Q: For the roasting reaction 4FeS_2 + 11O_2 \rightarrow 2Fe_2O_3 + 8SO_2, at a certain instant SO_2 is being formed at 4.0\times10^{-3}\,mol\,L^{-1}s^{-1}. The rate of consumption of O_2 at that instant is:

5.5\times10^{-3}\,mol\,L^{-1}s^{-1}. \dfrac{1}{11}\left(-\dfrac{d[O_2]}{dt}\right)=\dfrac{1}{8}\dfrac{d[SO_2]}{dt}, so -\dfrac{d[O_2]}{dt}=\dfrac{11}{8}(4.0\times10^{-3})=5.5\times10^{-3}\,mol\,L^{-1}s^{-1}.

Q: For the combustion C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O, at an instant CO_2 is being formed at 6.0\times10^{-3}\,mol\,L^{-1}s^{-1}. The rate of consumption of O_2 at that instant is:

1.0\times10^{-2}\,mol\,L^{-1}s^{-1}. \dfrac{1}{3}\dfrac{d[CO_2]}{dt}=\dfrac{1}{5}\left(-\dfrac{d[O_2]}{dt}\right), so -\dfrac{d[O_2]}{dt}=\dfrac{5}{3}(6.0\times10^{-3})=1.0\times10^{-2}\,mol\,L^{-1}s^{-1}.

Q: For a reaction the concentration of the reactant R is: [R]=0.240\,M at t=0, 0.180\,M at t=30\,s and 0.150\,M at t=60\,s. The average rate of disappearance of R over the first 60\,s is:

1.5\times10^{-3}\,mol\,L^{-1}s^{-1}. Average rate =\dfrac{\Delta[R]}{\Delta t}=\dfrac{0.240-0.150}{60}=\dfrac{0.090}{60}=1.5\times10^{-3}\,mol\,L^{-1}s^{-1}.

Q: For a reaction [A] falls uniformly (linearly) from 0.500\,M at t=0 to 0.300\,M at t=50\,s. The concentration of A at t=35\,s and the average rate of disappearance over the first 35\,s are, respectively:

[A]=0.360\,M and rate =4.0\times10^{-3}\,mol\,L^{-1}s^{-1}. Uniform rate =\dfrac{0.500-0.300}{50}=4.0\times10^{-3}; [A]_{35}=0.500-(4.0\times10^{-3})(35)=0.360\,M.

Q: In a gaseous reaction a reactant is being consumed at 3.0\times10^{-4}\,mol\,L^{-1}s^{-1} at a temperature where RT=20\,L\,atm\,mol^{-1}. Using p=CRT, the rate of decrease of its partial pressure is:

6.0\times10^{-3}\,atm\,s^{-1}. p=CRT\Rightarrow \dfrac{dp}{dt}=RT\dfrac{dC}{dt}=20\times3.0\times10^{-4}=6.0\times10^{-3}\,atm\,s^{-1}.

Q: The partial pressure of a gaseous reactant falls at 0.030\,atm\,s^{-1} at a temperature where RT=24\,L\,atm\,mol^{-1}. The rate of disappearance of the reactant expressed in concentration units is:

1.25\times10^{-3}\,mol\,L^{-1}s^{-1}. C=\dfrac{p}{RT}\Rightarrow \dfrac{dC}{dt}=\dfrac{1}{RT}\dfrac{dp}{dt}=\dfrac{0.030}{24}=1.25\times10^{-3}\,mol\,L^{-1}s^{-1}.

Q: For 2A + 3B \rightarrow C + 2D, the rate of the reaction defined as r=-\dfrac{1}{2}\dfrac{d[A]}{dt}=-\dfrac{1}{3}\dfrac{d[B]}{dt}=\dfrac{d[C]}{dt} equals 1.2\times10^{-3}\,mol\,L^{-1}s^{-1}. The rate of disappearance of B is:

3.6\times10^{-3}\,mol\,L^{-1}s^{-1}. -\dfrac{d[B]}{dt}=3r=3(1.2\times10^{-3})=3.6\times10^{-3}\,mol\,L^{-1}s^{-1}.

