is: Δs∘rxn=ΔH−Ts∘rxn, where Ts∘rxn stands for total species concentration.
This is a very useful equation, as it allows you to calculate Δs∘rxn if you know the other variables. You can also calculate Ts∘rxn if you know ΔH and the other species present in the reaction.
This article has explained how to use this equation to calculate Δs∘rxn for several reactions.
Check your calculations against a table of values for ΔH∘rxn(kJ/mol) and ΔS∘rxn(J/mol K)
7) Practice problems
8) Review questions
1) Calculate the temperature of the reaction
The temperature is given as 298 K. 2) Calculate the standard enthalpy of reaction
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Calculate Δs∘rxn for the Reaction 2no(g)+o2(g)→2no2(g)
The final reaction we will look at is the reaction between nitrogen and oxygen gases to form nitrous oxide. This reaction is an intermediate step in the process of denitrification, which reduces nitrate in soil to nitrogen gas.
To find the standard enthalpy change of this reaction, we will first need to determine its equilibrium constant and then calculate its ΔH∘rxn using that constant and the corresponding pressures of each gas.
The equilibrium constant, keq, for this reaction is given by the following expression:
\begin{equation} k_{\mathrm{eq}}=\frac{[N_{2}]}{[N_{2}O]}=1.44 \cdot 10^{5}\text{mol/mol} \end{equation}
Once we have determined keq, we can calculate ΔH∘rxn using the following expressions:
1) Calculate ΔS∘rxn for this reaction at 25°C.
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