Question

Catalyses breaks down hydrogen peroxide about \(10^{7}\) times faster than the uncatalyzed reaction. If the latter required one year, how much time would be needed by the catalase-catalyzed reaction?

Short answer

The catalyzed reaction would take approximately \(3.15\) seconds.

Step-by-step solution

- Understand the Problem

Identify that the catalytic reaction speed is given as \texttimes \(10^{7}\) times faster than the uncatalyzed reaction, which takes one year.

- Recognize the Time Reduction

Know that the catalase-catalyzed reaction should take \texttimes \(10^{7}\) less time than the uncatalyzed reaction.

- Calculate the Catalyzed Time

Divide the uncatalyzed reaction time (1 year) by \(10^{7}\) to get the time needed for the catalyzed reaction: \texttimes \frac{1 \text{ year}}{10^{7}} = 10^{-7} \text{ years}.

- Convert to a Familiar Unit

Convert \(10^{-7}\) years into seconds for a more intuitive understanding. First, convert to days: \texttimes 10^{-7} \text{ years} \times \frac{365 \text{ days}}{1 \text{ year}} = 3.65 \times 10^{-5} \text{ days}. Then, convert to seconds: \texttimes 3.65 \text{ days} \times \frac{24 \text{ hours}}{1 \text{ day}} \times \frac{60 \text{ minutes}}{1 \text{ hour}} \times \frac{60 \text{ seconds}}{1 \text{ minute}} = 3.65 \times 10^{-5} \times 86400 \text{ seconds} = 3.15 \text{ seconds}.

Key concepts

Enzyme Kinetics

Enzyme kinetics is the study of the rates of chemical reactions that are carried out by enzymes. These biological catalysts speed up reactions by lowering the activation energy needed to start the reaction.
In the context of the exercise, catalase is an enzyme that significantly speeds up the breakdown of hydrogen peroxide. The comparison highlights how much faster the catalyzed reaction is compared to the uncatalyzed reaction.
When you study enzyme kinetics, you often come across terms like Vmax (maximum rate of the reaction) and Km (Michaelis constant), which are used to describe the efficiency of an enzyme.

• Vmax: The maximum rate at which the enzyme can catalyze a reaction.
• Km: The substrate concentration at which the reaction rate is half of Vmax.

Understanding these parameters helps you grasp how fast an enzyme can convert its substrate into a product, which is crucial for biological and medical research.

Catalase Function

Catalase is an enzyme that is specifically designed to break down hydrogen peroxide (H2O2) into water (H2O) and oxygen (O2). This reaction is essential for protecting cells from oxidative damage caused by hydrogen peroxide, a byproduct of various metabolic processes.

• Hydrogen peroxide is harmful in high concentrations.
• Catalase ensures that hydrogen peroxide is broken down quickly and efficiently.
• This keeps cells safe from potential oxidative stress.

The exercise demonstrates how incredibly efficient catalase is: it speeds up the breakdown of hydrogen peroxide by a factor of 10 million compared to the uncatalyzed reaction. This efficiency has practical applications in medicine and industry, where controlling the levels of hydrogen peroxide is crucial.

Reaction Rate Enhancement

Reaction rate enhancement refers to the increase in the speed of a chemical reaction due to the presence of a catalyst, like an enzyme. In the exercise, catalase enhances the reaction rate dramatically, making it about 10 million times faster than if it occurred naturally without the enzyme.
This concept can be broken down into simple steps:

• A reaction without a catalyst, like the uncatalyzed breakdown of hydrogen peroxide, takes a long time.
• Introducing a catalyst, such as catalase, drastically reduces the time required.
• In the example, an uncatalyzed reaction taking one year would be completed in just over 3 seconds when catalyzed by catalase.

Mathematically, this is shown by dividing the uncatalyzed reaction time by the factor of the enzyme's catalytic enhancement. The result is a much shorter, more manageable time frame, illustrating the power of biological catalysts in chemical processes.