Question

Write the general equation for the rate law, and label the various factors.

Short answer

\[ \text{Rate} = k [A]^m [B]^n \] where k is the rate constant, [A] and [B] are the concentrations, and m and n are the reaction orders.

Step-by-step solution

Understand the Rate Law

The rate law of a reaction expresses how the rate depends on the concentration of the reactants. The general form of the rate law for a reaction involving reactants A and B can be written as: \[ \text{Rate} = k [A]^m [B]^n \] Here, k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B, respectively.

Identify the Rate Constant (k)

The rate constant (k) is a proportionality constant that links the rate of the reaction with the concentrations of the reactants. It is specific to a particular reaction at a given temperature.

Label the Concentrations of Reactants

In the rate law equation, [A] represents the concentration of reactant A, and [B] represents the concentration of reactant B. These are typically given in moles per liter (M).

Define the Reaction Orders (m and n)

The exponents m and n in the rate law equation are known as the reaction orders with respect to reactants A and B, respectively. These exponents indicate the power to which the concentration of each reactant is raised. They are usually determined experimentally.

Key concepts

Reaction Rate

The reaction rate measures how fast a reaction occurs. It tells us how quickly the reactants are transformed into products. In simple terms, it describes the speed at which the concentration of a reactant decreases or the concentration of a product increases with time. Factors that can affect the reaction rate include temperature, pressure, and the presence of a catalyst. For example, increasing the temperature generally makes molecules move faster, leading to more frequent and more energetic collisions between them, thus speeding up the reaction rate.

Rate Constant

The rate constant, denoted as k in the rate law equation, is a numerical value that represents the relationship between the reaction rate and the concentrations of the reactants. The rate constant is specific to each reaction and is influenced by factors like temperature and the presence of a catalyst. It's important to note that the rate constant does not change with the concentration of reactants; rather, it is a fixed value at a given temperature. The units of the rate constant can vary depending on the overall order of the reaction, which we'll discuss next. Generally, the units of k adjust to ensure that the rate law equation balances and the rate has the correct units of concentration per time (usually M/s).

Reaction Order

The reaction order tells us how the rate is affected by the concentration of each reactant. It is represented by the exponents m and n in the rate law equation: Rate = k [A]^m [B]^n Each exponent indicates the power to which the concentration of the reactant is raised. If m is 1, the reaction is first order with respect to A, meaning the rate doubles when [A] doubles. If n is 2, the reaction is second-order with respect to B, meaning the rate quadruples when [B] doubles. The overall reaction order is the sum of the individual orders (m + n). These values are usually determined through experiments and can provide crucial insights into the reaction mechanism.

Concentration of Reactants

The concentration of reactants is how much of each reactant is present in the reaction mixture, and it is typically measured in moles per liter (M). In the rate law Rate = k [A]^m [B]^n [A] and [B] represent the concentrations of reactants A and B. Changes in these concentrations over time can affect the rate of the reaction. If you increase the concentration of a reactant, there are more particles available to collide and react, which usually leads to an increase in the reaction rate. Monitoring these concentrations can help chemists understand how the reaction proceeds and how to control its rate by adjusting reactant levels. Understanding these principles can be very useful in industrial applications, where optimizing the speed of chemical reactions is often crucial.