Free NEET Chemistry multiple-choice questions on Integrated Rate Equations. Attempt each question and reveal the answer with a full explanation.
The slope of the plot of [A] vs t for a zero-order reaction is: -k +k -k/2.303 +k/2.303 For a zero-order reaction, the plot of concentration [A] versus time t is a straight line with: Negative slope and non-zero intercept Positive slope and zero intercept Negative slope and zero intercept Zero slope and non-zero intercept Which graph represents a first-order reaction? [A] t vs t is a straight line with a negative slope [A] t vs t is a straight line with a negative slope 1/[A] t vs t is a straight line with a positive slope [A] t vs 1/t is a straight line The rate constant of a reaction is 3 10 2 min -1 . What is the order of the reaction? First Zero Second Third For a zero-order reaction, the half-life period ( t 1/2 ) and the initial concentration ( a ) are related as: t 1/2 a t 1/2 1/a t 1/2 a 2 t 1/2 is independent of a Which of the following plots represents a zero-order reaction where [A] is the concentration of the reactant at time t ? A plot of [A] vs t is linear with a negative slope. A plot of [A] vs t is linear with a negative slope. A plot of 1/[A] vs t is linear with a positive slope. A plot of [A] vs t 2 is linear. For a first-order reaction, the time taken for 75 % completion is how many times the time taken for 50 % completion? 2 1.5 3 4 What is the order of reaction for the decomposition of N 2O 5 in the gas phase? 1 2 0 0.5 For a zero-order reaction, the time required for 50 % completion is 2 minutes. How much time is required for 100 % completion? 4 minutes 2 minutes 8 minutes 16 minutes For a first-order reaction, if the rate constant k is 2.303 10 -3 s -1 , what is the time required for the reactant to reduce from 1.0 M to 0.1 M ? 1000 s 100 s 2303 s 4606 s In a reaction A B , the initial concentration of A is 0.5 M . After 20 minutes, it becomes 0.25 M , and after 40 minutes, it becomes 0.125 M . The order of the reaction is: First order Zero order Second order Half order The rate constant for a zero-order reaction is 0.0030 mol L -1 s -1 . If the initial concentration of the reactant is 0.60 M , how long will it take for the concentration to become 0.30 M ? 100 s 200 s 50 s 300 s The half-life of a zero-order reaction is: Directly proportional to the initial concentration Inversely proportional to the initial concentration Independent of the initial concentration Directly proportional to the square of initial concentration For a reaction A → B , half-life is observed to be independent of the initial concentration of the reactants. What is the order of the reaction? First order Zero order Second order Third order Which of the following is the correct expression for the half-life of a zero-order reaction? t 1/2 = [A] 0 2k t 1/2 = 0.693 k t 1/2 = 1 k[A] 0 t 1/2 = [A] 0 k The rate constant of a first-order reaction is 0.0693 min -1 . How many minutes will it take for the concentration of the reactant to drop from 1.0 M to 0.25 M ? 20 min 10 min 30 min 40 min For a zero-order reaction, a plot of rate versus concentration of the reactant yields: A horizontal straight line A straight line passing through the origin A curve asymptotic to the axes A straight line with a negative slope The decomposition of N 2O 5 is a first-order reaction. In 20 minutes, the concentration of N 2O 5 falls from 0.4 M to 0.2 M . How much time will it take for the concentration to fall from 0.1 M to 0.05 M ? 