**ANSWER THE FOLLOWING QUESTIONS**

**1. Define average rate and instantaneous rate.**

**2. Define rate law and rate constant.**

**Rate constant**

**3. Derive integrated rate law for a zero order reaction A ⎯⎯→ product.**

**4. Define half life of a reaction. Show that for a first order reaction half life is independent of initial concentration.**

**First order reaction half-life**

**5. What is an elementary reaction? Give the differences between order and molecularity of a reaction.**

**6. Explain the rate determining step with an example.**

**7. Describe the graphical representation of first order reaction.**

**8. Write the rate law for the following reactions.**

**(a) A reaction that is 3/2 order in x and zero order in y.**

**(b) A reaction that is second order in NO and first order in Br**

_{2}.

**9. Explain the effect of catalyst on reaction rate with an example.**

**10. The rate law for a reaction of A, B and L has been found to be rate = k [A]**

^{2}[B] [L]^{3/2}.**How would the rate of reaction change when**

**(i) Concentration of [L] is quadrupled**

**(ii) Concentration of both [A] and [B] are doubled**

**(iii) Concentration of [A] is halved**

**(iv) Concentration of [A] is reduced to (1/3) and concentration of [L] is quadrupled.**

**11. The rate of formation of a dimer in a second order reaction is 7.5 × 10**

^{–3}mol L^{–1}s^{–1 }at 0.05 mol L^{–1}monomer concentration. Calculate the rate constant.^{2}

**12. For a reaction X + Y + Z ⎯⎯→ products the rate law is given by rate = k [X**

^{3/2}[Y]^{1/2}.

**What is the overall order of the reaction and what is the order of the reactionwith respect to z.**

**13.Explain briefly the collision theory of bimolecular reactions. (or) Derive**

^{9}collision per seconds at 298K and 1 atm pressure.

**14. Write Arrhenius equation and explains the terms involved.**

^{-1})

^{–1}mol

^{–1})

**15. The decomposition of Cl**

_{2}O_{7}at 500 K in the gas phase to Cl_{2}and O_{2}is a first order reaction.**After 1 minute at 500K, the pressure of Cl**

_{2}O_{7}falls from 0.08 to 0.04 atm.**Calculate the rate constant in s**

^{– 1}.

**17. Explain pseudo first order reaction with an example.**

**Example :**Acid hydrolysis of ester

**18. Identify the order for the following reactions**

**(i) Rusting of Iron**

**(ii) Radioactive disintegration of**

_{92}U^{238}**(iii) 2A + 3B ⎯⎯→ products ; rate = [A]**

^{1/2}[B]^{2}**(i) First order**

**(ii) First order**

**19. A gas phase reaction has energy of activation 200 kJ mol**

^{–1}. If the frequency factor of the reaction is 1.6 × 10^{13}s^{–1}. Calculate the rate constant at 600 K.**( e**

^{−40.09}= 3.8 × 10^{–18})

_{a}= 200 kJ mol

^{–1}

^{13}s

^{–1}

^{–1}mol

^{–1}

**20. For the reaction 2x + y ⎯⎯→ L. Find the rate law from the following data.**

**21. How do concentrations of the reactant influence the rate of reaction?**

**22. How do nature of the reactant influence rate of reaction. (or)**

**Titration between potassium per mangate and oxalic acid is carried out at 60°C where as**

**titration between potassium per manganate and ferrous ammonium sulphate at room**

**temperature. Give reason.**

_{4}vs FAS takes place at room temperature whereas titration between KMnO

_{4}vs Oxalic acid is heated to 60

**°**C. This is because oxidation of oxalate ion by KMnO4 is slow compared to reaction between KMnO

_{4}and Fe

^{2+}.

**23. The rate constant for a first order reaction is 1.54 × 10**

^{–3}s^{–1}. Calculate its half life time.**×**10

**s**

^{–3}^{–1}

_{1/2}= ?

**24. The half life of the homogeneous gaseous reaction SO2Cl**

_{2}⎯⎯→ SO_{2}+ Cl_{2}which obeys first orderkinetics is 8.0 minutes. How long will it take for the concentration of SO_{2}Cl_{2}to be reduced to 1% of the initial value?

