CUET UG Chemistry Booster Test – 3 Factors and Theories

According to the Arrhenius equation, reaction rate increases with temperature because a greater fraction of molecules possess energy equal to or greater than the activation energy (Ea). As a rule of thumb, a 10°C rise in temperature approximately doubles the rate constant for many reactions. Potassium permanganate decolourisation occurs more slowly at lower temperatures because fewer molecules possess sufficient activation energy for effective collisions. Statement 1 is incorrect because the decomposition rate of N₂O₅ is not identical at 0°C and 50°C. Higher temperature results in a faster decomposition rate. Therefore, Statements 2 and 3 are correct. Hence, the correct answer is A.

According to Maxwell-Boltzmann distribution and Arrhenius theory, increasing temperature increases the fraction of molecules possessing kinetic energy greater than the activation energy (Ea). These molecules undergo effective collisions, resulting in product formation. Since more molecules can overcome the activation energy barrier, the reaction rate increases significantly. Temperature does not directly lower Ea; instead, it increases the number of molecules capable of crossing the existing energy barrier. Hence, the correct answer is C.

The integrated Arrhenius equation is derived by first taking the natural logarithm of the Arrhenius equation, , to obtain a linear logarithmic form. Next, values corresponding to two different temperatures (T₁ and T₂) and their respective rate constants (k₁ and k₂) are substituted into the logarithmic equation. The resulting equations are then subtracted to eliminate the constant term ln A. Finally, the expression is rearranged and converted into common logarithmic form to obtain: log(k₂/k₁) = (Ea/2.303R) × ((T₂ − T₁)/(T₁T₂)) Thus, the correct sequence of steps is: 2 → 4 → 3 → 1 Hence, the correct answer is D.

The Arrhenius equation is expressed as: ln k = -Ea/RT + ln A This equation has the same form as the straight-line equation: y = mx + c Comparing the two equations: • y corresponds to ln k • x corresponds to 1/T • Slope (m) corresponds to -Ea/R • Intercept (c) corresponds to ln A Therefore, the correct matching is: 1. y-axis → c. ln k 2. x-axis → a. 1/T 3. Slope → d. -Ea/R 4. Intercept → b. ln A An Arrhenius plot of ln k against 1/T gives a straight line whose slope is negative because the activation energy term carries a negative sign. The intercept provides the frequency factor (A) information. This graphical representation is widely used to determine activation energy experimentally.

Threshold energy is defined as the minimum kinetic energy that colliding molecules must possess for a reaction to occur. Mathematically: Threshold Energy = Activation Energy + Energy already possessed by reactant molecules Only molecules having energy equal to or greater than threshold energy can undergo effective collisions and form products. Therefore, threshold energy exceeds activation energy by the amount of energy already possessed by reacting species. Hence, the correct answer is A.

For a first order reaction: Rate = k[R] Rate has units of mol L⁻¹ s⁻¹ and concentration has units of mol L⁻¹. Therefore, k = (mol L⁻¹ s⁻¹)/(mol L⁻¹) = s⁻¹ Thus, the rate constant of a first order reaction has units of reciprocal time. This is a characteristic feature of first order kinetics and is independent of the concentration unit used. Hence, the correct answer is C. s⁻¹.

In a potential energy diagram, when the activated complex decomposes and releases energy while forming products, the products lie at a lower energy level than the reactants. This energy difference is released to the surroundings and the enthalpy change (ΔH) becomes negative. Such reactions are known as exothermic reactions. Therefore, if energy is released during product formation, the reaction is exothermic. Hence, the correct answer is D. Exothermic reaction.

The final enthalpy change of a reaction depends solely on the energy difference between reactants and products. Since enthalpy is a state function, it depends only on the initial and final states and not on the reaction pathway. Therefore, the nature of the reactants and products determines the final enthalpy of reaction. Catalysts may lower activation energy but do not affect ΔH. Hence, the correct answer is B.

The Maxwell-Boltzmann distribution describes how molecular kinetic energies are distributed among a large number of molecules. This statistical model was developed through the contributions of James Clerk Maxwell and Ludwig Boltzmann. The distribution curve helps explain reaction rates, activation energy concepts, and the effect of temperature on chemical reactions. Therefore, the correct answer is B. Ludwig Boltzmann and James Clark Maxwell.

In a Maxwell-Boltzmann distribution, the total area under the curve represents total probability and must always remain equal to one. Therefore, Statement 1 is correct. When temperature increases, the distribution broadens and shifts toward higher kinetic energies. This means a larger fraction of molecules possess high energies, making Statement 3 correct. However, the total area under the curve does not double with temperature increase; it remains constant. Hence Statement 2 is incorrect. Therefore, Statements 1 and 3 are correct. Hence, the correct answer is C. 1 and 3 are correct.

According to the intermediate complex theory of catalysis, a catalyst first combines with one or more reactant molecules to form an intermediate complex. This intermediate complex is unstable and has a transitory existence. It provides an alternative reaction pathway having lower activation energy than the uncatalysed reaction. After the reaction proceeds through this pathway, the intermediate complex decomposes to form the products. During this decomposition, the catalyst is regenerated in its original form and is yielded along with the products. Thus, the catalyst is not consumed during the reaction and remains chemically unchanged at the end of the process. This is one of the most important characteristics of catalysts discussed in NCERT. The regeneration of the catalyst allows a small quantity of catalyst to convert a large amount of reactants into products. Therefore, the correct statement is that the catalyst is yielded along with the products after the intermediate complex decomposes.