20 minutes 10 minutes 40 minutes 5 minutes In a second-order reaction, if the initial concentration of the reactant is doubled, the time required for 50 % of the reaction to complete will: Decrease by half Double Remain unchanged Increase by four times Which of the following plots will be a straight line for a first-order reaction A Product ? [A] vs t 1/[A] vs t [A] vs t [A] 2 vs t Which of the following represents the expression for a first-order integrated rate equation? kt = ln [A] 0 [A] [A] = [A] 0 - kt 1 [A] - 1 [A] 0 = kt [A] = [A] 0 e kt For a first-order reaction A B , the plot of [A] t vs t is linear with a slope equal to: -k/2.303 -k k/2.303 -2.303/k In a first-order reaction, if the initial concentration is 1.0 M and the rate constant is k , the rate of the reaction after one half-life is: 0.5k k 0.25k 2k For a first-order reaction, if the rate constant is k , the time required for 75 % completion is: 1.386/k 0.693/k 2.303/k 3.465/k The decomposition of nitrous oxide ( N 2O ) on the surface of gold follows zero-order kinetics. This implies that: The rate of reaction is independent of the concentration of N 2O The rate of reaction depends on the square of the concentration of N 2O The half-life of the reaction is independent of the initial concentration The rate constant has units of s -1 The time required for 100 % completion of a zero-order reaction is: [A] 0/k k/[A] 0 [A] 0/2k 2/k For a first order reaction A -> B the reaction rate at reactant concentration of 0.01M is found to be 2.0 10 -5 mole L -1 s -1 . The half life period of the reaction is :- 300s 30s 220s 347s In a first-order reaction A -> B , if k is rate constant and initial concentration of the reactant A is 0.5 M, then the half-life is 2 k 2 k 0.5 2 k 0.693 0.5k Half-life period of a first-order reaction is 1386 seconds. The specific rate constant of the reaction is : 5.0 10 -2 s -1 5.0 10 -3 s -1 0.5 10 -2 s -1 0.5 10 -3 s -1 The correct difference between first and second order reactions is that A first-order reaction can catalyzed; a second-order reaction cannot be catalyzed The half-life of a first-order reaction does not depend on [A] 0 ; the half-life of a second-order reaction does depend on [A] 0 The rate of a first-order reaction does not depend on reactant concentrations; the rate of a second-order reaction does depend on reactant concentrations The rate of a first-order reaction does depend on reactant concentrations; the rate of a second-order reaction does not depend on reactant concentrations When initial concentration of the reactant is doubled, the half-life period of a zero order reaction Is tripled Is doubled Is halved Remains unchanged The rate constant for a first order reaction is 4.606 10 -3 s -1 . The time required to reduce 2.0 g of the reactant to 0.2 g is : 200 s 500 s 1000 s 100 s For a first order reaction A Products, initial concentration of A is 0.1 M, which becomes 0.001 M after 5 minutes. Rate constant for the reaction in min -1 is 0.9212 0.4606 0.2303 1.3818 For a first-order reaction, what is the ratio of the time required for 87.5 % completion ( t 87.5 % ) to the half-life ( t 1/2 )? 3 2 4 1.5 If the rate constant of a reaction is 0.03 s -1 , how much time does it take for 7.2 mol L -1 concentration of the reactant to get reduced to 0.9 mol L -1 ? (Given: log 2 = 0.301) 21.0 s 69.3 s 23.1 s 210 s For a certain reaction R Product, the plot of concentration [R] vs time has a negative slope as shown. The order of reaction is : 1 2.5 2 0 A first-order reaction has a specific reaction rate of 10 -2 s -1 . How much time will it take for 20 g of the reactant to reduce to 5 g ? 138.6 s 238.6 s 693.2 s 346.5 s If the rate constant for a first-order reaction is k , the time ( t ) required for the completion of 99.9 percent of the reaction is given by: t = 6.909 k t = 4.606 k t = 2.303 k t = 0.693 k A reaction is 50 percent complete in 2 hours and 75 percent complete in 4 hours. The order of the reaction is: First Zero Second Third In a first-order reaction, the time required for 99.9 % completion is approximately how many times the half-life ( t 1/2 )? 