Temperature dependence of reaction rate

Effect of temperature on kinetics

The temperature factor is one of the most significant parameters in kinetics. There is a fundamental general pattern: as the temperature increases, the rate of practically all chemical processes increases sharply. This feature is of immense practical importance in daily life, medicine, and laboratory practice.

Cooling is used to slow down undesirable processes. A classic example is the use of household or industrial refrigerators. Lowering the temperature effectively inhibits decomposition reactions and prevents the rapid spoilage of food products.

Conversely, heating is used to accelerate chemical processes. This is a standard procedure both in cooking and in laboratory practice, where solutions in test tubes and flasks are intentionally heated to accelerate reactant interaction.

A special case is the occurrence of reactions in aqueous solutions. Under normal conditions (at atmospheric pressure), maximum heating is limited by the boiling point of water, i.e., $100^\circ\text{C}$. To bypass this physical limitation, the autoclaving method is used. Increasing the pressure inside the autoclave (operating on the principle of a pressure cooker) makes it possible to heat water significantly above one hundred degrees. This provides additional acceleration of chemical processes and is widely used for reliable instrument sterilization.

Activation energy and reaction initiation conditions

For various reactions to start at all, vastly different degrees of heating are required. The range of required temperatures varies from several tens to thousands of degrees Celsius, which is associated with the need to overcome the activation energy.

A revealing example is the reaction between nitrogen and oxygen. Under normal conditions, $N_2$ and $O_2$ molecules present in atmospheric air are completely inert toward each other. However, at extremely high temperatures reaching about $2000^\circ\text{C}$, interaction begins with the formation of nitric oxide($II$):

$$N_2 + O_2 = 2NO$$

Another classic laboratory experiment is the interaction of metallic magnesium with water. If magnesium shavings ($Mg$) are placed in cold water, the chemical process does not proceed at all; its rate is zero. But as soon as the medium is heated, the picture changes: active gas evolution starts, and the reaction rate increases to very high values. As a result, a magnesium hydroxide precipitate forms and hydrogen gas is released:

$$Mg + 2H_2O = Mg(OH)_2\downarrow + H_2\uparrow$$

van 't Hoff rule and mathematical framework

The nature of the dependence of reaction rate on the degree of heating is determined by the van 't Hoff rule. It states that for every 10 °C increase in temperature, the rate of most chemical reactions increases by a factor of 2–4.

A key value in these calculations is the temperature coefficient of reaction rate (denoted as $\gamma$). It represents the ratio of the rates of a specific reaction at two temperatures that differ by exactly 10 °C (other things being equal). Mathematically, this is expressed by the basic formula:

$$ \gamma = \frac{v_{T+10}}{v_T} $$

If the system temperature changes by an arbitrary value, a more general relation is used to calculate the new rate:

$$ v_2 \approx v_1 \cdot \gamma^{\frac{T_2 - T_1}{10}} $$

Where:

• $v_1$ is the rate at the initial temperature $T_1$
• $v_2$ is the rate at the final temperature $T_2$
• $\gamma$ is the temperature coefficient

Analyzing this general formula, one can draw the main conclusion: the dependence of rate on temperature has a pronounced exponential character. Since the temperature variable ($T$) is in the exponent, the reaction rate increases very rapidly. Even if the value of the temperature coefficient $\gamma$ is small and close to the lower limit, the final increase in rate upon heating will be very significant.

At the same time, one must always remember the limitations. The van 't Hoff rule is approximate. In practice, with a sharp temperature drop (with a significant difference between $T_1$ and $T_2$), the non-constancy of the coefficient $\gamma$ manifests itself, and calculations using the formula become less accurate.

Briefly: answers to topical questions

Class and exam questions

What else to study on this topic

• Calculation of activation energy using the Arrhenius equation
• Thermodynamic causes of the exponential growth of reaction rate
• Features of reaction kinetics under autoclaving conditions
• Causes of deviation of real processes from the van 't Hoff rule at high temperatures

Other topics in "Chapter 6. Patterns of Chemical Reactions"

Prepared by WhiteCoat Pro faculty in accordance with the medical school curriculum. For educational purposes only.