Chemical Kinetics Class 12 MCQ

Explanation:
This problem compares the rate constants of first-order and zero-order reactions using their half-life expressions under the same starting concentration. In chemical kinetics, half-life behaves differently depending on reaction order. For a first-order process, the half-life stays constant and does not depend on concentration. In contrast, the half-life of a zero-order reaction changes directly with the initial concentration.

To analyze the situation, the standard half-life equations for both orders are used. The given concentration and time values help establish mathematical expressions for the two rate constants separately. Since the concentration becomes half in different times, the corresponding constants differ numerically. By evaluating the expressions carefully and comparing them through ratio form, the multiplying factor can be identified.

The comparison mainly focuses on how quickly concentration decreases in each kinetic model. A first-order reaction generally shows exponential decay, whereas a zero-order reaction decreases linearly with time. Because of this difference, their constants are related differently even under identical starting conditions.

This type of question checks understanding of integrated rate laws and the dependence of half-life on concentration for different reaction orders.

Explanation:
This question is based on the characteristic property of first-order reactions, where equal fractions of a substance decompose in equal intervals of time. In such reactions, the half-life remains constant regardless of the starting concentration. That means the time required for concentration to reduce by half will always stay the same throughout the reaction.

The given information shows that the concentration decreases from 0.8 M to 0.4 M in 15 minutes, representing one half-life. The second concentration change, from 0.1 M to 0.025 M, occurs in multiple stages. First, the concentration drops from 0.1 M to 0.05 M, and then from 0.05 M to 0.025 M. Each step represents another halving process.

Since the reaction follows first-order kinetics, each halving requires the same amount of time. Therefore, the total time depends on counting the number of half-life intervals involved rather than on the absolute concentration values. This makes first-order decay especially useful in radioactive processes and decomposition reactions.

The concept highlights the predictable exponential behavior commonly observed in many natural chemical transformations.

Explanation:
This question relates to the Maxwell–Boltzmann distribution curve, which describes how Molecular energies are distributed among particles in a gas. When temperature increases, molecules gain higher average kinetic energy, causing noticeable changes in the shape and position of the distribution curve. The peak of the curve shifts and the spread becomes broader because more particles acquire higher energies.

Although the curve changes shape with temperature, one important feature does not change. The total number of molecules in the system remains fixed if no particles are added or removed. Mathematically, this means the entire area enclosed under the distribution curve remains constant. The graph may become flatter and wider at higher temperatures, but the total probability represented by the curve is conserved.

The concept is significant in chemical kinetics because only molecules with energy greater than activation energy can participate effectively in reactions. As temperature rises, the fraction of such energetic molecules increases, leading to faster reaction rates.

This principle helps explain why heating generally speeds up reactions even though the total number of molecules in the system does not change.

Explanation:
This problem involves first-order kinetics, where the reaction rate depends directly on the concentration of the reactant. In a first-order process, the same fraction of reactant decomposes in equal intervals of time, regardless of the starting amount. This allows concentration ratios to be compared conveniently using the integrated rate equation.

The first condition shows conversion of reactant into product over one hour. By interpreting the amount of product formed, the remaining amount of reactant can be determined. This establishes a fractional conversion pattern for the reaction. The second condition involves a different starting quantity, but the fraction converted must be examined carefully.

In first-order reactions, time depends on the ratio between initial and remaining reactant amounts rather than on absolute values. If the fractional decomposition in the second case matches the first, the required time interval will also remain identical. Thus, comparing proportional conversion becomes more important than comparing actual mole values.

Such problems commonly appear in chemical kinetics to test understanding of exponential decay behavior and the concentration-independent nature of first-order half-life relationships.

Explanation:
This question examines how reaction rate depends on the concentration of one reactant. In chemical kinetics, the rate law expresses the relationship between rate and concentration through powers known as reaction orders. These powers indicate how sensitively the rate responds to concentration changes.

Here, the concentration of reactant B is doubled while all other conditions remain constant. Instead of increasing, the reaction rate decreases significantly. This suggests that B has an inverse influence on the rate. To determine the order mathematically, the rate law relationship is written in ratio form. The concentration term is raised to an unknown power, and the observed rate change is substituted into the equation.

Solving the resulting expression reveals the exponent associated with B. A negative order indicates that increasing concentration slows the reaction, which may happen in reactions involving catalyst poisoning, intermediate stabilization, or complex mechanisms.

This type of problem is important because it demonstrates that reaction orders are determined experimentally and may even take negative values depending on the mechanism involved.

Explanation:
This problem is based on the integrated rate law for first-order reactions. In such reactions, the rate depends directly on the amount of reactant remaining, causing exponential decay over time. As the reaction approaches completion, the remaining reactant becomes very small, making further decomposition progressively slower.

