Reaction Rate in Biochemistry: Concepts and Calculations

Reaction Rate and Its Calculation

Definition of Reaction Rate

The reaction rate (or velocity, v) is the speed at which a given reaction proceeds from reactants to products. It is typically expressed as the change in product concentration over a time interval.

• Reaction velocity (v): Expressed in units of M/sec (molarity per second).

• Graphical interpretation: In a plot of concentration vs. time, the reaction rate is the slope of the line tangent to any point.

• Mathematical expression: For a linear plot, the rate is calculated as the change in concentration divided by the change in time.

Equation:

$\text{Reaction\ Rate} = v = \frac{\Delta [\text{Product}]}{\Delta t}$

or for reactant disappearance:

$\text{Reaction\ Rate} = v = -\frac{\Delta [\text{Reactant}]}{\Delta t}$

Enzyme-Catalyzed Reactions

For enzyme-catalyzed reactions, the reaction rate typically decreases over time as substrate is consumed.

Example Calculation

Example: Calculate the reaction rate for A → B, given that [A]0 = 1.0 M, [B]0 = 0.0 M after 2 seconds: [A] = 0.42 M, [B] = 0.58 M.

• Solution: The change in [B] is 0.58 M over 2 seconds.

• Reaction rate: $v = \frac{0.58\ \text{M}}{2\ \text{s}} = 0.29\ \text{M/s}$

Practice Problem

Practice: Calculate the reaction rate for A → B, given that [A]0 = 2.0 M, [B]0 = 0.0 M after 4.4 seconds: [A] = 1.14 M, [B] = 0.86 M.

• Solution: The change in [B] is 0.86 M over 4.4 seconds.

• Reaction rate: $v = \frac{0.86\ \text{M}}{4.4\ \text{s}} = 0.20\ \text{M/s}$

Key Points

• Reaction rate is a fundamental concept in biochemistry, especially in enzyme kinetics.

• It is important to use the correct sign: positive for product formation, negative for reactant consumption.

• Units are typically M/s (moles per liter per second).