The examples of solving of typical tasks

1. Homogeneous reaction between A and B substances proceeds according to equation A + B = C, concentration of the A –substance equals 6 Mol/L, and B – substance – 5 Mol/L. The rate constant of the reaction equals 0,5 L²·Mol^-2·C^-1. Calculate the chemical reaction rate at an initial moment and at the moment when 45% of B-substance remains in reaction mixter.

                                                             Solution:

                             2A + B = C

According to the action masses law: υ = k·C²(A)·C(B)

  The chemical reaction rate at initial moment equals υ₀ =0,5·6²·5 = 90,0 mol/L·c. Some time later 45% of the B substance will remain in the reaction mixter and the concentration of B will be equal to C₁(B) = 0,45·5= 2,25 Mol/L it means that the B concentration decreases to: 5,0 –2,25 = 2,75. If the substances A and B react with each other in the ratio 2:1, the A concentration decreases to 5,5 Mol/L (2,75×2) and is equal to 0,5 Mol/L (6,0 –5,5).

  The chemical reaction rate at the moment, when 45% of the B substance remain in the reaction mixter, is υ₁ =0,5·(0,5)²·2,25 = 0,28 mol/L·c.

                                       The answer: υ₀ = 90,0 mol/L·c; υ₁ = 0,28 mol/L·c.

 

2. The glucose oxidation in the organism proceeds through some intermediate stages. The general reaction: C₆H₁₂O_6(s) + 6 O_2(g) = 6CO₂ + H₂O_(l)

  Write down the kinetic equation of this reaction. Determine, how does the reaction rate change: a) in the mountains, where the O₂ concentration is two times lower, in the pressure chamber, where the air pressure is two times as higher as atmospheric.

                             Solution:

Let’s write down the kinetic equation of glucose oxidation reaction:

                              υ = k·C⁶(O₂)

 Assume the initial concentration of O₂ as α Mol/L: C(O₂) = α Mol/L, then

                              υ₀ = k· α ⁶

a)   in the mountains C₁(O₂) = α/2 Mol/L

                              υ = k· (α/2) ⁶ = k· α ⁶/64.

Determine, how does the rate change:

    υ₁               k· α ⁶     1

   —— = ———— = ——

    υ₀              k· α ⁶∙64 64

 Consequently, the reaction rate decreases 64 times less.

 

 b) in pressure chamber C(O₂) = 2 α Mol/L

                               υ₂ = k·(2α)⁶ = 64 k∙ α ⁶

 Let’s determine how does the rate change

υ₂           k· α ⁶∙64        

—— = ———— = 64

υ₀               k· α ⁶     

 Consequently, the reaction rate increases 64 times more.

 

How many times will the glucose oxidation rate in organism decrease, if the body’s temperature decreases from 37⁰ to 30⁰. The temperature coefficient γ = 1,7?

Solution:

According to Vant-Goff’s rule

υ_t2

—— = γ ^t2-t1/10 = 1,7^37-30/10 = 1,5

υ_t1

Consequently, the reaction rate decreases in 1,5 times.

 

The reaction rate increases 16 times more if the temperature increases from 10⁰ to 50⁰C. Determine it’s temperature coefficient

Solution:

According to Vant-Goff’s rule

υ_{50                                                                     4}

—— = γ ^50-10/10; γ ⁴ =16, γ =     16 = 2

υ₁₀

Temperature coefficient of the reaction equals 2.

 

The medicine solution contains 500 active units in milliliter. In 40 days 20 units in ml will remain. This reaction is first-order. Calculate the rate constant and half-life of the reaction.

Solution:

For the first order reaction

 

   2,3     C₀

 k= —— ∙lg ——, where C₀ and C_τ – the initial and current

    τ        C_τ  concentrations, and τ –the time.

            

   τ =24· 40 days = 960 hours.

      

   2,3   500  2,3

k= —— ∙ lg—— = —— ∙1,4= 0,0034 h^-1

   960  20    960

            2,3∙lg2   0,692 0,692 

   τ_1/2= ——— = ——— =———= 203,5(hours)=8,5 days

               k           k    0,0034

4. 48 g of substrate remained in an hour past the beginning of fermentative reaction, and in 3 hours – 27 g. Determine the initial concentration of substrate for the first-order reaction.                               Solution:

For the first-order reaction:

   2,3    C₀

k = —— ∙lg ——

    τ       C_τ

    2,3  C₀            2,3    C₀             C₀       2,3      C₀

k = —— ∙lg —— k = —— ∙ lg——; 2,3∙lg—— =——∙lg——

     1     48             3      27             48     3    27

 

        2,763

     lgC₀ = ——— = 1,806;                  C₀ = 63,97 g of substrate.

                 1,53

5 How will the gas-phase reaction rate change: 4HCl + O₂ → 2Cl₂ + 2H₂O

if to increase three times more: 1) the O₂ concentration 2) the HCl concentration 3) the pressure in the system.