Q: For the redox reaction 2MnO_4^- + 5C_2O_4^{2-} + 16H^+ \rightarrow 2Mn^{2+} + 10CO_2 + 8H_2O, CO_2 is evolved at 5.0\times10^{-3}\,mol\,L^{-1}s^{-1}. The rate of disappearance of MnO_4^- is:

1.0\times10^{-3}\,mol\,L^{-1}s^{-1}. \dfrac{1}{2}\left(-\dfrac{d[MnO_4^-]}{dt}\right)=\dfrac{1}{10}\dfrac{d[CO_2]}{dt}, so -\dfrac{d[MnO_4^-]}{dt}=\dfrac{2}{10}(5.0\times10^{-3})=1.0\times10^{-3}\,mol\,L^{-1}s^{-1}.

Question 1

For the roasting reaction 4FeS_2 + 11O_2 ightarrow 2Fe_2O_3 + 8SO_2, at a certain instant SO_2 is being formed at 4.0	imes10^{-3}\,mol\,L^{-1}s^{-1}. The rate of consumption of O_2 at that instant is:

Accepted Answer

5.5	imes10^{-3}\,mol\,L^{-1}s^{-1}. \dfrac{1}{11}\left(-\dfrac{d[O_2]}{dt}ight)=\dfrac{1}{8}\dfrac{d[SO_2]}{dt}, so -\dfrac{d[O_2]}{dt}=\dfrac{11}{8}(4.0	imes10^{-3})=5.5	imes10^{-3}\,mol\,L^{-1}s^{-1}.

Question 2

For the combustion C_3H_8 + 5O_2 ightarrow 3CO_2 + 4H_2O, at an instant CO_2 is being formed at 6.0	imes10^{-3}\,mol\,L^{-1}s^{-1}. The rate of consumption of O_2 at that instant is:

Accepted Answer

1.0	imes10^{-2}\,mol\,L^{-1}s^{-1}. \dfrac{1}{3}\dfrac{d[CO_2]}{dt}=\dfrac{1}{5}\left(-\dfrac{d[O_2]}{dt}ight), so -\dfrac{d[O_2]}{dt}=\dfrac{5}{3}(6.0	imes10^{-3})=1.0	imes10^{-2}\,mol\,L^{-1}s^{-1}.

Question 3

For a reaction A \rightarrow products the concentration of A varies with time as [A]=0.50-0.02\,t-0.003\,t^2 (with [A] in mol\,L^{-1} and t in s). The instantaneous rate of disappearance of A at t=10\,s is:

Accepted Answer

0.08\,mol\,L^{-1}s^{-1}. -\dfrac{d[A]}{dt}=0.02+0.006\,t; at t=10\,s this is 0.02+0.06=0.08\,mol\,L^{-1}s^{-1}.

Question 4

For a reaction the concentration of the reactant R is: [R]=0.240\,M at t=0, 0.180\,M at t=30\,s and 0.150\,M at t=60\,s. The average rate of disappearance of R over the first 60\,s is:

Accepted Answer

1.5	imes10^{-3}\,mol\,L^{-1}s^{-1}. Average rate =\dfrac{\Delta[R]}{\Delta t}=\dfrac{0.240-0.150}{60}=\dfrac{0.090}{60}=1.5	imes10^{-3}\,mol\,L^{-1}s^{-1}.

Question 5

For a reaction [A] falls uniformly (linearly) from 0.500\,M at t=0 to 0.300\,M at t=50\,s. The concentration of A at t=35\,s and the average rate of disappearance over the first 35\,s are, respectively:

Accepted Answer

[A]=0.360\,M and rate =4.0	imes10^{-3}\,mol\,L^{-1}s^{-1}. Uniform rate =\dfrac{0.500-0.300}{50}=4.0	imes10^{-3}; [A]_{35}=0.500-(4.0	imes10^{-3})(35)=0.360\,M.

Question 6

In a gaseous reaction a reactant is being consumed at 3.0	imes10^{-4}\,mol\,L^{-1}s^{-1} at a temperature where RT=20\,L\,atm\,mol^{-1}. Using p=CRT, the rate of decrease of its partial pressure is:

Accepted Answer

6.0	imes10^{-3}\,atm\,s^{-1}. p=CRT\Rightarrow \dfrac{dp}{dt}=RT\dfrac{dC}{dt}=20	imes3.0	imes10^{-4}=6.0	imes10^{-3}\,atm\,s^{-1}.

