CUET UG Chemistry Booster Test – 3 Rate Law and Order

At the macroscopic level, chemists study measurable properties of a chemical reaction such as the amount of reactants consumed, the amount of products formed, and the rates at which these changes occur. These observations can be made without considering individual molecules. Chemical kinetics focuses on how quickly reactants disappear and products form. Therefore, chemists are interested in concentration changes and reaction rates rather than molecular orientation or microscopic collision details. Macroscopic observations provide practical information about how a reaction proceeds and how its speed changes with time.

Chemical reactions may occur over vastly different time scales. Some reactions such as precipitation reactions occur almost instantaneously, whereas reactions like rusting take days or months. The hydrolysis of starch occurs at a moderate rate. It is not completed immediately, but it also does not require extremely long periods of time. Therefore, it is classified as a moderate-speed reaction. NCERT uses such examples to demonstrate that reaction rates vary considerably depending on the nature of the reactants and reaction conditions.

The symbol Δ represents the change in a quantity and is defined as: where: • = initial concentration at time • = final concentration at time For reactants, concentration decreases during the reaction. Therefore, is usually negative. This negative value is the reason a minus sign is introduced in the rate expression: to make the reaction rate positive.

The expression: represents the rate of change of product concentration with respect to time. Because the derivative is used, the expression corresponds to an instantaneous rate rather than an average rate. Since product concentration increases during the reaction, the expression is positive and is known as the instantaneous rate of appearance of the product. Thus:

For a reactant: As the reaction proceeds, reactants are consumed. Therefore: Substituting into the expression gives a negative value for Δ[R]. This negative value indicates the disappearance of reactants. To express reaction rate as a positive quantity, the rate expression includes a negative sign: This convention ensures that reaction rates remain positive.

The hydrolysis of butyl chloride follows the general kinetic principle that reaction rate decreases as reactant concentration decreases. At the start of the reaction, the concentration of butyl chloride is maximum, leading to the largest number of effective molecular collisions and hence the highest rate. The given intervals correspond to: • 3 = 0–50 s • 2 = 100–150 s • 1 = 300–400 s • 4 = 700–800 s Since concentration continuously decreases with time: 0–50 s > 100–150 s > 300–400 s > 700–800 s Therefore, the decreasing order of average rates is: 3 > 2 > 1 > 4 Hence, Option A is correct.

The average rate of a reaction is defined as the change in concentration divided by the corresponding time interval. The calculated value represents the average behavior of the reaction during that specific interval and is treated as constant for that interval. However, reaction rates generally change continuously with time. Therefore, average rate cannot accurately describe the exact rate at a particular instant. For that purpose, instantaneous rate is used. Hence, Option D is correct.

For reactants, the average rate is written as: Therefore, Statement 2 is correct because the negative sign makes the rate positive. Statement 4 is also correct because average rates can be calculated over different time intervals to study how the reaction rate changes with time. Statement 1 is incorrect because the complete expression for reactant disappearance includes a negative sign. Statement 3 is incorrect because the hydrolysis of butyl chloride slows down as the reaction proceeds. Hence, Statements 2 and 4 are correct.

Reaction rate is defined as: If concentration is measured in mol L⁻¹ and time is measured in minutes, the unit becomes: Thus, the standard unit of average rate under these conditions is: This unit indicates the change in concentration occurring every minute.

For gaseous reactions, concentration can be expressed in terms of partial pressure because concentration and pressure are directly proportional at constant temperature. Therefore, reaction rates may be expressed as: which means change in pressure per unit time. Since the unit given is: the reacting species are gaseous in nature. Pressure units are not generally used for solids, liquids, or aqueous solutions when expressing reaction rates.

According to NCERT, the hydrolysis of butyl chloride demonstrates how reaction rates decrease as reactants are consumed. During the earliest interval (0–50 s), the reactant concentration is highest and therefore the average rate is maximum. This corresponds to 1.90 × 10⁻⁴ mol L⁻¹ s⁻¹. As the reaction progresses, the concentration of butyl chloride decreases and the rate falls. During 100–150 s, the average rate becomes 1.58 × 10⁻⁴ mol L⁻¹ s⁻¹. Between 300–400 s, the rate decreases further to 1.10 × 10⁻⁴ mol L⁻¹ s⁻¹. At the later stage of the reaction, between 700–800 s, only a small concentration of reactant remains. Consequently, the average rate becomes 0.4 × 10⁻⁴ mol L⁻¹ s⁻¹. Therefore, the correct matching is: 1-c, 2-d, 3-b, 4-a

A concentration-time plot is a graph showing how the concentration of reactants or products changes with time. According to NCERT, such plots are fundamental tools in chemical kinetics because they allow chemists to determine average and instantaneous rates of reaction. For the hydrolysis of butyl chloride, the concentration of reactant decreases continuously with time. Consequently, the reaction rate also decreases. By plotting concentration against time, the changing behavior of the reaction becomes visually apparent. The slope of the concentration-time curve at any point provides information about reaction rate. Average rates are obtained from secants connecting two points, while instantaneous rates are determined using tangents. Therefore, the graph demonstrating the decrease in average rate over time is called a concentration-time plot.

