# Chemical Kinetics

## NCERT InText Questions

Question 1: For the reaction R → P, the concentration of a reactant changes from 0.03M to 0.02M in 25 minutes. Calculate the average rate of reaction using units of time both in minutes and seconds.

R_(av)=(-Δ[R])/(Δt)=(-[R_2-R_1])/(t_2-t_1)

=(0.02-.03)/(25)=(-(-0.01))/(25)

=4xx10^(-4) M mi\n^(-1)=6.66

=6.66xx10^(-6) M s^(-1)

Question 2: In a reaction, 2A → Products, the concentration of A decreases from 0.5 mol L-1 to 0.4 mol L-1 in 10 minutes. Calculate the rate during this interval.

R_(av)=(-1Δ[A])/(2 Δt)=-1/2xx([A]_2-[A]_1)/(t_2-t_1)

=-1/2xx(0.4-0.5)/(10)=-1/2xx(-0.1)/(10)

=5xx10^(-3) M mi\n^(-1)

Question 3: For a reaction A + B → Product, the rate law is given by r=k[A]^(1/2)[B]^2 What is the order of this reaction?

Answer: Order of reaction =1/2+2=(1+4)/2=5/2=2.5

Question 4: The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

Answer: The reaction can be written as: X→Y

As per rate law,

Rate =k[X]^2

If [X] is increased 3 times, then rate can be given as follows:

Rate =k[3X]^2

=9k[X]^2=9 ra\te

So, the rate increases by 9 times.

Question 5: A first order reaction has a rate constant 1.15 × 10-3 s-1. How long will 5 g of this reactatn take to reduce to 3 g?

Answer: Given [A]0 = 5g, [A] = 3 g and k=1.15xx10^(-3)s^(-1)

For 1st order reaction,

t=(2.303)/(k)lo\g\([A]_0)/([A])

=(2.303)/(1.15xx10^(-3)s^(-1))\lo\g\5/3

=2.00xx10^3(lo\g 1.667)

=443.8  s

Question 6: Time required to decompose SO2Cl2 to half of its initial amount is 6.0 minutes. If the decomposition is a first order reaciton, calculate the rate constant of the reaction.

k=(0.693)/(t_(1/2))=(0.693)/(60)

=1.155xx10^(-2)mi\n^(-1)

=1.925xx10^(-4)s^(-1)

Question 7: What will be the effect of temperature on rate constant?

Answer: The rate of most of the chemical reactions increases with increase in temperature. The rate constant nearly doubles with rise in temperature by 10° for a chemical reaction.

Question 8: The rate of the chemical reaction doubles for an increase of 10K in absolute temperature from 298K. Calculate Ea.

Answer: Given, T1 = 298 K, T2 = 308 K, k1 = k, and k2 = 2k

We know,

lo\g\(k_2)/(k_1)=(E_a)/(2.303k)((T_2-T_1)/(T_1T_2))

Or, lo\g\(2k)/k=(E_a)/(2.303xx8.314)((308-298)/(308xx298))

Or, lo\g\ 2=(E_a)/(2.303xx8.314)xx(10)/(308xx298)

Or, E_a=((log\ 2)(2.303xx8.314)(308xx298))/(10)

=52897.7 J mo\l^(-1)

=52.8 kJ mo\l^(-1)

Question 9: The activation energy for the reaction

2HI(g)→H_2+I_2(g)

Is 209.5 kJ mol-1 at 581K. Calculate the fraction of molecules of reactants having energy equal to or greater than activation energy.

Answer: Fraction of molecule having energy equal to or greater than activation energy can be calculated as follows:

x=n/N=e^(-(E_a)/(RT))

So, In x=(-E_a)/(RT)

Or, lo\g x=-(209.5xx10^3)/(2.303xx8.314xx581)=-18.8323

So, x=an\ti\lo\g\(-18.8323)=1.471xx10^(-19)