CUET UG Chemistry Booster Test – 3 Rate Law and Order

According to NCERT, the rate law expresses the relationship between the rate of a chemical reaction and the concentration of reactants. It is generally represented as: Rate = k[A]ˣ[B]ʸ where x and y are experimentally determined exponents and k is the rate constant. Statement 2 is correct because the rate law generally cannot be predicted from the balanced chemical equation, especially for complex reactions. It must be determined experimentally. Statement 4 is also correct because the rate law directly relates the reaction rate to the molar concentrations of reactants. Statement 1 is incorrect because balanced chemical equations provide stoichiometric information but do not generally reveal the reaction mechanism or rate law. Statement 3 is incorrect because the exponents appearing in the rate law are not necessarily equal to the stoichiometric coefficients of the balanced equation. Such equality occurs only for elementary reactions. Therefore, Statements 2 and 4 are correct.

An elementary reaction occurs in a single molecular step. Since the balanced equation directly represents the actual collision event, the exponents in the rate law are equal to the stoichiometric coefficients of the reactants. For example: A + B → Products Rate = k[A][B] In contrast, complex reactions occur through several elementary steps, and their experimentally determined rate laws may not match the stoichiometric coefficients. Therefore, the reaction described is an elementary reaction.

For a general rate law: Rate = k[A]ˣ[B]ʸ The overall order of the reaction is: n = x + y The value of n is important because the units of the rate constant depend on the order of the reaction. For example: • Zero order → mol L⁻¹ s⁻¹ • First order → s⁻¹ • Second order → L mol⁻¹ s⁻¹ Thus, n represents the overall order of the reaction.

The units of the rate constant vary with reaction order. Common units: • Zero order → mol L⁻¹ s⁻¹ • First order → s⁻¹ • Second order → L mol⁻¹ s⁻¹ Since the given unit is: s⁻¹ the reaction must be first order. Therefore, the reaction is a first-order reaction.

As a reaction proceeds, reactants are consumed and their concentrations decrease. Since reaction rate generally depends on reactant concentration, fewer reactant molecules are available for effective collisions. For hydrolysis of butyl chloride: 1.90 × 10⁻⁴ mol L⁻¹ s⁻¹ → 0.4 × 10⁻⁴ mol L⁻¹ s⁻¹ The gradual decrease in rate indicates that the reaction speed is directly related to the amount of reactant remaining in the system. Therefore, the rate fundamentally depends on reactant concentration.

For the hydrolysis of butyl chloride, the reactant concentration decreases continuously as the reaction proceeds. Since the reaction rate depends on reactant concentration, the instantaneous rate also decreases with time. Given times: 1. 250 s 2. 350 s 3. 450 s 4. 600 s The highest instantaneous rate occurs at 250 s and the lowest at 600 s. Therefore: 250 s > 350 s > 450 s > 600 s Hence the decreasing order is: 2 > 4 > 1 > 3 Thus, Option A is correct.

In chemical kinetics: −d[R]/dt represents the rate of disappearance of reactant R. +d[P]/dt represents the rate of appearance of product P. The expression: k[A]ˣ[B]ʸ represents the general rate law. The equation: d[R]/dt = −k[R] represents the differential rate equation for a first-order reaction. Thus: 1 → d 2 → b 3 → c 4 → a Hence, Option A is correct.

The differential rate equation relates the reaction rate to concentration. However, experimentally we usually measure concentrations at different times. To connect these measurable quantities with the rate constant, the differential rate equation must be integrated. The integrated rate equation provides a direct mathematical relationship between: • Concentration • Time • Rate constant This allows experimental determination of reaction order and rate constants. Therefore, integration is necessary to relate measured concentration-time data to the rate constant.

The order of a reaction is defined as the sum of the powers of concentration terms appearing in the experimentally determined rate law. For example: Rate = k[A]¹/²[B] Order = 1/2 + 1 = 3/2 Thus, order can be: • Zero • Fractional • Integral Therefore: 1. Correct 2. Correct Statement 1 is incorrect because order is not always a whole number. Statement 4 is incorrect because order is determined experimentally, not purely theoretically. Hence, Option A is correct.

The order of a reaction is the sum of the powers of concentration terms appearing in the rate law. Given: Rate = k[A]³⁄²[B]⁻¹ Overall order: = 3/2 + (−1) = 3/2 − 1 = 1/2 Therefore, the reaction is a half-order reaction. Fractional orders are common in experimentally determined rate laws and indicate complex reaction mechanisms. Hence, Option B is correct.

