CUET UG Chemistry Booster Test – 3 Basics of Chemical Kinetics

Thermodynamic studies indicate that graphite is more stable than diamond under ordinary conditions. Therefore, the conversion of diamond into graphite is thermodynamically feasible. This makes Statement 1 correct. However, the conversion occurs at an extremely slow rate because of a very high activation energy barrier. Consequently, no noticeable change is observed during a human lifetime, making Statement 2 correct. Statement 3 is incorrect because thermodynamic feasibility is determined by thermodynamics, not by kinetics. Chemical kinetics only determines how rapidly the conversion occurs. Statement 4 is correct because the spontaneous tendency of diamond to convert into graphite arises from the greater thermodynamic stability of graphite. Thus, Statements 1, 2 and 4 are correct.

A negative Gibbs energy change indicates that the reaction is thermodynamically feasible. However, thermodynamics provides no information regarding the speed of the reaction. If no observable change occurs over many years despite ΔG being negative, the reaction must be proceeding at an extremely slow rate. This generally occurs when the activation energy barrier is very high. Only a very small fraction of molecules possess sufficient energy to cross this barrier, resulting in a negligible reaction rate. Therefore, the correct interpretation is not that the reaction is impossible, but that the kinetics are extremely unfavorable. This distinction between feasibility and rate is one of the most important concepts in chemical kinetics.

Thermodynamics is concerned with energy changes and spontaneity of reactions. It can predict whether a reaction is feasible under specified conditions by using parameters such as Gibbs energy. However, thermodynamics cannot answer questions regarding how quickly a reaction will occur. A thermodynamically feasible reaction may occur in a fraction of a second or may take millions of years. The study of reaction speed, activation energy and reaction mechanisms belongs to chemical kinetics. Therefore, the principal limitation of thermodynamics is that it provides no information about the time required for a reaction to proceed.

A catalyst provides an alternative reaction pathway having a lower activation energy. As a result, a greater fraction of molecules can undergo successful collisions, increasing the reaction rate. However, a catalyst does not alter the initial and final thermodynamic states of the system. Therefore, Gibbs energy change (ΔG), enthalpy change (ΔH) and equilibrium constant remain unchanged. The catalyst accelerates both forward and backward reactions equally and only affects the speed with which equilibrium is attained. Hence, ΔG remains unchanged while the reaction becomes faster due to a decrease in activation energy.

A catalyst lowers the activation energy for both forward and reverse reactions. Consequently, both reactions proceed more rapidly. Since the catalyst affects both directions equally, the ratio of forward and reverse rate constants remains unchanged. Therefore, the equilibrium constant is unaffected. The catalyst only reduces the time required to attain equilibrium. It does not change the equilibrium composition, equilibrium constant or position of equilibrium. Thus, the equilibrium state remains exactly the same, although it is reached more quickly.

Many chemical reactions do not occur in a single step. Instead, they proceed through a sequence of elementary reactions collectively known as the reaction mechanism. Among these elementary steps, one step is usually slower than all the others. This slowest step acts as a bottleneck and limits the speed of the entire reaction. Therefore, it is called the rate determining step (RDS). No matter how rapidly the other steps occur, the overall reaction cannot proceed faster than the slowest step. Chemical kinetics uses this concept extensively to explain reaction rates and derive rate laws. Thus, for complex reactions, the overall reaction rate is governed primarily by the slowest elementary step rather than the average speed of all steps.

For a first-order reaction: The unit of rate is: and the unit of concentration is: Therefore, Hence, the rate constant of a first-order reaction has units of reciprocal time. This property is unique because the numerical value of the first-order rate constant remains independent of concentration units.

The average rate of a reaction is defined as the change in concentration divided by the time interval during which that change occurs. Since the calculation is performed over a measurable interval of time, it provides only the average behavior during that interval. In reality, reaction rates generally change continuously as concentrations of reactants and products change. Therefore, the true rate at a specific instant is called the instantaneous rate, which is obtained by considering an extremely small time interval approaching zero. Thus, average rate cannot accurately represent the exact reaction rate at a particular instant because it is based on a finite time interval.

