CUET UG Chemistry Booster Test – 3 Rate Law and Order

According to NCERT, the rate law of a reaction cannot generally be predicted from the balanced chemical equation alone. This is because many chemical reactions are complex and proceed through a sequence of elementary steps involving intermediates. The balanced equation only provides information about the overall stoichiometric relationship between reactants and products and does not reveal the actual mechanism. In a multi-step reaction, one elementary step is usually slower than the others. This slowest step is called the rate-determining step. Since the overall rate depends primarily on this step, the rate law is governed by the molecular events occurring in the slow step rather than by the overall stoichiometric equation. Therefore, the exponents in the rate law are not necessarily equal to the stoichiometric coefficients in the balanced equation. For this reason, the true rate law must be determined experimentally.

The given rate law is: Rate = k[CH₃COOC₂H₅]¹[H₂O]⁰ According to NCERT, the exponents in a rate law indicate how the reaction rate depends on reactant concentrations. Since the exponent of water is zero, the concentration term becomes: [H₂O]⁰ = 1 Therefore, the rate law simplifies to: Rate = k[CH₃COOC₂H₅] This means that the rate depends only on the concentration of ethyl acetate and remains unaffected by changes in the concentration of water. Such situations are commonly observed when water is present in very large excess, causing its concentration to remain effectively constant throughout the reaction. Hence, the reaction rate is independent of water concentration, making Option B correct.

According to NCERT, the unit of the rate constant depends on the overall order of reaction. For a second-order reaction: Rate = k[A]² or Rate = k[A][B] The unit of rate is: mol L⁻¹ s⁻¹ Therefore: k = (mol L⁻¹ s⁻¹)/(mol L⁻¹)² = L mol⁻¹ s⁻¹ The given unit matches exactly with the unit of a second-order rate constant. Therefore, the reaction must be second order. A second-order reaction indicates that the rate depends on either the square of one concentration term or the product of two first-power concentration terms. Hence, the correct inference is that the reaction is second order.

For an n-th order reaction: Rate = k[A]ⁿ The unit of rate is: mol L⁻¹ s⁻¹ Therefore: k = Rate/[A]ⁿ Substituting units: k = (mol L⁻¹ s⁻¹)/(mol L⁻¹)ⁿ Simplifying: k = (mol L⁻¹)¹⁻ⁿ s⁻¹ This expression gives the general unit of the rate constant for any n-th order reaction. It shows that the unit of k changes with the order of reaction, which is why determining the unit of k can help identify reaction order experimentally. Thus, the correct answer is: (mol L⁻¹)¹⁻ⁿ s⁻¹

Statement 1 is correct because the average rate represents the rate over a finite time interval and does not accurately describe the rate at a particular instant. Statement 2 is correct because NCERT defines instantaneous rate as the slope of the tangent drawn to the concentration-time curve at a specific time. Statement 3 is correct because reactant concentration decreases during a reaction, making Δ[R] negative. To express the reaction rate as a positive quantity, the rate is written as: Rate = -Δ[R]/Δt Statement 4 is incorrect because instantaneous rate is obtained when Δt approaches zero, not infinity. Therefore, Statements 1, 2 and 3 are correct.

According to NCERT, the concentration dependence of reaction rate is represented by the differential rate equation. The instantaneous rate of a reaction is obtained by determining the slope of the tangent drawn at a particular point on a concentration-time curve. Although this method provides accurate information about the rate at a specific instant, it is not always convenient in practice. Drawing an exact tangent at a chosen point and measuring its slope accurately can be difficult, especially when experimental data contain small errors. Since the determination of reaction order and rate law depends on accurate rate measurements, graphical uncertainties may affect the final results. To overcome these difficulties, NCERT introduces integrated rate equations. These equations relate directly measurable concentrations at different times to the rate constant without requiring repeated tangent measurements. Thus, the inconvenience arises from the practical difficulty of measuring tangent slopes accurately.

