6 The nuclear transnutation reaction of X is a first order r

6. The nuclear transnutation reaction of X is a first order react ion It the half-life of X is 188.5 hours, how much would a sample weighing 14.55 mg today weigh at the sane tine tomorrow? Answer 7. The decomposition of a compound is known to be a first order reaction. If the half-life of the reaction ia 6.25 minutes at 65c what is the value of the rate constant for the reaction at this temperature? Answer 8. Write the equilibriun law for the following chemical reaction TiO2(s) + C(o) + 2Cl2(8) TC4(R)+CO2(8) Answer 9. The following reactions occur at 500 K. Arrange them in order of increasing tendency to proceed to completion (least greatest tendency) K 4.0x 108 K, 1.3x 10 K 2.5x 1010 Kp= 3,0 x 10-11 Answer: 10. For the reaction so2c12(g) solo . cl2(g) the addition of more chlorine gas will cause the reaction to shift to the Answer: 11. For the reaction s02c121g) s02g) Cl2(g) the removal of sultur dioxide gas will cause the reaction to shift to the Answer:

Solution

Ans. #6. Integrated rate law for first order reaction-

            ln [A]_t / [A]_o ) = - (0.693 / t_1/2)t             ------------- equation 1

            where,

                        [A]_t = Concentration of reactant at time t

                        [A]_o = Initial concentration of reactant     

                        t = time of progression of reaction

                        t_1/2 = Half-life

Putting the values in equation 1-

            ln ([A]_t / 14.55 mg) = - (0.693 / 188.5 hr) x 24 hr

            Or, 2.303 log ([A]_t / 14.55 mg) = - 0.0882

            Or, log ([A]_t / 14.55 mg) = -0.0882 / 2.303 = -0.03829

            Or, [A]_t / 14.55 mg = antilog (-0.03829) = 0.9156

            Or, [A]_t = 0.9156 x 14.55 mg = 13.32

Therefore, amount remaining after 1 day (24 hr) = 13.32 mg

#7. Half-life of a first order reaction is given by-

t_1/2 = 0.693 / k                                                           ; where, k = rate constant

Or, k = 0.693 / t_1/2 = 0.693 / 6.25 min

Hence, k = 0.11 min^-1

#8. Equilibrium constant, Keq = [TiCl₄] [CO₂] / [Cl₂]²

Note: the “solid” phases are NOT included in Keq expression.

#9. Greater is the value of Kp, greater is the concertation of products and lower is the concertation of reactions at equilibrium. That is, greater is Kp, greater is the completion of reactions.

So, correct order (least to greatest tendency) of completion is-

            4 (smallest Kp) < 2 < 3 < 1 (highest Kp)

#10. Le Chatelier’s principle states “if a dynamic equilibrium is disturbed by changing the conditions (Concentration, Volume, Pressure, temperature, etc.), the position of equilibrium shifts to counteract the change to reestablish an equilibrium”.

# When Cl₂ (product) is added to the equilibrium mixture, the reaction proceeds in backward direction (to the left to form reactants) to re-establish equilibrium.

#11. Following Le Chatelier’s principle, removal of SO₂(product) from equilibrium mixture will shift the equilibrium towards the right to form more SO₂ and re-establish the equilibrium.