The enzyme urease catalyzes the reaction of urea, (NH₂CONH₂), with water to produce carbon dioxide and ammonia. In water, without the enzyme, the reaction proceeds with a first-order rate constant of 4.15 × 10^-5 s^-1 at 100°C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 3.4 × 10⁴ s^-1 at 21°C. (b) If the rate of the catalyzed reaction were the same at 100°C as it is at 21°C, what would be the difference in the activation energy between the catalyzed and uncatalyzed reactions?

Key Concepts

Enzyme Catalysis

Enzymes are biological catalysts that speed up chemical reactions by lowering the activation energy required for the reaction to occur. They achieve this by providing an alternative reaction pathway, which stabilizes the transition state. In the case of urease, it facilitates the breakdown of urea into carbon dioxide and ammonia, significantly increasing the reaction rate compared to the uncatalyzed process.

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products. The presence of a catalyst, such as an enzyme, reduces this energy barrier, allowing reactions to proceed more quickly and at lower temperatures, which is crucial for biological processes.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to the temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation is essential for comparing the effects of temperature and catalysts on reaction rates, allowing for the calculation of differences in activation energy between catalyzed and uncatalyzed reactions.