In a concentration-time graph for a reactant, the concentration continuously decreases as the reaction proceeds. Since the curve slopes downward from left to right, any tangent drawn to the curve also possesses a negative slope. According to NCERT, the instantaneous rate of disappearance of a reactant is obtained from the slope of the tangent drawn at a specific point on the concentration-time curve. Because reactant concentration decreases with time, Δ[R]/Δt is negative. To ensure that reaction rates are expressed as positive quantities, the negative sign is introduced into the rate expression: Rate = -d[R]/dt The negative slope therefore reflects the consumption of reactant during the reaction. Thus, the slope of the tangent on the reactant concentration curve is inherently negative.

According to NCERT, the instantaneous rate of disappearance of a reactant is defined as: Rate = -d[R]/dt The slope of the reactant concentration-time curve is negative because reactant concentration decreases with time. If the slope itself were used directly, the reaction rate would be negative. Since reaction rates are conventionally expressed as positive quantities, a negative sign is included in the rate expression. This converts the negative slope into a positive rate value. For example, if the slope at a particular instant is -2 × 10⁻⁴ mol L⁻¹ s⁻¹, the instantaneous rate becomes +2 × 10⁻⁴ mol L⁻¹ s⁻¹. Therefore, the instantaneous rate is equal to the negative of the slope.

The average rate of reaction is calculated over a finite time interval Δt. However, the instantaneous rate describes the reaction rate at a specific moment. To obtain this value, the time interval must become extremely small. Mathematically, the instantaneous rate is obtained by taking the limit: Rate = lim (Δt→0) (-Δ[R]/Δt) This limiting process converts the average rate expression into a differential expression: Rate = -d[R]/dt According to NCERT, this derivative represents the slope of the tangent drawn at the chosen point on the concentration-time curve. Since the tangent touches the curve at only one point, the interval considered is infinitesimally small. Therefore, Δt effectively becomes dt, an infinitesimally small time interval.

In chemical kinetics, the average rate of reaction is expressed as: where Δ[R] represents the change in concentration during a finite time interval Δt. However, chemists are often interested in the rate at a particular instant rather than over a time interval. According to NCERT, the instantaneous rate is obtained by making the time interval smaller and smaller until it approaches zero. Mathematically, this process is represented by taking the limit as Δt approaches zero: This derivative gives the slope of the tangent drawn to the concentration-time curve at a specific point. It represents the exact rate at that instant. Therefore, the transformation from -Δ[R]/Δt to -d[R]/dt is achieved by applying the limit as Δt approaches zero.

According to NCERT, the rate of reaction is expressed in terms of changes in concentration divided by time. When the stoichiometric coefficients of reactants and products are equal, the numerical rate of disappearance of reactants becomes equal to the numerical rate of appearance of products. For example: The rate expression becomes: Since both coefficients are equal to one, no additional stoichiometric factor is needed. This means that the decrease in reactant concentration per unit time is exactly equal to the increase in product concentration per unit time. Therefore, the rate of disappearance of reactants equals the rate of appearance of products. Hence, Option D is correct.

For a general reaction: NCERT defines the rate of reaction as: This ensures that the reaction rate has the same value regardless of which reactant or product is chosen. For the given reaction: the stoichiometric coefficient of Br⁻ is 5. Therefore, The negative sign indicates disappearance of reactant concentration with time. Division by 5 accounts for the stoichiometric requirement that five bromide ions are consumed for every reaction event. Hence, the correct rate expression is:

For gaseous reactions at constant temperature, NCERT states that concentration is directly proportional to partial pressure through the ideal gas equation. Thus: • Concentration of species corresponds to partial pressure of species. • Rate of reaction corresponds to the rate of change of partial pressure. • Rate of decrease of a reactant corresponds to the rate of decrease in partial pressure. • Rate of increase of a product corresponds to the rate of increase in partial pressure. Therefore, the correct matching becomes: 1-b, 2-c, 3-d, 4-a This relationship is useful because pressure measurements are often easier to perform experimentally than concentration measurements in gas-phase systems.

For gaseous reactions, partial pressure can be used in place of concentration because pressure is directly proportional to concentration at constant temperature. If the partial pressure of reactant A decreases by x atm during time t, then: The rate of disappearance of reactant is defined as: Substituting the value: Thus, the average rate of disappearance is a positive quantity equal to x/t. The positive sign is used because reaction rates are conventionally reported as positive values even though reactant concentration or pressure decreases with time.