What is the rule of thumb for how reaction rate changes as the temperature changes?

Reaction rates are influenced by several factors, such as concentration of reactants, temperature, presence of a catalyst, and surface area of reactants. In this exercise, we will focus on how temperature affects the reaction rate.

The Arrhenius equation is a mathematical equation that illustrates the dependency of reaction rate (`k`) on temperature (`T`). The equation is given by: \( k = A e^{-\frac{E_a}{RT}} \) Where: - \(k\) is the reaction rate constant, - \(A\) is the pre-exponential factor (also called frequency factor), which represents the frequency of collisions between reactants, - \(e\) is the base of the natural logarithm (~2.718), - \(E_a\) is the activation energy of the reaction (in J/mol), - \(R\) is the gas constant (8.314 J/(mol K)), - \(T\) is the temperature in Kelvin (K).

According to the Arrhenius equation, an increase in temperature leads to an increase in the reaction rate constant (`k`). A higher temperature means that the reactants have more kinetic energy, which increases the likelihood of successful collisions and the rate of the reaction. The rule of thumb for the effect of temperature on reaction rate is that the rate approximately doubles for every 10°C increase in temperature. It's important to note that this rule is a generalization and can vary for different reactions.

Suppose the reaction rate is `k1` at temperature `T1` and `k2` at temperature `T2`. If the temperature rises by 10°C, we can apply the rule of thumb to estimate how the reaction rate will change: 1. Convert the 10°C temperature increase to Kelvin: \( \Delta T = 10 °C * \frac{1 K}{1 °C} = 10 K \) 2. Calculate the new temperature: \( T2 = T1 + \Delta T \) 3. Estimate the new reaction rate: \( k2 ≈ 2 * k1 \) Keep in mind that this rule of thumb is an approximation and the actual change in reaction rate may differ. In summary, the rule of thumb for how reaction rate changes as the temperature changes is that the reaction rate approximately doubles for every 10°C increase in temperature. This can be explained using the Arrhenius equation, which shows the dependency of the reaction rate on temperature.