How Temperature Affects Reaction Rate Arrhenius Equation Activation Energy and Examples
Till now we know that temperature influences the rate of a reaction. If the temperature increases the rate of reaction increases and if the temperature decreases the rate of reaction decreases. If we took an example that the time taken to melt a metal will be much higher at a lower temperature but it will decrease if we increase the temperature. Reaction kinetics is one of the most advanced studies in the field of physical chemistry, and it deals with the study of chemical reactions or processes. The engineers and scientists get help from the information about these factors affecting the rate of a chemical reaction to economically scale up the reactions to industrial scale in various industries. Therefore it is very important for us to know how the rate of a chemical reaction gets affected.
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Effect of Temperature
The rate of a chemical reaction can be affected by one of the parameters that is temperature. We have seen milk boiling on a gas stove. On the flame of the stove, the rate of a specific quantity of milk boils depends. The milk boils in less time if the flame height is maximum, and the milk takes more time to boil if the flame height is minimum. Here the flame height resembles the temperature.
Temperature dependence of the rate constant:
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The equation is,
K = Aexp(-Ea /RT)
K = The rate constant of the reaction
A = The Arrhenius Constant
Ea = Activation Energy for the reaction (in Joules mol−1)
R = Universal Gas Constant
T = Temperature in absolute scale (in kelvins)
lnk = -(Ea/R)(1/T) + lnA
The milk attains its boiling point in less time, if the temperature is high, and the milk takes more time to attain its boiling point, if the temperature is low. That is not the only reaction that gets affected by temperature. Most of the chemical reactions in their reaction rate show a change with the varying in temperature. for every 10oC rise in temperature, The rate constant for a chemical reaction gets doubled.
If we see the other effect of temperature, when we cook, if we keep the gas at a low temperature, the food cooks slowly. But if we increase the temperature, to its maximum, the food cooks quickly. Therefore the rate of reaction got increased by the temperature. By the Arrhenius equation, this dependence of rate on temperature can be explained. Let’s learn about and deduce this equation.
Arrhenius Equation
Svante Arrhenius extended the work of J.H Van’t Hoff in 1889 and proposed an equation that relates temperature and the rate constant for a reaction quantitatively. The proposed equation is known as the Arrhenius Equation.
Here is the equation on the temperature dependence of the rate of a chemical reaction which is known as the Arrhenius Equation.
K = Aexp(-Ea /RT)
Where,
K = The rate constant of the reaction
A = The Arrhenius Constant
Ea = Activation Energy for the reaction (in Joules mol-1)
R = Universal Gas Constant
T = Temperature in absolute scale (in kelvins)
We knew that the rates of reaction increase with an increase in temperature but it was not known on how to predict the relation between temperature and reaction rates quantitatively. Arrhenius Equation has enabled us to overcome this problem. It is an empirical relation that is used to model the variation of the rate constant with the temperature, which in turn gives information about the rates of chemical reactions at different temperatures.
Fun Facts
If the temperature increases the rate of reaction increases and if the temperature decreases the rate of reaction decreases.
If we took an example that the time taken to melt a metal will be much higher at a lower temperature but it will decrease if we increase the temperature.
Going back to the rate law equation, it follows that a higher rate of constant results in a higher reaction rate. This makes sense because as temperature increases, molecules move faster and collide more frequently, resulting in an increased fraction of molecules with higher energy than the activation energy.
Due to chemical bonds having been broken and made, they also usually give out or take in energy such as heat or light because. It reacts with oxygen in water or in the air to create a new compound called iron oxide (rust), when iron rusts. No mass is lost or gained in every chemical reaction due to change in temperature.
FAQs on Temperature Dependence on Rate of Reactions in Chemical Kinetics
1. What is the effect of temperature on the rate of a chemical reaction?
An increase in temperature increases the rate of a chemical reaction because more particles have sufficient energy to react. When temperature rises:
- The kinetic energy of reactant molecules increases.
- Particles collide more frequently.
- A larger fraction of molecules have energy ≥ activation energy (Ea).
2. Why does increasing temperature increase reaction rate?
Increasing temperature increases reaction rate because a greater fraction of molecules exceed the activation energy (Ea). According to the Maxwell–Boltzmann distribution:
- Higher temperature shifts the distribution to higher energies.
- More molecules have enough energy to overcome the energy barrier.
- The number of successful collisions increases.
3. What is the Arrhenius equation for temperature dependence of reaction rate?
The Arrhenius equation is k = A e-Ea/(RT), which relates rate constant to temperature. In this equation:
- k = rate constant
- A = frequency factor
- Ea = activation energy (J mol-1)
- R = gas constant (8.314 J mol-1 K-1)
- T = temperature (K)
4. How does temperature affect the rate constant k?
Temperature increases the rate constant (k) exponentially according to the Arrhenius equation. Because k = A e-Ea/(RT):
- Higher T makes the exponent less negative.
- The value of e-Ea/(RT) increases.
- The reaction proceeds faster.
5. What is activation energy in temperature-dependent reactions?
Activation energy is the minimum energy required for reactant molecules to form products. It represents the energy barrier that must be overcome for a reaction to occur.
- Symbol: Ea
- Unit: J mol-1 or kJ mol-1
- Higher Ea means stronger temperature dependence.
6. How do you calculate activation energy using temperature and rate constants?
Activation energy can be calculated using the two-temperature Arrhenius form: ln(k2/k1) = Ea/R (1/T1 − 1/T2). Steps:
- Convert temperatures to Kelvin.
- Substitute k1, k2, T1, T2.
- Use R = 8.314 J mol-1 K-1.
- Solve for Ea.
7. What happens to reaction rate when temperature is increased by 10°C?
For many reactions, the rate approximately doubles when temperature increases by 10°C. This empirical observation is known as the temperature coefficient rule.
- Valid for many reactions near room temperature.
- Exact increase depends on activation energy.
- Not a strict law but a useful approximation.
8. How does temperature affect endothermic and exothermic reaction rates?
Temperature increases the rate of both endothermic and exothermic reactions because it raises molecular kinetic energy. The effect depends on activation energy, not on whether the reaction is endothermic or exothermic.
- Higher T increases effective collisions.
- Both types react faster at higher temperatures.
- Thermodynamics (ΔH) and kinetics (rate) are different concepts.
9. How is the Arrhenius equation represented graphically?
The Arrhenius equation is represented by plotting ln k vs 1/T, giving a straight line. From the linear form:
- ln k = ln A − Ea/(RT)
- Slope = −Ea/R
- Intercept = ln A
10. Can you give an example of temperature dependence in a chemical reaction?
An example of temperature dependence is the decomposition of hydrogen peroxide: 2H2O2(aq) → 2H2O(l) + O2(g). At higher temperatures:
- The rate constant increases.
- Oxygen gas is produced faster.
- The reaction proceeds more rapidly.