The rate law expresses the reaction rate in terms of reactant concentrations. For example: The order of the reaction is defined as: that is, the sum of the powers of concentration terms appearing in the rate law expression. The order of reaction is determined experimentally and need not be related to the stoichiometric coefficients of the balanced equation. It may be zero, fractional, integral or even negative in certain cases. Therefore, the correct definition is the sum of powers of reactant concentrations appearing in the rate law.

The passage states that the representation of reaction rate in terms of the concentrations of reactants is known as the rate law. For a general reaction: the rate law can be written as: This expression relates the reaction rate to reactant concentrations and contains the rate constant k. The rate law is also known as the rate equation or rate expression. It forms the foundation for determining reaction order, predicting reaction behavior and analyzing kinetic data. Hence, the correct term is rate law or rate equation.

The Arrhenius equation, k = Ae^(-Ea/RT) shows the relationship between temperature and the rate constant of a reaction. According to NCERT, the rate constant increases with increasing temperature because a greater fraction of molecules acquires energy equal to or greater than the activation energy (Ea). Conversely, when temperature decreases, the fraction of energetic molecules decreases significantly. Food spoilage occurs through various chemical and biochemical reactions. Refrigeration slows these reactions by reducing the kinetic energy of molecules. As a result, fewer molecules can overcome the activation energy barrier, leading to a decrease in the rate constant. Since reaction rate is directly related to the rate constant, spoilage reactions proceed much more slowly. This principle explains why refrigerated food remains fresh for longer periods. The process does not change molecularity or spontaneity; it simply reduces the number of effective molecular collisions. Therefore, refrigeration works because decreasing temperature causes an exponential decrease in the rate constant.

According to NCERT, the rate law of a reaction generally cannot be predicted from the balanced chemical equation. It must be determined experimentally. Therefore, Rate law prediction matches with "must be determined experimentally." Activation energy is defined as the minimum amount of energy required for reactant molecules to undergo effective collisions and form products. Hence, Activation energy matches with "minimum energy required for an effective collision." Molecularity refers to the number of reacting species participating in an elementary reaction. Since it represents an actual count of particles, it can never be zero or fractional. Thus, Molecularity matches with "cannot be zero or a non-integer." Reaction order is the sum of the powers of concentration terms in the rate equation. It is experimentally determined and may be zero, integral, or fractional. Therefore, Reaction order matches with "can be zero and even a fraction." Thus, the correct matching is: 1-c, 2-b, 3-d, 4-a

The Arrhenius equation states that the rate constant increases with increasing temperature. As temperature rises, a greater fraction of molecules possesses energy greater than the activation energy, resulting in more effective collisions and a faster reaction rate. The decomposition of N₂O₅ is a first-order reaction. For first-order reactions, half-life is inversely proportional to the rate constant: t½ = 0.693/k Thus, a larger rate constant corresponds to a shorter half-life. Among the given temperatures, 50°C provides the highest rate constant and therefore the shortest half-life. At 25°C, the rate constant is lower, producing an intermediate half-life. At 0°C, the rate constant is smallest, resulting in the longest half-life. Hence, the correct order from shortest half-life to longest half-life is: 50°C → 25°C → 0°C or 3 → 1 → 2

A zero-order reaction is one in which the reaction rate becomes independent of reactant concentration. According to NCERT, this situation may occur when a catalytic surface becomes completely saturated by reactant molecules. At high pressure, all available active sites on the catalyst surface are occupied. Once saturation is achieved, increasing the concentration or pressure of the reactant cannot increase the number of reacting molecules on the surface. As a result, the reaction rate remains constant. A classic example is the decomposition of HI on a gold surface. Since the catalyst surface is already fully occupied, the rate no longer depends on reactant concentration. The rate law becomes: Rate = k This is the defining characteristic of a zero-order reaction. Therefore, the correct kinetic classification is zero order reaction.