NCERT explains that although differential rate equations accurately represent reaction rates, they are not always convenient for experimental analysis. Measuring instantaneous rates repeatedly through tangent slopes can be difficult. To overcome this limitation, the differential rate equation is integrated mathematically. Integration converts the rate equation into an integrated rate equation, which directly relates concentration and time. These quantities can be measured experimentally with greater ease and accuracy. For example, integrated rate equations allow chemists to determine rate constants and reaction orders using concentration measurements at different times. This approach avoids the need to construct tangents and calculate slopes repeatedly. Therefore, the mathematical solution to the graphical difficulty is the integration of the differential rate equation.

For a zero-order reaction, the integrated rate equation is: [R] = [R]₀ − kt This equation is in the form of a straight-line equation: y = c + mx where: y = [R] c = [R]₀ m = −k x = t Therefore, when concentration [R] is plotted against time t, a straight line is obtained. The slope of this line is equal to −k, and the intercept is equal to the initial concentration [R]₀. According to NCERT, this graphical relationship is commonly used to verify zero-order kinetics and determine the value of the rate constant experimentally. Hence, the graph of [R] versus t provides a straight line with slope equal to −k.

For a complex reaction, chemists first propose a plausible reaction mechanism consisting of several elementary steps. This provides a framework for understanding how reactants are converted into products. The next step is identifying the rate-determining step, which is the slowest elementary step. Since the overall reaction rate is governed by this step, the rate law is formulated using the molecular events occurring in it. Once the rate law is obtained, the exponents of concentration terms are examined. The sum of these exponents gives the overall order of the reaction. Therefore, the logical sequence is: 1. Postulate mechanism 2. Identify slow step 3. Formulate rate law 4. Determine order by summing exponents Thus, the correct sequence is 1, 2, 3, 4.

The thermal decomposition of HI on a gold surface at high pressure becomes independent of concentration because the catalyst surface becomes saturated. Therefore, it exhibits zero-order kinetics. For the reaction: Rate = k[H₂O₂][I⁻] the sum of exponents is: 1 + 1 = 2 Hence, it is second order. For acetaldehyde decomposition: Rate = k[CH₃CHO]³ᐟ² the exponent is 3/2, which is fractional. Therefore, it is a fractional-order reaction. A reaction whose rate constant has unit s⁻¹ is first order because first-order rate constants always possess this unit. Thus, the correct matching is: 1-c, 2-d, 3-a, 4-b

According to NCERT, some reactions occurring on solid catalytic surfaces exhibit zero-order kinetics under specific conditions. When the pressure of gaseous reactants becomes very high, the catalyst surface becomes completely covered by reactant molecules. In such a situation, all available active sites are occupied. Since no additional reactant molecules can adsorb on the catalyst surface, increasing the concentration or pressure further does not increase the reaction rate. The rate becomes constant and independent of reactant concentration. The decomposition of ammonia on a hot platinum surface is an example of such behavior. Once surface saturation is achieved, the reaction follows zero-order kinetics because the catalyst surface rather than reactant concentration becomes the limiting factor. Therefore, high pressure causing complete surface saturation results in zero-order behavior.

According to NCERT, elementary reactions occur in a single step, and their reaction order is equal to their molecularity. However, many real reactions proceed through several intermediate steps and are therefore classified as complex reactions. In complex reactions, the experimentally determined rate law often differs from the stoichiometric equation. As a result, reaction orders may become fractional, zero, or values that do not correspond to stoichiometric coefficients. The reaction between chloroform and chlorine is a well-known example of a fractional-order reaction. Such behavior indicates that the reaction proceeds through a complex mechanism involving intermediates and multiple elementary steps. Therefore, whenever reaction exponents differ significantly from stoichiometric coefficients, the reaction is generally classified as a complex reaction.

The method of initial rates is one of the most important experimental techniques used to determine reaction order. In this method, several experiments are performed with different initial concentrations of reactants. The initial rate of reaction is measured immediately after mixing the reactants. By changing the concentration of one reactant while keeping others constant, the effect of concentration on reaction rate can be studied. Statement 1 is correct because the method relies on measuring initial rates at different initial concentrations. Statement 2 is also correct because concentration variation is an essential part of the procedure. Statement 3 is incorrect because the method determines reaction order experimentally and does not directly provide molecularity. Statement 4 is incorrect because the method can be applied to reactions of any order. Therefore, Statements 1 and 2 are correct.

