# 7.3 Effect of Temperature on the Rate of Reactions The rate of a chemical reaction is highly dependent on temperature. Generally, an increase in temperature leads to an increase in the reaction rate. ## Collision Theory and Temperature According to **collision theory**, a reaction occurs when reactant molecules collide with sufficient energy and in the correct orientation. The effect of temperature can be explained by this theory: - **Increased Kinetic Energy**: An increase in temperature raises the average kinetic energy of the molecules. - **Increased Molecular Speed**: As molecules gain kinetic energy, their average speed increases. - **Increased Collision Frequency**: Faster-moving molecules collide more frequently. However, not all collisions result in a reaction. For a collision to be *effective*, two conditions must be met: 1. The colliding molecules must possess a minimum amount of energy, known as the **activation energy ($E_a$)**. 2. The molecules must be in the **correct spatial orientation** at the moment of impact. ## The Maxwell-Boltzmann Distribution At any given temperature, the reactant molecules do not all have the same kinetic energy. The **Maxwell-Boltzmann distribution curve** illustrates how kinetic energy is distributed among a population of molecules at a constant temperature. - The peak of the curve represents the most probable kinetic energy. - The **activation energy ($E_a$)** is a threshold on this curve. Only molecules with kinetic energy equal to or greater than $E_a$ can react upon collision. - The shaded area under the curve to the right of $E_a$ represents the fraction of molecules with sufficient energy to react. ### Effect of Increasing Temperature When the temperature is increased (e.g., from $T_1$ to $T_2$, where $T_2 > T_1$): - The distribution curve flattens and shifts to the right. - The fraction of molecules possessing the required activation energy ($E_a$) increases significantly. - This leads to a higher number of effective collisions per unit time, thereby increasing the reaction rate. A general rule of thumb is that for many reactions, the rate **doubles or triples for every 10 K (or 10°C) increase in temperature**. This is often referred to as the **Temperature Coefficient ($Q_{10}$)**. ## The Arrhenius Equation In 1889, Svante Arrhenius quantitatively described the relationship between temperature, activation energy, and the rate constant ($k$) with the **Arrhenius equation**. $$k = A e^{-E_a / RT}$$ Where: - $k$ is the **rate constant**. - $A$ is the **Arrhenius constant** or **pre-exponential factor**. It is related to the frequency of collisions and the probability of correct orientation. - $E_a$ is the **activation energy** (in J/mol). - $R$ is the **universal gas constant** ($8.314 \, J \cdot K^{-1} \cdot mol^{-1}$). - $T$ is the **absolute temperature** (in Kelvin, K). This equation shows that the rate constant $k$ increases exponentially as the temperature $T$ increases. Since the reaction rate is directly proportional to $k$, the rate of reaction also increases with temperature. ## Possible Questions/Answers **Q:** Why does increasing temperature speed up a reaction? **A:** Increasing temperature increases the average kinetic energy of molecules. This results in more frequent collisions and, more importantly, a larger fraction of molecules having energy equal to or greater than the activation energy ($E_a$), leading to more effective collisions. **Q:** What is activation energy ($E_a$)? **A:** It is the minimum amount of energy that reactant molecules must possess for a collision to result in a chemical reaction. **Q:** State the Arrhenius equation and define its terms. **A:** The Arrhenius equation is $k = A e^{-E_a / RT}$. - $k$: rate constant - $A$: pre-exponential factor (related to collision frequency and orientation) - $E_a$: activation energy - $R$: universal gas constant - $T$: absolute temperature in Kelvin