Question 7

The partial pressure of a gaseous reactant falls at 0.030\,atm\,s^{-1} at a temperature where RT=24\,L\,atm\,mol^{-1}. The rate of disappearance of the reactant expressed in concentration units is:

Accepted Answer

1.25	imes10^{-3}\,mol\,L^{-1}s^{-1}. C=\dfrac{p}{RT}\Rightarrow \dfrac{dC}{dt}=\dfrac{1}{RT}\dfrac{dp}{dt}=\dfrac{0.030}{24}=1.25	imes10^{-3}\,mol\,L^{-1}s^{-1}.

Question 8

For 2A + 3B ightarrow C + 2D, the rate of the reaction defined as r=-\dfrac{1}{2}\dfrac{d[A]}{dt}=-\dfrac{1}{3}\dfrac{d[B]}{dt}=\dfrac{d[C]}{dt} equals 1.2	imes10^{-3}\,mol\,L^{-1}s^{-1}. The rate of disappearance of B is:

Accepted Answer

3.6	imes10^{-3}\,mol\,L^{-1}s^{-1}. -\dfrac{d[B]}{dt}=3r=3(1.2	imes10^{-3})=3.6	imes10^{-3}\,mol\,L^{-1}s^{-1}.

Question 9

For the gaseous decomposition A(g) \rightarrow 2B(g) + C(g) carried out in a rigid vessel, the partial pressure of A is falling at 0.010\,atm\,s^{-1} at an instant. The rate of increase of the total pressure at that instant is:

Accepted Answer

0.020\,atm\,s^{-1}. p_A falls at 0.010, p_B rises at 0.020, p_C rises at 0.010; \dfrac{dp_{tot}}{dt}=-0.010+0.020+0.010=+0.020\,atm\,s^{-1}.

Question 10

For the redox reaction 2MnO_4^- + 5C_2O_4^{2-} + 16H^+ ightarrow 2Mn^{2+} + 10CO_2 + 8H_2O, CO_2 is evolved at 5.0	imes10^{-3}\,mol\,L^{-1}s^{-1}. The rate of disappearance of MnO_4^- is:

Accepted Answer

1.0	imes10^{-3}\,mol\,L^{-1}s^{-1}. \dfrac{1}{2}\left(-\dfrac{d[MnO_4^-]}{dt}ight)=\dfrac{1}{10}\dfrac{d[CO_2]}{dt}, so -\dfrac{d[MnO_4^-]}{dt}=\dfrac{2}{10}(5.0	imes10^{-3})=1.0	imes10^{-3}\,mol\,L^{-1}s^{-1}.

Question 11

In a reaction the amount of product x (in mol\,L^{-1}) formed up to time t (in s) is x=0.4\,t-0.01\,t^2. The rate of formation of the product at t=15\,s is:

Accepted Answer

0.10\,mol\,L^{-1}s^{-1}. \dfrac{dx}{dt}=0.4-0.02\,t; at t=15\,s this is 0.4-0.30=0.10\,mol\,L^{-1}s^{-1}.

Question 12

For A \rightarrow products with [A]_0=0.80\,M, the fraction of A reacted is 0.20 at t=100\,s and 0.50 at t=250\,s. The average rate of disappearance of A between 100\,s and 250\,s is:

Accepted Answer

1.6	imes10^{-3}\,mol\,L^{-1}s^{-1}. [A]_{100}=0.80(0.80)=0.64, [A]_{250}=0.80(0.50)=0.40; average rate =\dfrac{0.64-0.40}{150}=1.6	imes10^{-3}\,mol\,L^{-1}s^{-1}.

