B Calculate The Rate Constant at 537.0 C

Introduction

The rate constant of a chemical reaction is a fundamental parameter that describes how quickly the reaction proceeds. Temperature plays a significant role in determining this constant. The Arrhenius equation provides a mathematical relationship between the rate constant and temperature.

At higher temperatures, molecules have more kinetic energy, leading to more frequent and energetic collisions between reactants. This generally results in a higher rate constant. However, the relationship is not linear and follows an exponential pattern.

Arrhenius Equation

The equation shows that the rate constant increases exponentially with temperature. The activation energy (E_a) represents the minimum energy required for the reaction to occur.

Worked Example

Let's calculate the rate constant at 537.0°C (810.15 K) using the following values:

• Pre-exponential factor (A): 1.2 × 10¹² s⁻¹
• Activation energy (E_a): 80,000 J/mol

Using the Arrhenius equation:

k(810.15) = 1.2 × 10¹² × e^{−80,000/(8.314 × 810.15)}

First, calculate the exponent:

−80,000/(8.314 × 810.15) ≈ −1.166

Then, calculate e^−1.166 ≈ 0.311

Finally, multiply by the pre-exponential factor:

k(810.15) ≈ 1.2 × 10¹² × 0.311 ≈ 3.732 × 10¹¹ s⁻¹

So, the rate constant at 537.0°C is approximately 3.732 × 10¹¹ s⁻¹.

Interpreting Results

The calculated rate constant provides insight into the reaction's speed at the given temperature. A higher rate constant indicates a faster reaction. However, it's important to consider other factors that may affect the actual reaction rate, such as concentration and catalyst presence.

Temperature has a significant impact on reaction rates. The Arrhenius equation shows that even small temperature increases can lead to substantial increases in the rate constant, following an exponential pattern.