Catalysts affect only the rate at which equilibrium is attained and do not alter the thermodynamic parameters of a reaction. The Gibbs energy change of a reaction remains unaltered in the presence of a catalyst. Similarly, catalysts cannot catalyse non-spontaneous reactions because spontaneity depends on thermodynamic feasibility and not on reaction rate. The equilibrium constant also remains unchanged because it depends only on temperature and the thermodynamic properties of the system. A catalyst merely lowers the activation energy by providing an alternate reaction pathway with a lower energy barrier. This alternate pathway increases the rate of both forward and backward reactions equally. Consequently, equilibrium is reached faster, but the position of equilibrium remains unchanged. These principles are clearly explained in NCERT under the topic of catalysis and catalyst mechanism.

Collision theory was developed by Max Trautz and William Lewis and is based on the kinetic theory of gases. According to this theory, reactant molecules are treated as hard spheres and reactions occur when molecules collide effectively. The theory provides a deeper understanding of why reactions occur at different rates by considering both the energy possessed by colliding molecules and the orientation during collision. Hence, collision theory offers insight into the energetic aspects, such as activation energy and threshold energy, and mechanistic aspects, such as how molecules collide and rearrange to form products. This makes it more informative than simply using the Arrhenius equation, which primarily describes the temperature dependence of reaction rates. NCERT specifically states that collision theory provides greater insight into the energetic and mechanistic aspects of reactions.

The collision theory developed by Max Trautz and William Lewis is based on the kinetic theory of gases. The kinetic theory explains the behaviour of gas molecules in terms of their continuous random motion and collisions. Collision theory extends these ideas to chemical reactions by assuming that reactant molecules behave as hard spheres. According to this theory, reactions occur only when molecules collide with sufficient energy and proper orientation. The frequency and effectiveness of collisions determine the reaction rate. Thus, the kinetic theory of gases provides the theoretical framework upon which collision theory is constructed. NCERT clearly mentions that collision theory is based on the kinetic theory of gases and uses its principles to explain chemical reaction rates.

The hydrolysis reaction of ethyl acetate can be represented as: CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH The stoichiometric ratio between ethyl acetate and water is 1:1. Therefore, 0.01 mol of ethyl acetate requires 0.01 mol of water for complete hydrolysis. Initially, 10 mol of water is present. Since only 0.01 mol water participates in the reaction, the remaining amount of water is: Water remaining = Initial water − Water consumed = 10 − 0.01 = 9.99 mol Because water is present in very large excess, its concentration remains nearly constant throughout the reaction. This is the basis of pseudo-first-order kinetics discussed in NCERT. The reaction appears to follow first-order kinetics even though it is fundamentally a second-order reaction. Therefore, the exact amount of water remaining after completion is 9.99 mol.

The inversion of cane sugar refers to the hydrolysis of sucrose in the presence of water. The chemical equation is: C₁₂H₂₂O₁₁ + H₂O → C₆H₁₂O₆ + C₆H₁₂O₆ Here, sucrose (cane sugar) reacts with water to produce glucose and fructose. When arranged from left to right exactly as they appear in the equation, the sequence is sucrose, water, glucose and fructose. This reaction is commonly used in NCERT to explain pseudo-first-order kinetics because water is generally present in large excess. Due to the excess concentration of water, its concentration remains nearly constant during the reaction, causing the reaction to behave like a first-order reaction even though it is actually bimolecular. Understanding the correct order of reactants and products is important for interpreting the reaction mechanism and kinetic treatment of inversion of cane sugar.

A catalyst provides an alternative reaction pathway with lower activation energy. This reduction in activation energy increases the rate of the forward reaction. However, the catalyst does not selectively act only on the forward reaction. It also lowers the activation energy of the reverse reaction by the same amount. As a result, both forward and backward reactions are accelerated equally. Since both reaction rates increase proportionately, the equilibrium constant and equilibrium position remain unchanged. The only effect is that equilibrium is reached more rapidly. NCERT clearly states that catalysts do not affect the thermodynamic properties of a reaction or alter equilibrium composition. Therefore, when a catalyst lowers the activation energy for the forward reaction, it catalyzes the reverse reaction to the same extent.

According to the intermediate complex theory of catalysis, the catalyst first combines with reactants to form an intermediate complex. This complex is unstable and exists only for a very short duration. Because of its temporary nature, NCERT describes it as having a transitory existence. The intermediate complex provides an alternative reaction pathway with lower activation energy. After formation, it rapidly decomposes into products while regenerating the catalyst. The transitory existence of the intermediate complex is essential because a stable complex would prevent product formation and reduce catalytic efficiency. Therefore, the term "intermediate complex" specifically refers to the short-lived species formed during catalytic reactions.

Collision theory states that not all molecular collisions lead to product formation. For a collision to be effective, molecules must possess sufficient kinetic energy equal to or greater than the threshold energy and must collide with proper orientation. Proper orientation allows existing bonds to break and new bonds to form efficiently. The steric factor accounts for the probability that molecules are oriented correctly during collision. Statement 1 is correct because orientation is necessary for bond rearrangement. Statement 2 is correct because steric factor represents orientation requirements. Statement 4 is also correct because proper orientation is one of the conditions for effective collision. Statement 3 is incorrect because molecules must have kinetic energy equal to or greater than the threshold energy, not less than it. Therefore, statements 1, 2 and 4 are correct.

According to collision theory, molecules must collide with both sufficient energy and proper orientation for a reaction to occur. In reactions such as the formation of methanol from bromoethane, the reacting molecules must approach each other in a specific arrangement so that old bonds can break and new bonds can form. If the molecules collide with improper orientation, the required atomic interactions do not occur. As a result, no products are formed, and the molecules simply bounce back after collision. Such collisions are termed ineffective collisions due to improper orientation. NCERT explains that the steric factor accounts for this orientation requirement. Therefore, when molecules rebound without product formation because of incorrect alignment, the phenomenon is called improper orientation.