CUET UG Chemistry Booster Test – 3 Rate of Reaction

Chemical kinetics is the branch of chemistry that studies the speed or rate of chemical reactions. It focuses on how quickly reactants are converted into products and investigates the factors affecting reaction rates. Reaction rates are generally measured through changes in concentration of reactants or products with time. Questions such as how rapidly food spoils, how quickly medicines act, or how fast fuel burns in an engine are answered using principles of chemical kinetics. This branch also helps chemists understand reaction mechanisms and the influence of temperature, catalysts, and concentration on reaction speed. Therefore, chemical kinetics is the correct branch for studying reaction rates.

Thermodynamic calculations indicate that graphite is more stable than diamond under ordinary conditions. Therefore, the conversion of diamond into graphite is thermodynamically feasible. However, feasibility alone does not determine the speed of a reaction. The conversion has an extremely high activation energy barrier and proceeds at an imperceptibly slow rate. As a result, diamonds remain unchanged for practical time scales, leading to the common belief that "diamond is forever." This example highlights the difference between thermodynamics and kinetics. Thermodynamics predicts whether a reaction can occur, while kinetics determines how fast it occurs.

Chemical reactions occur at different rates depending on the nature of reactants and reaction conditions. Rusting of iron is a very slow process that may take days, weeks, or months to become noticeable. Therefore, it is classified as a very slow reaction. Precipitation of silver chloride occurs immediately when solutions containing Ag⁺ and Cl⁻ ions are mixed. Hence, it is considered an instantaneously fast reaction. Hydrolysis of starch takes place at a moderate speed and requires measurable time for completion. Inversion of cane sugar is slower than precipitation reactions but faster than rusting and is therefore classified as a slow to moderate reaction. Thus, the correct matching is: 1 → b 2 → c 3 → a 4 → d Hence, Option B is correct.

The instantaneous rate of formation of a product is represented by the derivative of concentration with respect to time: Since product concentration increases during the reaction, the expression is positive. The derivative indicates that the rate is measured at a specific instant rather than over a finite time interval. Therefore, represents the instantaneous rate of appearance of the product.

For reactants: Since reactant concentration decreases with time, Δ[R] is negative. Therefore, Statement 1 is correct. Reaction rates are conventionally expressed as positive quantities. Hence, a negative sign is introduced in the rate expression for reactants: Thus, Statement 2 is correct. Statement 3 is incorrect because product concentration increases and Δ[P] is already positive. Statement 4 is incorrect because square brackets denote molar concentration, not molality.

The average rate of a reaction is calculated over a finite time interval: However, to determine the exact rate at a particular instant, the time interval must become infinitesimally small. Mathematically: This process converts the finite difference expression into a differential expression: This transformation is achieved through differentiation, which is a fundamental concept of calculus. The derivative represents the slope of the concentration–time curve at a particular point and gives the instantaneous rate of reaction.

The average rate is calculated using concentration changes over a finite time interval. The calculated value represents the overall behavior of the reaction during that interval and is treated as constant throughout the interval. However, reaction rates generally change continuously with time because reactant concentrations decrease as the reaction proceeds. Therefore, the average rate cannot provide the exact speed of the reaction at a specific instant. To determine the exact rate at a particular moment, the concept of instantaneous rate is used.

The question compares different time intervals commonly used in chemical kinetics. The total reaction lifetime represents the complete duration of the reaction and is therefore the largest time interval. Among the finite intervals: The symbol dt represents an infinitesimally small interval used in differential calculus for defining instantaneous rate. Since dt approaches zero, it is smaller than any measurable finite time interval. Thus, the decreasing order is: Using the shuffled numbering: 3 > 4 > 1 > 2 Hence, Option A is correct.

The given rate unit is: The term represents molar concentration, while indicates that the change is measured per second. Therefore, the rate was obtained by measuring how the concentration of reactants or products changed with time. This is the standard unit used in chemical kinetics for reactions occurring in solutions.