10 times 5 times 100 times 2 times The rate of a first-order reaction is 1.5 10 -2 mol L -1 min -1 at 0.5 M concentration of reactant. The half-life of the reaction is: 23.1 min 0.347 min 8.73 min 7.53 min In a first-order reaction, the concentration of reactant decreases from 0.8 M to 0.4 M in 15 minutes . The time taken for the concentration to change from 0.1 M to 0.025 M is: 30 minutes 15 minutes 7.5 minutes 60 minutes The half-life of a reaction is doubled as the initial concentration of the reactant is doubled. The order of the reaction is: 0 1 2 3 For a first-order reaction, the time required for 99 % completion is how many times the time required for the completion of 90 % of the reaction? 2 3 4 10 For a zero-order reaction A Product , what is the ratio of t 75 % to t 50 % ? 1.5 2.0 1.75 3.0 For a zero-order reaction, the time required for 100 % completion is: [A] 0 / k k / [A] 0 [A] 0 / 2k 2k / [A] 0 The decomposition of N 2O 5 in CCl 4 is a first-order reaction with a rate constant k = 6.2 10 -4 s -1 . If the initial concentration of N 2O 5 is 1.24 mol L -1 , what is the rate of reaction at the start? 7.69 10 -4 mol L -1 s -1 6.2 10 -4 mol L -1 s -1 5.0 10 -4 mol L -1 s -1 1.24 10 -4 mol L -1 s -1 For a second-order reaction, the plot of 1/[A] t versus time t gives a straight line with a slope equal to: k -k k/2.303 -k/2.303 The rate constant for a first-order reaction is k . The time t required for the completion of 3/4 th of the reaction is: 2.303 k 4 2.303 k 3 k 2.303 4 2.303 k 4 3 For a second-order reaction, if the initial concentration of the reactant is doubled, the half-life of the reaction will: Be halved Be doubled Remain constant Increase by four times A substance 'A' decomposes following first-order kinetics. If it takes 30 minutes for 50 % decomposition, the time required for 87.5 % decomposition is: 90 minutes 60 minutes 120 minutes 45 minutes The half-life period of a first-order reaction is 10 minutes. The time required for the concentration of the reactant to change from 0.08 M to 0.01 M is: 30 minutes 20 minutes 40 minutes 10 minutes Which of the following graphs represents the variation of half-life ( t 1/2 ) with initial concentration ( a ) for a second-order reaction? A hyperbola showing t 1/2 a = constant A straight line passing through the origin A straight line parallel to the x-axis A straight line with a negative slope For a first-order reaction, the time taken for 90 % completion is approximately how many times the time taken for 50 % completion? 3.3 2.0 1.1 4.4 The rate constant of a first-order reaction is 0.0693 min -1 . What is the time required for 75 % completion of the reaction? 20 min 10 min 30 min 40 min The half-life of a first-order reaction is t 1/2 . The time required for 93.75 % completion of the same reaction is: 4 t 1/2 3 t 1/2 5 t 1/2 2 t 1/2 The half-life for a zero-order reaction is 100 min when the initial concentration is 2.0 M . What is the rate constant k ? 0.01 mol L -1 min -1 0.02 mol L -1 min -1 0.005 mol L -1 min -1 0.00693 min -1 For a first-order reaction, the ratio of the time taken for 99.9 % completion to the half-life ( t 1/2 ) of the reaction is: 10 5 2 100 Radioactive iodine-131 has a half-life of 8 days. If a sample has an initial activity of 100 mCi , what will be the activity after 32 days? 6.25 mCi 12.5 mCi 3.125 mCi 25 mCi If the rate constant for a first-order reaction is k , the time ( t ) required for the completion of 99.9 % of the reaction is given by: t = 6.909 k t = 4.606 k t = 2.303 k t = 0.693 k