The thermal decomposition of gaseous ammonia on a hot platinum surface at high pressure is a classic example of a zero-order reaction. Under these conditions, the platinum surface becomes completely covered by ammonia molecules. Since all active catalytic sites are occupied, increasing the concentration of ammonia does not increase the reaction rate. The rate therefore becomes independent of reactant concentration. The rate law is: Rate = k which is the characteristic feature of a zero-order reaction. Hence, the decomposition of ammonia on a hot platinum surface follows zero-order kinetics.

The overall order of a reaction is the sum of the exponents of concentration terms in the experimentally determined rate law. Given: Rate = k[CHCl₃]¹[Cl₂]¹ᐟ² Therefore: Order = 1 + 1/2 = 3/2 = 1.5 Since the order is fractional, the reaction is called a fractional-order reaction. Hence, the overall order is 3/2.

The method of initial rates is used to determine the dependence of reaction rate on reactant concentrations. In this method: • Concentration of one reactant is changed. • Concentration of the other reactant is kept constant. • Initial reaction rate is measured. By comparing how the rate changes with concentration, the powers appearing in the rate law can be determined experimentally. Thus, the initial rate of NO₂ formation is measured by varying one reactant concentration while keeping the other constant.

Experimental observations show: • Doubling [NO] increases rate four times. Therefore order with respect to NO is 2. • Doubling [O₂] increases rate two times. Therefore order with respect to O₂ is 1. Hence the rate law becomes: Rate = k[NO]²[O₂] Therefore: 1. Correct 2. Correct 3. Correct Statement 4 is incorrect because the experimentally determined exponents are the same as the stoichiometric coefficients in this particular reaction. Hence, Statements 1, 2 and 3 are correct.

Molecularity is defined as the number of reacting species that collide simultaneously in an elementary reaction. Since a chemical reaction must involve at least one reacting species, molecularity can never be zero. Possible molecularities are: • Unimolecular = 1 • Bimolecular = 2 • Termolecular = 3 Unlike order, molecularity cannot be: • Zero • Fractional • Negative Therefore, molecularity can never be zero.

A bimolecular reaction is an elementary reaction in which two reacting species collide simultaneously to produce products. For the decomposition of hydrogen iodide: 2HI → H₂ + I₂ two HI molecules participate in the elementary collision event. Therefore, the molecularity of the reaction is two. Since molecularity is determined by the number of reacting species involved in an elementary step, the reaction is classified as bimolecular. Thus, the decomposition of hydrogen iodide is a bimolecular reaction.

For an elementary reaction, the balanced chemical equation directly represents the actual molecular event occurring during the reaction. Therefore, the exponents appearing in the rate law are equal to the stoichiometric coefficients of the reactants. Since: Order = Sum of exponents in the rate law and Molecularity = Number of reacting species participating both become numerically equal for elementary reactions. For example: A + B → Products Rate = k[A][B] Order = 2 Molecularity = 2 Hence, order and molecularity are the same for elementary reactions.

For a second-order reaction: Rate = k[A]² or Rate = k[A][B] Rate has units: mol L⁻¹ s⁻¹ Therefore: k = (mol L⁻¹ s⁻¹)/(mol L⁻¹)² = L mol⁻¹ s⁻¹ The unit of the rate constant depends only on the overall order of the reaction. Since the derived order is 2, the unit of k is: L mol⁻¹ s⁻¹ Hence, Option B is correct.

Complex reactions occur through multiple elementary steps. The overall rate of the reaction is governed by the slowest step because subsequent steps cannot proceed faster than this bottleneck step. In the decomposition of hydrogen peroxide catalysed by iodide ion, the first step forms the intermediate IO⁻ and is the slowest step. Since it is the rate-determining step, the overall rate depends on the rate of formation of IO⁻. Therefore, the slow formation of the intermediate dictates the overall reaction rate.

The stoichiometric equation suggests a very high order if one incorrectly assumes all molecules collide simultaneously. Such a collision is practically impossible. In reality, the reaction proceeds through several elementary steps. Among these steps, one is slower than the others and acts as the rate-determining step. The experimentally observed second-order behavior indicates that the slowest elementary step is bimolecular. Therefore, the overall rate is controlled by the slowest bimolecular step rather than by a ten-molecule collision.