Problem 29 - Chemistry Matter and Change

Question

Determine the overall reaction order for a reaction between \(A\) and \(B\) for which the rate law is rate \(=k[A]^{2}[B]^{2}\) .

Step-by-Step Solution

Answer

The overall reaction order is 4.

Step 1: Understand the Rate Law

A rate law expresses the reaction rate in terms of the concentration of the reactants and a rate constant. For the reaction given, the rate law is rate \(= k[A]^{2}[B]^{2}\). Here, \([A]\) and \([B]\) represent the concentrations of reactants \(A\) and \(B\), respectively, and \(k\) is the rate constant. The exponents indicate the order with respect to each reactant.

Step 2: Identify the Order with Respect to Each Reactant

In the rate law rate \(= k[A]^{2}[B]^{2}\), the order with respect to \(A\) is the exponent of \([A]\), which is 2, and the order with respect to \(B\) is the exponent of \([B]\), which is also 2.

Step 3: Calculate the Overall Reaction Order

The overall reaction order is the sum of the orders with respect to each reactant. For this reaction, it is \(2\) from \(A\) plus \(2\) from \(B\), making the overall reaction order \(2 + 2 = 4\).

Key Concepts

Rate Law

The concept of a rate law is fundamental in understanding how the speed of a chemical reaction changes with varying concentrations of reactants. In simple terms, a rate law is a mathematical equation that links the rate of a reaction to the concentrations of the reactants involved and a proportionality constant called the rate constant. Typically, a rate law is expressed as:

• Rate = k imes [Reactant]^n
• Where "k" denotes the rate constant, and "n" is the order of the reaction with respect to that reactant.

The rate law for our particular problem is rate \(= k[A]^2[B]^2\), indicating that both reactants, \([A]\) and \([B]\), influence the reaction rate. The exponents 2 for both reactants mean the reaction is second-order with respect to each reactant. This gives us vital clues about how reactant concentration impacts the reaction rate.

Reaction Rate

Reaction rate refers to how fast a reaction proceeds, and it can vary depending on several factors, most notably the concentration of reactants. The rate law equation helps in determining this rate simply by plugging in the concentration values into the equation. For instance, using the given rate law:

• Rate = k imes [A]^2 imes [B]^2

In such a scenario, if we were to double the concentration of reactant \([A]\), since the reaction is second order with respect to \([A]\), the rate would increase by a factor of four, assuming \([B]\) remains constant.Therefore, the reaction rate is directly affected by how the concentrations of the reactants change, helping chemists control and manipulate reaction speeds by adjusting conditions accordingly.

Rate Constant

The rate constant, often denoted as \(k\), is a unique number for every chemical reaction at a given temperature and is central to the rate law's utility. It acts as a proportionality factor linking the concentration terms with the reaction rate. The unit for the rate constant depends on the overall reaction order and facilitates the proper balance in the rate equation.Understanding that the rate constant is constant under a specific condition is essential. It does not change with concentration changes but is instead influenced by aspects like temperature and the presence of a catalyst. By determining \(k\), one can predict how the reaction rate will react to changes in reactants' concentrations, making it a crucial factor in experimental and industrial chemistry.

Concentration of Reactants

The concentration of reactants is one of the primary variables influencing the rate of a chemical reaction. In our example, the concentrations of substances \(A\) and \(B\) are both present in the rate law:

• Rate = k imes [A]^2 imes [B]^2

This means that both reactants play an active role in determining the overall reaction rate, with the squared terms suggesting higher sensitivity to concentration changes.If you increase the concentration of a reactant, it generally results in an increased reaction rate, more so when the exponent is higher, as seen in our reaction law. This concept allows chemists to adjust the speed of a reaction by carefully controlling the amounts of reactants present. Ensuring appropriate concentrations is vital for both experimental accuracy and practical applications, like in the synthesis of substances on an industrial scale.