Suppose the rate law is: Rate = k[A]ⁿ When concentration of A is tripled: New Rate = k(3[A])ⁿ = 3ⁿ × Rate According to the question, the rate increases by a factor of 9. Therefore: 3ⁿ = 9 3ⁿ = 3² n = 2 This means the reaction is second order with respect to reactant A. Since changing the concentration of B has no effect on the rate, B must have order zero and therefore does not appear in the rate law. Hence, the rate law becomes: Rate = k[A]²

According to NCERT, an intermediate is a species that is formed during one step of a reaction mechanism and consumed in a subsequent step. Because it is both produced and consumed during the reaction sequence, it does not appear in the overall balanced chemical equation. In the catalytic decomposition of hydrogen peroxide by iodide ions, the species IO⁻ is formed in the first elementary step and consumed in the second elementary step. Therefore, it exists only temporarily during the reaction pathway. This behavior perfectly matches the definition of an intermediate. Intermediates provide important evidence regarding reaction mechanisms and help explain how reactants are transformed into products through multiple elementary steps. Hence, IO⁻ is classified as an intermediate.

According to NCERT, molecularity refers to the number of reacting species participating in an elementary reaction. While unimolecular and bimolecular elementary reactions are common, termolecular reactions are extremely rare. For a termolecular reaction to occur, three reactant molecules must collide simultaneously at exactly the same instant. In addition, all three molecules must possess sufficient kinetic energy and proper orientation for bond breaking and bond formation. The probability of satisfying all these requirements simultaneously is extremely small. Therefore, reactions that appear to involve three molecules usually proceed through a sequence of bimolecular elementary steps rather than a single termolecular collision. This is why termolecular mechanisms are statistically improbable and rarely observed experimentally.

An elementary reaction is a reaction that occurs in a single kinetic step. Therefore, Statement 1 is correct. For elementary reactions, the rate law can be directly written from the molecular event occurring in that step. Consequently, the reaction order becomes equal to the molecularity. Hence, Statement 2 is correct. Molecularity is defined as the number of reacting species involved in an elementary step. Since it represents an actual count of molecules, it can never be fractional or zero. Therefore, Statement 4 is correct. Statement 3 is incorrect because molecularities of four or five are extremely rare due to the very low probability of simultaneous collisions involving so many particles. Thus, Statements 1, 2 and 4 are correct.

If the reaction occurred as a single elementary step, its molecularity would be equal to the total number of reacting species, which is ten. Such a process would correspond to a tenth-order reaction. However, NCERT explains that experimentally observed reaction orders often differ from stoichiometric coefficients because most reactions proceed through complex mechanisms involving several elementary steps. Since the experimentally determined order is only two, the reaction cannot occur through a single ten-molecule collision. Instead, it must proceed through a sequence of elementary steps. One of these steps acts as the rate-determining step and is likely bimolecular in nature. Therefore, the experimentally observed second-order behavior provides evidence that the reaction follows a complex multi-step mechanism rather than a single elementary process.

According to NCERT, when a reaction occurs through multiple elementary steps, the overall reaction rate is controlled by the slowest step, known as the rate-determining step. In the alkaline decomposition of hydrogen peroxide catalysed by iodide ions, the first step produces the intermediate IO⁻ and proceeds slowly. The second step consumes IO⁻ rapidly to form oxygen and regenerate iodide ions. Since the second step is much faster, the overall rate cannot exceed the rate at which the intermediate is supplied by the first step. Therefore, the formation rate of IO⁻ determines the overall rate of oxygen production. This situation is analogous to a bottleneck in a production line where the slowest process controls the overall output. Hence, the overall rate is dictated by the rate of formation of the intermediate IO⁻.

In a multi-step reaction mechanism, each elementary step proceeds at its own rate. According to NCERT, the slowest step controls the overall reaction rate because subsequent steps cannot proceed faster than intermediates are supplied by the slow step. Given: R₁ > R₂ > R₃ This means Step 3 has the smallest rate and is therefore the slowest step in the sequence. Since intermediates generated by earlier steps must pass through Step 3 before products can be formed, the overall reaction rate becomes limited by Step 3. This step functions as the kinetic bottleneck of the entire reaction pathway. Therefore, Step 3 is the rate-determining step and governs the overall speed of the reaction.