A first-order reaction has a rate constant of 2.303 10 -3 s -1 . The time required for 40 g of this reactant to reduce to 10 g is: 602.1 s 301.0 s 230.3 s 460.6 s The decomposition of a substance follows first-order kinetics. If its concentration is reduced to 1/8 of its initial value in 24 minutes, the rate constant k is: 0.0866 min -1 0.0288 min -1 0.1155 min -1 0.0433 min -1 For a chemical reaction, the rate constant is k = 2.0 10 -2 L ∙ mol -1 s -1 . If the initial concentration of the reactant is 0.1 M , the half-life is: 500 s 34.65 s 50 s 100 s For a first-order reaction, what is the ratio of the time taken for 99 % completion ( t 99 % ) to the time taken for 90 % completion ( t 90 % )? 2 3 10 4.606 The decomposition of N 2O 5 follows first-order kinetics. The life-time ( 1/k ) of the reaction is the time in which the concentration of reactant reduces to: 1/e of its initial value Half of its initial value One-fourth of its initial value Zero The rate constant of a first-order reaction is 10 -3 s -1 . The time required for 1/4 th of the reaction to be completed is: (Given 4 = 0.602, 3 = 0.477 ) 287 s 1386 s 693 s 2303 s The decomposition of HI on a gold surface is zero-order. If the rate constant is 0.05 M s -1 , what is the rate of the reaction when [HI] = 0.1 M ? 0.05 M s -1 0.005 M s -1 0.5 M s -1 0.025 M s -1 For a first-order reaction, the time required for 93.75 % completion is how many times the half-life? 4 3 2 5 In a first-order reaction, the time taken for the reactant concentration to decrease from 1.0 M to 0.25 M is 20 minutes. What is the rate constant of the reaction? 0.0693 min -1 0.693 min -1 0.0346 min -1 0.1386 min -1 For a reaction A Products , a plot of [A] vs time ( t ) gives a straight line with a negative slope. The order of the reaction is: 1 0 2 0.5 The half-life of a reaction is 10 minutes. If the initial concentration is 2.0 M and the reaction is second-order, what will be the half-life if the initial concentration is increased to 4.0 M ? 5 minutes 20 minutes 10 minutes 2.5 minutes A radioactive isotope has a half-life of 5 years. After 20 years, the fraction of the sample that remains is: 1/16 1/8 1/4 1/32 The slope of the plot of 1/[A] versus time ( t ) for a second-order reaction is: k -k -k/2.303 /k Which of the following is correct for the t 1/2 of a second-order reaction? It is inversely proportional to the initial concentration. It is directly proportional to the square of initial concentration. It is independent of the initial concentration. It is directly proportional to the initial concentration. A first-order reaction is 90 % complete in 40 minutes. What is the time required for 99.9 % completion? 120 minutes 80 minutes 160 minutes 100 minutes For a reaction A Products , the concentration of A changes from 0.1 M to 0.025 M in 40 minutes . If the reaction follows first-order kinetics, what is the rate constant? 0.0346 min -1 0.0173 min -1 0.0693 min -1 0.0086 min -1 The time for 75 % completion of a zero-order reaction is: 1.5 t 1/2 2 t 1/2 3 t 1/2 1.33 t 1/2 Radioactive decay follows which order of kinetics? First order Zero order Second order Fractional order The integrated rate equation for a second-order reaction 2A Product is given by: 1 [A] = 1 [A] 0 + kt [A] = [A] 0 - kt ln [A] = ln [A] 0 - kt 1 [A] 2 = 1 [A] 0 2 + 2kt The slope of the plot of [A] vs t for a first-order reaction is: -k/2.303 -k k/2.303 -2.303/k For a reaction A B , the rate of reaction quadruples when the concentration of A is doubled. The half-life of this reaction is: Inversely proportional to initial concentration Independent of initial concentration Directly proportional to initial concentration Directly proportional to the square of initial