**25. The time for half change in a first order decomposition of a substance A is 60 seconds.Calculate the rate constant. How much of A will be left after 180 seconds.**

_{1/2}= 60sec k = ?

_{0}] = 100

**26. A zero order reaction is 20% complete in 20 minutes. Calculate the value of the rate constant.**

**In what time will the reaction be 80% complete?**

_{0}] = 100 [A] = 80

**27. The activation energy of a reaction is 225 k cal mol**

^{–1}and the value of rate constant at 40°C**is 1.8 × 10**

^{–5}s^{–1}. Calculate the frequency factor A._{a }= 225 k cal.mol

^{–1}= 225000 cal .mol

^{–1}

**×**10

^{–5}s

^{–1}

^{–1}mol

^{–1}

**°**C = 40 + 273 = 313 K

**28. Benzene diazonium chloride in aqueous solution decomposes according to the equation C**

_{6}H_{5}N_{2}Cl ⎯⎯→**C**

_{6}H_{5}**Cl + N**

_{2}. Starting with an initial concentration of 10 g L^{–1}, the volume of N_{2}gas obtained at 50°C at different intervals of time was found to be as under:

**Show that the above reaction follows the first order kinetics. What is the value of the rate constant?**

**29. From the following data, show that the decomposition of hydrogen peroxide is a reaction of the first order :**

**Where t is the time in minutes and V is the volume of standard KMnO**

_{4}solution required for titrating the same volume of the reaction mixture.**30. A first order reaction is 40% complete in 50 minutes. Calculate the value of the rate constant.In what time will the reaction be 80% complete?**

_{0}] = 100 [A] = 60 k = ?

**II. EXAMPLES**

**Example-1**

**Consider the oxidation of nitric oxide to form NO**

_{2}

**2NO(g) + O**

_{2}(g) ⎯⎯→ 2NO_{2}(g)

**(a) Express the rate of the reaction in terms of changes in the concentration of NO, O**

_{2}and NO_{2}.**(b) At a particular instant, when [O**

_{2}] is decreasing at 0.2 mol L^{–1}s^{–1}at what rate is [NO_{2}]**increasing at that instant?**

**Example-2**

**What is the order with respect to each of the reactant and overall order of the following reaction?**

^{–}is 1

^{−}is 1

^{+}is 2

**Example-3**

**The rate of the reaction x + 2y → product is 4 × 10**

^{–3}mol L^{–1}s^{–1}, if [x] = [y] = 0.2 M and rate constant at 400 K is 2 × 10^{–2}s^{–1}, What is the overall order of the reaction.^{9}[Y]

^{6}

**×**10

^{–3}= 2

**×**10

^{–2}

**×**(0.2)

^{a}(0.2)

^{b}

**Example-4**

**A first order reaction takes 8 hours for 90% completion. Calculate the time required for**

**80% completion. (log 5 = 0.6989 ; log 10 = 1)**

_{0}] = 100

**Example-5**

**The half life of a first order reaction x → products is 6.932 × 10**

^{4}s at 500 K. What percentage of x would be decomposed on heating at 500 K for 100 min. (e^{0.06}= 1.06)_{1/2}= 6.932 × 10

^{4}s

**Example-6**

**Show that in case of first order reaction, the time required for 99.9% completion is nearly ten times the time required for half completion of the reaction.**

**t**

_{99.9%}**Example-7**

**The rate constant of a reaction of a reaction at 400 and 200 K are 0.04 and 0.02 s**

^{–1}respectively. Calculate the value of activation energy._{1}= 200 K k

_{1}= 0.02 s

^{–1}

_{2}= 400 K k

_{1}= 0.04 s

^{–1}

^{ –1}mol

^{–1}

_{a}= ?

