Question

Write the reaction rate expressions for these reactions in terms of the disappearance of the reactants and the appearance of products: (a) \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \longrightarrow 2 \mathrm{HI}(g)\) (b) \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)\) (c) \(5 \mathrm{Br}^{-}(a q)+\mathrm{BrO}_{3}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow\) $$ 3 \mathrm{Br}_{2}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) $$

Short answer

The rate of reaction expressions for the given reactions are: \n(a) -d[H2]/dt = -d[I2]/dt = 1/2 * d[HI]/dt \n(b) -1/2 * d[H2]/dt = -d[O2]/dt = 1/2 * d[H2O]/dt \n(c) -1/5 * d[Br-]/dt = -d[BrO3-]/dt = -1/6 * d[H+]/dt = 1/3 * d[Br2]/dt = 1/3 * d[H2O]/dt

Step-by-step solution

Write the rate of reaction for H2 + I2 -> 2HI

The rate of reaction for the reaction process is given as -1/a * d[A]/dt = -1/b * d[B]/dt = 1/c * d[C]/dt for the generic reaction aA + bB -> cC where A and B are reactants and C is the product. For the first process \(H_{2}(g) + I_{2}(g) \rightarrow 2HI(g)\), the rate of reaction would be -1/1 * d[H2]/dt = -1/1 * d[I2]/dt = 1/2 * d[HI]/dt

Write the rate of reaction for 2H2 + O2 -> 2H2O

Similar to the first step, the rate of reaction for the process \(2H_{2}(g) + O_{2}(g) \rightarrow 2H_{2}O(g)\), would be -1/2 * d[H2]/dt = -1/1 * d[O2]/dt = 1/2 * d[H2O]/dt

Write the rate of reaction for 5Br- + BrO3- + 6H+ -> 3Br2 + 3H2O

For the process \(5Br^{-}(a q) + BrO_{3}^{-}(a q) + 6H^{+}(a q) \rightarrow 3Br_{2}(a q) + 3H_{2}O(l)\), the rate of reaction expression would be -1/5 * d[Br-]/dt = -1/1 * d[BrO3-]/dt = -1/6 * d[H+]/dt = 1/3 * d[Br2]/dt = 1/3 * d[H2O]/dt

Key concepts

Chemical Kinetics

Chemical kinetics is the study of the rates of chemical processes. It is a branch of physical chemistry that deals with understanding the speed or rate at which reactants are converted into products in a chemical reaction. This field of study is crucial because it allows scientists to understand how different conditions, such as temperature, pressure, and concentration of reactants, can affect the speed of chemical reactions.

The rate of a reaction is typically expressed in terms of the change in concentration of either reactants or products over time. It's important for students to understand that chemical kinetics doesn't just measure the rate of a reaction but also provides insights into the reaction mechanism—the detailed steps through which reactants actually become products.

Reactants and Products

In a chemical equation, substances that undergo the chemical change are called reactants, and the substances formed as a result of the chemical change are called products. The rate of reaction is determined by observing the rate of disappearance of the reactants or the rate of appearance of the products over time. For example, in the reaction of hydrogen and iodine forming hydrogen iodide \(\mathrm{H}_2(g) + \mathrm{I}_2(g) \longrightarrow 2 \mathrm{HI}(g)\), \(\mathrm{H}_2\) and \(\mathrm{I}_2\) are the reactants, and HI is the product.

It is essential to remember that the relationship between the disappearance of reactants and the appearance of products is determined by the stoichiometry of the reaction. This stoichiometric relationship is used to write balanced rate expressions for the reaction under study.

Differential Rate Expressions

Differential rate expressions describe the rate of reaction in terms of the rate of change in concentration of reactants and products. The general form of the rate expression for a chemical reaction \(aA + bB \longrightarrow cC\) is given by \-1/a * d[A]/dt = -1/b * d[B]/dt = 1/c * d[C]/dt\. This form is called the differential rate law, and it shows how the rate of the reaction is proportional to the changes in concentrations of reactants and products with respect to time.

For instance, in the reaction \(2H_{2}(g) + O_{2}(g) \longrightarrow 2H_{2}O(g)\), the differential rate law can be written as \-1/2 * d[H2]/dt = -1/1 * d[O2]/dt = 1/2 * d[H2O]/dt\. This indicates that the disappearance of \(H_2\) and \(O_2\) and the formation of \(H_2O\) are all related and can determine the rate at which the reaction occurs. Such insights are fundamental to understanding and predicting how chemical reactions will behave under different conditions.