Question 13

For 2H_2S + SO_2 ightarrow 3S + 2H_2O, at an instant H_2S is being consumed at 4.0	imes10^{-3}\,mol\,L^{-1}s^{-1}. The rate of formation of sulfur (S) at that instant is:

Accepted Answer

6.0	imes10^{-3}\,mol\,L^{-1}s^{-1}. \dfrac{1}{2}\left(-\dfrac{d[H_2S]}{dt}ight)=\dfrac{1}{3}\dfrac{d[S]}{dt}, so \dfrac{d[S]}{dt}=\dfrac{3}{2}(4.0	imes10^{-3})=6.0	imes10^{-3}\,mol\,L^{-1}s^{-1}.

Question 14

For 2NO_2(g) ightarrow 2NO(g) + O_2(g) in a closed rigid vessel, at an instant -\dfrac{dp_{NO_2}}{dt}=8.0	imes10^{-3}\,atm\,s^{-1}. The rate of increase of the total pressure at that instant is:

Accepted Answer

4.0	imes10^{-3}\,atm\,s^{-1}. p_{NO} rises at 8.0	imes10^{-3}, p_{O_2} rises at 4.0	imes10^{-3}, p_{NO_2} falls at 8.0	imes10^{-3}; net \dfrac{dp_{tot}}{dt}=+4.0	imes10^{-3}\,atm\,s^{-1}.

Question 15

For A + 3B \rightarrow 2C carried out in a 2\,L closed vessel, 0.60\,mol of C is produced in 50\,s. The average rate of consumption of B over this period is:

Accepted Answer

9.0	imes10^{-3}\,mol\,L^{-1}s^{-1}. [C] rises at \dfrac{0.60/2}{50}=6.0	imes10^{-3}; -\dfrac{d[B]}{dt}=\dfrac{3}{2}\dfrac{d[C]}{dt}=\dfrac{3}{2}(6.0	imes10^{-3})=9.0	imes10^{-3}\,mol\,L^{-1}s^{-1}.

Question 16

For A + B ightarrow P: Exp 1 [A]=0.10, [B]=0.20, rate =2.0	imes10^{-3}; Exp 2 [A]=0.20, [B]=0.20, rate =8.0	imes10^{-3}; Exp 3 [A]=0.20, [B]=0.40, rate =8.0	imes10^{-3} (all in mol,\,L,\,s units). The rate law is:

Accepted Answer

Rate=k[A]^2. Exp 1ightarrow2: [A] doubles, rate 	imes4\Rightarrow order 2 in A. Exp 2ightarrow3: [B] doubles, rate unchanged \Rightarrow order 0 in B. Hence Rate=k[A]^2.

Question 17

A reaction is second order overall with Rate=k[A]^2. When [A]=0.050\,M the rate is 4.0	imes10^{-4}\,mol\,L^{-1}s^{-1}. The rate constant k is:

Accepted Answer

0.16\,L\,mol^{-1}s^{-1}. k=\dfrac{Rate}{[A]^2}=\dfrac{4.0	imes10^{-4}}{(0.050)^2}=\dfrac{4.0	imes10^{-4}}{2.5	imes10^{-3}}=0.16\,L\,mol^{-1}s^{-1}.

Question 18

A reaction has the rate law Rate=k[A]^{1/2}[B]^2. If [A] is increased 4-fold and [B] is doubled, the rate becomes:

Accepted Answer

8 times the original. Factor =(4)^{1/2}(2)^2=2	imes4=8.

Question 19

The rate constant of a reaction of overall order \dfrac{5}{2} has the units:

Accepted Answer

mol^{-3/2}\,L^{3/2}\,s^{-1}. k has units (mol\,L^{-1})^{1-n}s^{-1}; for n=\dfrac{5}{2} this is (mol\,L^{-1})^{-3/2}s^{-1}=mol^{-3/2}L^{3/2}s^{-1}.

Question 20

A first-order reaction has k=2.0	imes10^{-2}\,s^{-1}. At an instant its rate is 3.0	imes10^{-4}\,mol\,L^{-1}s^{-1}. The concentration of the reactant at that instant is:

Accepted Answer

1.5	imes10^{-2}\,M. For first order Rate=k[A], so [A]=\dfrac{Rate}{k}=\dfrac{3.0	imes10^{-4}}{2.0	imes10^{-2}}=1.5	imes10^{-2}\,M.

Chemical Kinetics — JEE Main Chemistry MCQs with Solutions

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