**Example-8**

**Rate constant k of a reaction varies with temperature T according to the following**

**Arrhenius equation**

**Where E**

_{a}

**is the activation energy. When a graph is plotted for log k Vs 1/T astraight line with a slope of –4000 K is obtained. Calculate the activation energy**

**III EVALUATE YOURSELF**

**Evaluate Yourself-1**

**(1) Write the rate expression for the following reactions, assuming them as elementary reactions.**

**(i) 3A + 5B**

_{2}⎯⎯→ 4CD (ii) X_{2}+ Y_{2}⎯⎯→2XY

**(2) Consider the decomposition of N**

_{2}O_{5}(g) to form NO_{2}(g) and O_{2}(g). At a particular instant N_{2}O_{5}disappears at a rate of 2.5 × 10^{–2}mol dm^{–3}s^{–1}. At what rate are NO_{2 }and O_{2}formed? What is the rate of the reaction?**Evaluate Yourself-2**

**(1) For a reaction, X + Y ⎯⎯→ product ; quadrupling [x], increases the rate by a factor of 8.**

**Quadrupling both [x] and [y], increases the rate by a factor 16. Find the order of the**

**reaction with respect to x and y. What is the overall order of the reaction?**

**(2) Find the individual and overall order of the following reaction using the given date**

**2NO**

_{(g)}+Cl_{2(g)}⎯⎯→2NOCl

_{(g)}

**(1)rate = k [X]**

^{a}[Y]^{b}⎯ ⎯→ (1)**8 rate = k [4X]**

^{a}[Y]^{b}⎯ ⎯→ (2)**16 rate = k [4X]**

^{a}[Y]^{b}⎯⎯→ (3)

^{a}

^{b}

^{− 1})

_{2}= 1

_{2}[O

_{2}]–1

**Evaluate Yourself-3**

**(1) In a first order reaction A→ products 60% of the given sample of A decomposes in 40 min.**

**What is the half life of the reaction?**

**(2) The rate constant for a first order reaction is 2.3 10 –4 s –1. If the initial concentration of the reactant is 0.01 M. What concentration will remain after 1 hour?**

**(3) Hydrolysis of an ester in an aqueous solution was studied by titrating the liberated carboxylic acid against sodium hydroxide solution. The concentrations of the ester at**

**different time intervals are given below.**

**Show that, the reaction follows first order kinetics.**

_{0}] = 100

_{1/2}= ?

**Evaluate Yourself-4**

**For a first order reaction the rate constant at 500 K is 8 × 10**

^{–4}s^{–1}. Calculate the frequency factor, if the energy of activation for the reaction is 190 kJ mol^{–1}.

**IV ADDITIONAL QUESTIONS WITH ANSWERS**

**1. Define rate of a reaction.**

**Rate is defined as change in concentration of reactant or product with respect to time.**

**2. Give the unit of rate of reaction for (i) aqueous reaction (ii) Gaseous reaction**

**(i) mol L**

^{–1}s^{–1}(ii) atm s^{–1}**3. How to determine rate of a reaction.**

**4. Differentiate rate and rate constant.**

**5. Define molecularity.**

**It is the total number of reactant speciesthat are involved in an elementary step.**

**6. Define order of a reaction.**

**7. Derive an expression of half life of a zero order reaction.**

**8. Give general expression for half life of nth order reaction.**

**9. Draw a plot of concentration vs time for zero order reaction.**

**10. Give examples of first order reaction.**

**11. Give two examples of zero order reaction.**

**12. Give units of rate constant of**

**(a) first order reaction (b) zero order reaction**

**(a) sec**

^{–1 }(b) mol L^{–1}s^{–1}**13. What is collision frequency?**

**14. Why molecularity can never be more than 3?**

**15. Define activation energy?**

**16. What is the usefulness of Arrhenius equation.**

**17. Mention the factors affecting rate of reaction.**

**18. What does the slope represent in the following graphs.**

**19. Which of the following reaction is fast. Give reason.**

**20. Which of the two reacts faster? Why?**

**(i) Powdered CaCO**

_{3}with dil. HCl**(ii) Lump of CaCO**

_{3}as marble with dil. HCl

**21. Derive integrated rate law for a first order reaction A ⎯⎯→ product.**

**A ⎯⎯→ Product**

_{0}]

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