To compare the required times, the percentages must first be converted into fractions of reactant remaining. For 90% completion, a small fraction remains unreacted, while for 99% completion, the remaining fraction becomes much smaller. Using the logarithmic form of the first-order rate equation, the time required is directly proportional to the logarithm of the ratio of initial to remaining concentration.

By evaluating the logarithmic ratios for both cases and comparing them, the relationship between the two times can be obtained. The calculation demonstrates how dramatically the required time increases as completion approaches 100%. This behavior is characteristic of exponential processes where complete consumption theoretically requires infinite time.

The question highlights the mathematical nature of first-order decay and the practical difficulty of achieving nearly complete conversion in chemical systems.

Explanation:
This question focuses on the relationship between half-life and initial concentration for reactions of different orders. In kinetics, each reaction order has a characteristic half-life expression. Observing how half-life changes with concentration helps identify the reaction order experimentally.

For zero-order reactions, half-life depends directly on initial concentration. In first-order reactions, half-life remains constant and independent of concentration. Higher-order reactions show inverse dependence on concentration raised to specific powers. The question states that half-life varies inversely with the square of the initial concentration, which provides the key clue.

To determine the order mathematically, the general half-life expression for an nth-order reaction is considered. The exponent of concentration in the given proportionality is compared with the standard form. Matching these exponents allows the reaction order to be identified systematically.

This method is widely used in experimental kinetics because half-life measurements are often easier to obtain than full concentration–time data. The problem demonstrates how concentration dependence alone can reveal the underlying reaction order without directly analyzing the complete rate law.

Explanation:
Radioactive decay follows first-order kinetics, meaning the substance decreases by equal fractions during equal intervals of time. The half-life represents the time required for the quantity of radioactive material to reduce to half of its original amount. This property remains constant throughout the decay process.

In this problem, the sample decreases from 10 g to 1.25 g over a period of 12 years. The reduction occurs stepwise through repeated halving. First, 10 g becomes 5 g, then 5 g becomes 2.5 g, and finally 2.5 g becomes 1.25 g. Counting these stages reveals how many half-lives have elapsed during the total decay period.

Once the number of half-life intervals is known, the total time can be divided equally among them to determine the duration of one half-life. This approach avoids complicated logarithmic calculations and directly uses the definition of radioactive half-life.

Such problems are common in nuclear Chemistry and help explain applications like radiocarbon dating, medical tracers, and prediction of radioactive substance stability over time.

Explanation:
This question deals with thermal decomposition following first-order kinetics. In first-order reactions, the half-life remains constant and the concentration decreases exponentially with time. The given information states that 50% decomposition occurs in 126 minutes, which directly represents one half-life of the reaction.

For 90% decomposition, only 10% of the original substance remains. The first-order integrated rate equation relates time to the logarithm of the ratio between initial and remaining concentration. By substituting the remaining fraction into the equation and using the known half-life relationship, the required time can be estimated systematically.

Unlike zero-order reactions, where concentration decreases linearly, first-order decay slows progressively because the amount of reactant continuously decreases. Therefore, reaching higher percentages of decomposition requires disproportionately longer times. This explains why the time for 90% completion is much greater than the half-life value.

Such decomposition behavior is commonly observed in radioactive decay, Pharmaceutical degradation, and many thermal chemical processes where exponential kinetics governs concentration changes over time.

Explanation:
The temperature coefficient indicates how many times a reaction rate increases when temperature rises by 10 °C. A coefficient of 2 means the reaction rate doubles for every 10-degree increase in temperature. This concept is closely related to collision theory and activation energy in chemical kinetics.

In this problem, the temperature changes from 30 °C to 70 °C, giving a total increase of 40 °C. This increase can be divided into four separate intervals of 10 °C each. Since the rate doubles during every interval, the multiplication effect occurs repeatedly rather than only once.

The overall increase is therefore calculated using repeated multiplication of the temperature coefficient. This creates a geometric progression where the rate enhancement becomes increasingly large with successive temperature rises. The concept explains why many reactions proceed extremely rapidly at high temperatures.

Temperature strongly influences Molecular kinetic energy, increasing both collision frequency and the fraction of molecules capable of overcoming activation energy barriers during chemical reactions.

Explanation:
This question involves dimensional analysis of the rate law in chemical kinetics. The rate of a reaction generally has units of concentration per unit time, commonly written as mol L^-1 s^-1. The units of the rate constant vary depending on the overall reaction order.

The general rate equation expresses reaction rate as the product of the rate constant and concentration terms raised to different powers. To maintain dimensional consistency, the units of the rate constant adjust according to the total order of the reaction. By comparing the units on both sides of the rate equation, the required order can be identified.

For some reaction orders, concentration units appear in the denominator or numerator of the rate constant. However, there is one special case where the concentration terms disappear completely from the dimensional balance. In that situation, the rate constant ends up carrying exactly the same units as the reaction rate itself.

This type of question is important because unit analysis provides a quick method for identifying reaction order without solving detailed kinetic equations.