# Can the summation of activation energy and reactant's initial internal energy change with temperature?

Look at the graph. The orange arrow represents the summation of activation energy and reactant's initial internal energy. Can it change with temperature? Is there any specific name for this summation?

• There's certainly a name, it's the energy of the transition state. – orthocresol Jul 7 '17 at 19:00
• Is it fixed for a specific reaction irrespective of temperature? @orthocresol – Hisab Jul 7 '17 at 19:12
• The average internal energy increases with temperature as more reactant rotational and vibrational energy levels become populated as described by the Boltzmann distribution. So does the population in the transition state (even though it exists only fleetingly, fs to ps). Thus reactions get faster as the temperature increases because a larger fraction of molecules have enough energy to cross the potential energy barrier assumed constant, independent of temperature as this is determined by electronic configuration of atoms in a molecule. – porphyrin Jul 7 '17 at 21:27
• Activation energy= Energy of transition state - Energy of Reactants. Of which temperature energy of reactants in considered here? – Hisab Jul 7 '17 at 21:42
• The activation energy is determined experimentally and over a small temperature range is often independent of temperature. ($d\ln(k_{obs})/dt = E_a/(RT^2)$) From a stat. mech. approach the activation energy is the difference in zero point energies between reactants and transition state. – porphyrin Jul 8 '17 at 11:24

No. As the label at the y-axis indicates, we are talking about potential energy. Potential energy itself does not mean anything, only energy differences can be meaningfully interpreted. (It is the same with heights, to quantify how tall a mountain is you give its height with respect to the sea level.)

The activation energy is defined as the difference between the transition state's energy and the reactant's initial internal energy, and has therefore a physical meaning. The reactant's initial internal energy itself is just some arbitrary value. Unless you define some reference point, which is not the case in your figure.

Therefore the orange arrow ("the summation of activation energy and reactant's initial internal energy") is conceptually wrong.

Furthermore, a change in temperature does not change your potential curve. This curve is a minimum energy path. It represents the ground state of the system at each point along the reaction coordinate. But when we have a ground state, then there are excited states as well. And thermal energy makes the system partially occupy these states (either statistically in the classical sense or by probability distributions in the quantum mechanical sense). Effectively the reactant will be higher in energy, but potential remains the same! This is actually the way you can reach the transition state.

Think of it like there is a ladder on the floor. The floor will be the ground state, and on the top of the ladder there is the transition state. Now the higher the temperature, the higher you can step on the ladder. With high enough temperature you can reach the transition state and descend on the other side towards the products.

• //With high enough temperature you can reach the transition state// doesn't that mean that this state must have a definite value of potential energy? Maybe I can't measure it, but it does have a definite value, doesn't it? – Hisab Jul 7 '17 at 20:11
• The transition state has a definite value, just in the same sense as the reactants and product have a definite value. You can't measure this value directly since it is an potential. But you can very well measure the activation energy. – Feodoran Jul 7 '17 at 20:16
• If I try to start the reaction at a high temperature, the reactants will already have a high internal energy and they will need less energy to reach the transition state, meaning the activation energy will be less at a higher temperature. But again, I have read that activation energy doesn't change with temperature. So, there's something wrong with my understanding. Please, help me. – Hisab Jul 7 '17 at 20:16
• The activation energy is defined with respect to the reactants ground state at 0K and does not change! With the energy of the reactants we have to be careful. There are two different quantities here (I'm not sure about their correct names): The first one the ground state at 0K and is given by the potential energy curve in your figure. This one is a fixed property of the system and does not change on external conditions. The second one includes the thermal energy of the reactants, therefore it depends on temperature. A reactions is only possible if this energy is above the activation barrier. – Feodoran Jul 7 '17 at 20:25
• //A reactions is only possible if this energy is above the activation barrier.// Which energy needs to be above the activation barrier? The potential energy of the reactants or the thermal energy of the reactants or the summation of both of them? – Hisab Jul 7 '17 at 20:40