For gaseous reactions, reaction rates may be expressed as: which means change in pressure per second. If the time unit changes from seconds to minutes, only the denominator changes: The pressure unit remains atm because the quantity being measured is still pressure. Thus, the new unit becomes:

The hydrolysis of butyl chloride demonstrates a common kinetic trend: reaction rates decrease as the concentration of reactants decreases. Initially, the concentration of C₄H₉Cl is highest, resulting in the largest number of effective molecular collisions and hence the highest reaction rate. As the reaction proceeds, reactant molecules are consumed. Consequently, the frequency of successful collisions decreases, causing the average rate to decline. Experimental data for successive time intervals clearly show that the calculated average rates become progressively smaller with time. This observation forms the basis of many rate laws in chemical kinetics. The dependence of rate on reactant concentration is one of the most important concepts in understanding reaction mechanisms and predicting reaction behavior. Therefore, the correct conclusion is that reaction rates generally decrease as reactant concentrations decrease.

When average rates calculated over equal time intervals continuously decrease, the reaction is said to exhibit decelerating behavior. This occurs because the concentration of reactants decreases as the reaction progresses. Since reaction rate commonly depends on reactant concentration, fewer reactant molecules are available for effective collisions at later stages of the reaction. Consequently, the rate becomes smaller with time. Such behavior is characteristic of concentration-dependent reactions and is observed in many first-order and higher-order reactions. The hydrolysis of butyl chloride provides a classic example where average rates become progressively smaller over identical time intervals. Therefore, the reaction is best described as a concentration-dependent decelerating reaction.

The instantaneous rate represents the exact speed of a reaction at a particular moment. It is obtained mathematically by taking the limit of the average rate as the time interval approaches zero. Thus, Statement 2 is correct. The derivative dc/dt gives the slope of the tangent to the concentration–time curve at a particular instant. Therefore, Statement 3 is correct. Graphically, the instantaneous rate is determined by drawing a tangent to the concentration–time curve and calculating its slope. Hence, Statement 4 is also correct. Statement 1 is incorrect because a secant line represents average rate, not instantaneous rate.

The average rate expression is: When the time interval Δt becomes infinitesimally small, the finite difference transforms into a differential expression: This expression is the first derivative of concentration with respect to time. In calculus, the derivative measures the rate at which one quantity changes relative to another. Chemical kinetics uses this concept to define the instantaneous rate of reaction. The derivative corresponds to the slope of the tangent to the concentration–time graph at a specific instant. Hence, the mathematical principle involved is differentiation, giving the first derivative.

For a reactant concentration–time graph, the slope of the tangent is negative because reactant concentration decreases with time. Given: The instantaneous rate of disappearance of a reactant is defined as: Substituting the slope: Therefore, the instantaneous rate is positive.

In most chemical reactions, products are absent at the beginning of the reaction or are present in negligible amounts. Therefore, the concentration of products generally starts from zero or a very small value. As the reaction proceeds, reactants are converted into products. Consequently, the concentration of products increases with time. When product concentration is plotted against time, the resulting curve rises upward. The slope of this curve at any point represents the instantaneous rate of appearance of the product: Initially, the slope may be large because reactant concentration is high. As the reaction progresses, the slope gradually decreases because the reaction rate usually slows down. Therefore, the graph typically starts near zero and rises upward.

Consider the reaction: According to the balanced equation, two moles of HI are consumed to produce one mole of H₂ and one mole of I₂. Therefore, the disappearance of HI occurs at twice the rate at which either H₂ or I₂ appears. To define a unique rate of reaction independent of the species chosen, the rate of disappearance or appearance is divided by the respective stoichiometric coefficient: This adjustment ensures that all expressions yield the same numerical value for the reaction rate.

For the reaction: The stoichiometric coefficient of I₂ is 1. The general rate expression is: Since the coefficient of I₂ is 1, the multiplier is: Thus, the rate expression for I₂ remains unchanged.

For gases at constant temperature, the ideal gas equation establishes a direct proportionality between concentration and partial pressure. Therefore, a change in concentration corresponds directly to a change in partial pressure. Because of this relationship, reaction rates for gaseous systems can be expressed as: or instead of concentration-based expressions. This principle allows chemists to monitor gaseous reactions experimentally using pressure measurements.

For a gaseous reaction: The rate of disappearance of reactant A is: The rate of appearance of product B is: To obtain a unique overall rate of reaction, each expression must be divided by its stoichiometric coefficient: Therefore: 1 → b 2 → c 3 → d 4 → a Hence, Option A is correct.