concentration The rate constant for a first-order reaction is k . The time required for 90 % completion is approximately: 2.303/k 1.151/k 0.693/k 4.606/k If 60% of a first order reaction was completed in 60 minutes, 50% of the same reaction would be completed in approximately 45 minutes 60 minutes 40 minutes 50 minutes (log 4 = 0.60, log 5 = 0.69) The rate of a first-order reaction is 0.04 mol l -1 s -1 at 10 seconds and 0.03 mol l -1 s -1 at 20 seconds after initiation of the reaction. The half-life period of the reaction is : 24.1 s 34.1 s 44.1 s 54.1 s If the rate constant for a first order reaction is k, the time (t) required for the completion of 99% of the reaction is given by: t = 2.303/k t = 0.693/k t = 6.909/k t = 4.606/k If the half-life ( t 1/2 ) for a first order reaction is 1 minute, then the time required for 99.9% completion of the reaction is closest to : 10 minutes 2 minutes 4 minutes 5 minutes The decomposition of dimethyl ether is a first-order reaction and is followed by increase in pressure in a closed vessel. The rate constant is given by: k = 2.303 t log P i 2P i - P t k = 2.303 t log P i P i - P t k = 2.303 t log 2P i P i - P t k = 2.303 t log P t P i The rate constant for a second-order reaction is 8 10 -5 M -1 min -1 . How long will it take for the concentration of reactant to drop from 1.0 M to 0.5 M ? 1.25 10 4 min 6.25 10 3 min 2.5 10 4 min 1.25 10 3 min What is the half-life of a first-order reaction if the rate constant is 6.93 10 -3 min -1 ? 100 min 10 min 69.3 min 0.693 min For a first-order reaction A B , the rate constant k = 0.693 min -1 . If we start with 10 mol/L , the rate of the reaction after 1 minute will be: 3.465 mol L -1 min -1 6.93 mol L -1 min -1 0.693 mol L -1 min -1 10 mol L -1 min -1 For the reaction A(g) 2B(g) + C(g) , the initial pressure was P 0 . After time t , the total pressure was P t . The rate constant k for the first-order reaction is: k = 2.303 t 2P 0 3P 0 - P t k = 2.303 t P 0 2P 0 - P t k = 2.303 t P 0 P 0 - P t k = 2.303 t 2P 0 P t For a gaseous reaction A(g) → 2B(g) + C(g) , the total pressure at time t is P t and the initial pressure is P 0 . The integrated rate equation for this first-order reaction is: k = 2.303 t ጒog 2P 0 3P 0 - P t k = 2.303 t ጒog P 0 P t k = 2.303 t ጒog P 0 2P 0 - P t k = 2.303 t ጒog 2P 0 P 0 - P t A first-order reaction is 20 % complete in 10 minutes. What is the time required for 80 % completion? 72.1 min 40 min 80 min 100 min For a reaction X(g) Y(g) + Z(g) , the pressure of the system increases from 100 mm Hg to 150 mm Hg in 10 minutes. If the reaction is first-order, the rate constant is: 0.0693 min -1 0.693 min -1 0.02303 min -1 0.1 min -1 For a gaseous reaction A(g) B(g) + C(g) , the rate constant is k . If the initial pressure is P i and the total pressure at time t is P t , the expression for k is: k = 2.303 t P i 2P i - P t k = 2.303 t P i P i - P t k = 2.303 t P i P t k = 2.303 t 2P i P t The rate constant k for a certain reaction is 2.5 10 -2 min -1 . If we start with 10 moles/L of reactant, the rate of reaction after 20 minutes is: 0.152 mol L -1 min -1 0.250 mol L -1 min -1 0.062 mol L -1 min -1 0.015 mol L -1 min -1 For a reaction A B , the rate constant is 0.5 s -1 . If the initial concentration of A is 2.0 M , the concentration of A after 2 seconds is: 0.736 M 1.0 M 0.25 M 0.5 M For a second-order reaction, the time required for the concentration to drop from C to C/2 is t . The time required for the concentration to drop from C/2 to C/4 is: 2t t t/2 4t 2A ->[k] B is a zero-order reaction, where k = 1.0 mol L -1 min -1 . If the initial concentration of A is 2 M, then the time taken to complete 75% of the reaction will be 1.5 min 0.75 min 1.0 min 2.0 min