Question

Estimate the rate of the reaction,$$\mathrm{H}_{2} \mathrm{SeO}_{3}+6 \mathrm{I}^{-}+4 \mathrm{H}^{+} \longrightarrow \mathrm{Se}+2 \mathrm{I}_{3}^{-}+3 \mathrm{H}_{2} \mathrm{O}$$given that the rate law for the reaction at \(0^{\circ} \mathrm{C}\) is$$\text { rate }=\left(5.0 \times 10^{5} \mathrm{~L}^{5} \mathrm{~mol}^{-5} \mathrm{~s}^{-1}\right)\left[\mathrm{H}_{2} \mathrm{SeO}_{3}\right]\left[\mathrm{I}^{-}\right]^{3}\left[\mathrm{H}^{+}\right]^{2}$$. The reactant concentrations are \(\left[\mathrm{H}_{2} \mathrm{SeO}_{3}\right]=2.0 \times 10^{-2} M\), \(\left[\mathrm{I}^{-}\right]=2.0 \times 10^{-3} M,\) and \(\left[\mathrm{H}^{+}\right]=1.0 \times 10^{-3} M\).

Short answer

The rate of the reaction is 8.0 x 10^-11 L mol^-1 s^-1.

Step-by-step solution

Write down the rate law

The rate of the reaction is given by the rate law equation: rate = k[H2SeO3][I-]^3[H+]^2 where k is the rate constant (5.0 x 10^5 L^5 mol^-5 s^-1).

Substituting the concentrations into the rate law

Substitute the given concentrations into the rate law: rate = (5.0 x 10^5 L^5 mol^-5 s^-1)(2.0 x 10^-2 M)(2.0 x 10^-3 M)^3(1.0 x 10^-3 M)^2.

Calculate the rate

Perform the multiplication of the concentrations along with the rate constant: rate = (5.0 x 10^5)(2.0 x 10^-2)(8.0 x 10^-9)(1.0 x 10^-6) = (5.0 x 10^5) x (2.0 x 10^-2) x (8.0 x 10^-9) x (1.0 x 10^-6) L^5 mol^-5 s^-1.

Find the numerical value of the rate

Multiply the values together to find the rate: rate = 5.0 x 10^5 x 2.0 x 10^-2 x 8.0 x 10^-9 x 1.0 x 10^-6 = 8.0 x 10^-11 L mol^-1 s^-1.

Key concepts

Rate Law

Understanding the rate law is fundamental in studying the speed of chemical reactions. It's a mathematical equation that relates the reaction rate with the concentrations of the reactants. The general form of a rate law expresses the reaction rate as a product of the rate constant (\( k \)) and the concentrations of the reactants raised to some powers, typically denoted as exponents. These exponents give us the reaction order with respect to each reactant. For instance, if a rate law is given as \(rate = k[A]^m[B]^n\), then the reaction is mth order with respect to \(A\) and nth order with respect to \(B\).

The power of each concentration value indicates the sensitivity of the rate to changes in that particular reactant's concentration. By knowing the rate law, chemists can make predictions about how fast a reaction will proceed under different conditions and how changes in the concentration of one or more reactants will affect the reaction speed.

Reaction Kinetics

Reaction kinetics delves into the factors that influence the speed of a chemical reaction and how this speed can be modulated. It encompasses the study of reaction rates and mechanisms. The roadmap of a chemical reaction from reactants to products is called the reaction mechanism and involves a series of steps, each with its own characteristic speed. Each of these steps is an elementary reaction that directly affects the overall rate.

Temperature, catalysts, and reactant concentrations significantly influence reaction kinetics. As temperature increases, reaction speed typically increases due to higher collision rates and more energetic particle interaction. Catalysts are substances that enhance the rate by providing alternative reaction pathways with lower activation energy. Understanding kinetics is crucial for controlling processes in industries, such as pharmaceuticals, where reaction time and yield impact productivity and cost.

Concentration Dependence

The concentration dependence in the context of chemical reactions indicates how the rate of reaction is affected by changes in the concentration of the reactants. It is a central concept in reaction kinetics. The rate law provides a precise mathematical representation of this relationship. For typical rate laws of the form \(rate = k[A]^m[B]^n\), the exponents m and n tell us how the rate will change with varying concentrations.

If the exponent is one (\( m = 1 \) or \( n = 1 \) ), the reaction rate is directly proportional to the concentration of that reactant. If greater than one, the reaction rate increases more than proportionally with an increase in the reactant concentration, signifying a greater sensitivity. If the exponent is zero, the reaction rate is independent of that reactant's concentration. The understanding of concentration dependence is crucial for chemists to predict how much reactants are needed and the timing required to achieve a certain level of reaction progress.

Rate Constant

The rate constant, symbolized by \( k \), is the proportionality coefficient in the rate law equation. It is essential for determining the intrinsic reaction rate under specific conditions. The value of the rate constant is unique for every chemical reaction at a given temperature and does not depend on reactant concentrations. However, it is sensitive to changes in temperature and the presence of a catalyst.

The units of the rate constant will vary depending on the overall reaction order, which is the sum of the exponents in the rate law. For example, in a second-order reaction where the sum is two, \( k \) might have units of \( L/(mol\cdot s) \). Notably, the magnitude and units of the rate constant provide insight into the likelihood and time scale of a reaction, helping chemists to control and optimize the process.