Chemical kinetics uses both differential and integrated rate equations. A differential rate equation expresses the rate of reaction in terms of concentration change at a particular instant. However, experimental measurements are often made by observing concentration or pressure changes over a period of time. To connect measurable quantities with the rate constant, the differential rate equation is mathematically integrated. The resulting expression is known as the integrated rate equation. According to NCERT, integrated rate equations relate concentration, pressure, or other measurable quantities directly to time and the rate constant. For example, in gaseous reactions, partial pressure measurements can be used in place of concentration. By integrating the rate law, one obtains equations that allow determination of the rate constant from experimental data. Therefore, the equation obtained through integration of rate expressions is called the integrated rate equation.

According to collision theory, molecules must collide with sufficient energy and proper orientation for a reaction to occur. However, even when molecules possess adequate energy, many collisions fail because the molecules are not oriented correctly for bond breaking and bond formation. To account for this observation, the factor "P" is introduced into collision theory. This factor is called the steric factor or probability factor. It represents the fraction of collisions that occur with the proper orientation required for product formation. For simple molecules, the steric factor is often close to unity. For complex molecules, the value may be very small because only a limited number of orientations lead to successful reactions. Thus, the steric factor helps explain why experimentally observed reaction rates are often lower than those predicted solely on the basis of collision frequency. Therefore, factor P is known as the steric factor or probability factor.

Collision theory was developed by Max Trautz and William Lewis to explain chemical reaction rates. The theory assumes that molecules behave like hard spheres that move continuously and collide with one another. However, experimental observations show that not every collision results in product formation. According to NCERT, effective collisions require two important conditions. First, colliding molecules must possess energy greater than or equal to the threshold energy. Second, the molecules must approach one another with a suitable orientation that allows bond breaking and bond formation. Complex molecules often have many possible orientations, but only a few of them are favorable for reaction. As a result, many collisions are ineffective despite occurring frequently. This explains why observed reaction rates are lower than those predicted by simple collision frequency calculations. Therefore, all collisions do not lead to product formation because of improper orientation and insufficient energy.

The Maxwell-Boltzmann distribution describes the distribution of molecular energies in a system. According to NCERT, the total area under the distribution curve remains constant because it represents the total number of molecules present. Therefore, Statement 1 is correct. As temperature increases, the distribution curve broadens and shifts so that a larger fraction of molecules possesses energy greater than the activation energy (Ea). Consequently, Statement 2 is correct. Because more molecules now possess sufficient energy for reaction, the number of effective collisions increases. Hence, Statement 4 is also correct. Statement 3 is incorrect because a rise of 10°C generally increases the reaction rate, often approximately doubling it, rather than halving the rate constant. Therefore, Statements 1, 2, and 4 are correct.

The hydrolysis of ethyl acetate normally involves two reactants: ethyl acetate and water. Therefore, the actual molecularity of the reaction is two. However, when water is present in very large excess, its concentration changes negligibly during the reaction. Under these conditions, the concentration of water is effectively constant and becomes part of the rate constant. The rate law can then be written in terms of only the concentration of ethyl acetate. As a result, the reaction appears to follow first-order kinetics even though two reactants participate in the reaction. According to NCERT, such reactions are known as pseudo first-order reactions. The term "pseudo" indicates that the experimentally observed order differs from the actual molecularity because one reactant is present in large excess. Thus, hydrolysis of ethyl acetate in excess water is a classic example of a pseudo first-order reaction.

For a first-order reaction, the integrated rate equation leads to the expression: t½ = 0.693/k where k is the first-order rate constant. This equation shows that the half-life depends only on the value of the rate constant and is completely independent of the initial concentration of the reactant. This property is unique and extremely important. Regardless of how much reactant is present initially, the time required for the concentration to decrease to half of its value remains the same. Radioactive decay and many decomposition reactions exhibit this behavior. According to NCERT, the concentration independence of half-life is a characteristic feature of first-order reactions and is widely used in kinetic analysis. Therefore, the half-life of a first-order reaction is constant and does not depend on the initial concentration of the reacting species.