Solution:

Assume the concentrations of HCl and O₂ as X and Y then

               υ = k·C (HCl)·C(O₂) = kX⁴∙Y

After the increase of the concentrations 3 times more they will be equal to 3X for HCl and 3Y for O₂, that’s why:

   1) υ₁ = k∙X⁴∙3Y = 3k∙X⁴∙Y. The rate increases:

                     υ₁   3k∙X⁴∙Y

                  —— = ———— = 3

                     υ     kX⁴∙Y

2) υ₂ = k∙(3X)⁴∙Y =81 ∙ kX⁴∙Y,             υ₂ / υ = 81

            3). The pressure increase leads to the increase of the concentrations of gaseous reactants in the same way,that’s why:

υ₃ = k∙(3X)⁴∙3Y = 243∙ kX⁴∙Y;              υ₃ / υ = 243

 

Question for self-control

1. What does the chemical kinetics study? What is it’s practical aim?

2. What is called the chemical reaction rate, in what units is it measured?

3. Give the definition and examples of homogeneous and heterogeneous reactions. How are their rates found?

4 In what cases the right part of expression υ = ΔC/ Δt have the sign + or –? How is the value υ called?

5. What factors does the chemical reaction rate depend on? Formulate the action masses law?

6. What is called the rate constant? What is the physical meaning of this value? Does the rate constant depend on temperature, nature of reactants, their concentration?

7. Will the value of rate constant change: 1) if one catalyst is substituted by another       2) if the concentrations of reactants change.

8. What is the molecularity of a reaction, the order of a reaction? Give examples uni-, bi-, termolecular reactions, reactions of the nil, first, second, third-orders.

9. Write down the kinetic equations for the following chemical reactions:

             a)H_2(g) + Cl_2(g) → 2HCl_(g)

                  b)2NO_(g) + O_2(g) → 2NO_2(g)

                     c) CaO_(s) + CO_2(g) → CaCO_3(s)

   d) 4NH_3(g) + 3O_2(g) → 2N_2(g) + 6H₂O_(g)

                    e) FeO_(s) + H_2(g) → Fe_(s) + H₂O_(l)

10 How does the pressure influence on the reaction rate?

11 What formulas express the Vant-Goff’s rule the Arrenius equation, which determines the relationship of reaction rate and temperature?

12 What is called the temperature coefficient of reaction rate? What values can it accept?

13 Why does the temperature increasing raises the reaction rate? What molecules are called the active?

14 Does the temperature coefficient of reaction rate depend on activation energy?

15 Does the value of reaction activation energy (for heterogeneous catalysis) depend on catalyst surface area, and it’s structure.

16 The rate of which reactions depends on the temperature in a greater extend: e which have not large activation energy or vice versa.

17 In what case does the reaction rate depend on the temperature in a greater extend: if it proceeds with catalyst or not.

18 What is the activated complex, the activation energy? Show the energy diagram of the reaction, which proceeds with formation of the activated complex.

19 The essence of catalysis. The mechanism of homogeneous and heterogeneous catalysis. The essence of fermentative catalysis.

 

Tasks for self-solution

 

1 During the interaction of SO₂ and O₂ the concentration of the last one decreased by 0,25 Mol/L in an hour. How did the SO₂ concentration change and what is the average reaction rate? The answer: decreased by 0,5 Mol/L; 6,94 Mol/L∙c.

2 During the ammonia synthesis 0,9 Mol/L of H₂ have reacted to this moment, but it’s initial concentration equals 1,4 Mol/L. Determine the concentration of remained hydrogen and reacted nitrogen.

3 Find the rate constant of reaction: 2A + B → C, if it’s rate equal 0,018 Mol/L∙min. Concentrations of A and B at this moment are equal to 0,5 and 0,6 Mol/L respectively.

4 Homogeneous reaction proceeds according to the equation A + 2B → C, it’s rate constant at a given temperature equals 0,4 L²/Mol²∙C and initial concentrations were 0,3 Mol/L of A substance and o,5 Mol/L of B substance. Calculate the reaction rate at the same temperature at initial moment and the moment, when 0,1 Mol/L of A substance have reacted. The answer: 0,03 and 0,0072 Mol/L∙c.

5 How many times should we increase the H₂ concentration in the first case and the pressure in the second case, if it is necessary to increase 216 and 256 times higher the reaction rate of the NH₃ synthesis.         

The answer: to increase 6 and 4 times higher.

6. The temperature coefficient of reaction equals 2,5. How would it’s rate change a) if the temperature increases from 80⁰C to 140⁰C b) if the reaction mixture cools from 50⁰C to 30⁰C. The answer: a)increases 244 times higher b) decreases 6,25 times lower.

6 One of the reactions has been over in 16 minutes at 150⁰ C. If the temperature coefficient of the reaction rate is 2,5, calculate how long would it takes to finish this reaction if it proceeds a) at 200⁰C b) at 80⁰C. The answer: a)9,8s.b)162,77 h.

8. How many times will the reaction rate increase higher at 298⁰ K, if it’s activation energy decreases by 4 kJ/M. The answer: 5 times more.

 

Laboratory works