Fundamentals of General Chemistry. Terms and Problems in Tests In 2 parts. P.1. Terms and Examples in Tasks. Study guide

7 . 2 . W o r k e d e x a m p l e s

Example 1. Calculate the pH of aqueous 5.0 10–2 mol/L nitric acid.

Answer

Nitric acid (table 7.1) is a strong acid and is fully dissociated in water

HNO3(aq) + H2O(l) H3O+(aq) + NO−3 (aq).

Therefore, the concentration of H3O+ (hydronium or oxonium ions) is the same as the initial concentration of HNO3

[H3O+] = С(HNO3) = 5.0 10–2 mol/L

pH = −log [H3O+] = −log (5.0 10–2) = – (–2 + 0.7) = 1.3.

Example 2. In what direction does the chemical equilibrium of the reaction

Cr2O27−(aq) + 2OH−(aq) 2CrO24−(aq) + H2O(l)

shift when KOH is added to the solution?

Answer

In basic solution orange Cr2O27− (dichromate) is converted into yellow

CrO24− (chromate). We use the Le Chatelier’s principle, which states that the position of chemical equilibrium always shifts in direction that tends to reduce that change in conditions. If OH− (KОН) is added to the equilibrium mixture, the chemical equilibrium shifts to the right-hand side to consume the excess alkali.

Example 3. Explain how does external pressure change the chemical equilibrium in the system

2SO2(g) + O2(g) 2SO3(g).

Answer

A change of pressure affects in the chemical equilibrium of reaction involving gaseous components if the reaction is accompanied by a change in the volume of the system. According to Le Chatelier’s principle, an increase in external pressure will shift chemical equilibrium towards the reaction that will reduce the volume of system.

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According to the equation

2SO2(g) + O2(g) 2SO3(g)

the forward reaction involves three moles of gaseous reactants going to two moles of gaseous products. In the reverse reaction the number of moles of gas increases. In order to encourage the forward reaction, the external pressure could be increased. The reverse reaction proceeds by a decrease in the external pressure.

7 . 3 . T a s k s f o r s e l f - c o n t r o l

1. The self-ionization constant of water Kw at 25 оС is: А) 10−14; B) 10−18; C) 10−23.

2. The concentration of KOH in aqueous solution is 10−4 mol/L. The pH of this solution is:

А) 1; B) 4; C) 10; D) 11.

3. The self-ionization constant of water Kw at 20 оС is 0.69·10–14. The pH of a neutral solution under these conditions is:

А) рН = 7.00; В) рН = 7.08; С) рН = 6.90; D) рН = 13.84.

6. For the reaction

2NO(g) + O2(g) 2NO2(g) the units of the equilibrium constant:

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8. If [H2] = 18.14 mol/L; [I2] = 0.41 mol/L; [HI] = 19.38 mol/L, then the value of the equilibrium constant for the reaction

2HI(г) H2(г) + I2(г)

9. For a chemical equilibrium

H2SO4(aq)  H+(aq) + HSO−4 (aq) the dissociation constant expression is:

11. Among the following acids, the strongest is: А) H2Te, Ka1 = 2.3∙ 10−3;

B)HCN, Ka = 1 ∙ 10−10;

C)HBr, Ka = 1 ∙ 109;

D)HI, Ka = 1 ∙ 1011.

12. Among the following acids, the weakest is: А) HClO, Ka = 2.95∙10−8;

B)HClO2, Ka = 1.1∙ 10−2;

C)HClO3, Ka = 1∙ 103;

D)HClO4, Ka = 1∙ 108.

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13.The solubility of salts in the row AgCl – AgBr – AgI decreases. The values for the solubility constant Ksp in this row:

A) does not change; B) increases;

C) decreases.

14.The solubility constant Ksp for CaSO4 is 9.1∙10−6. The solubility of СaSO4 in mol/L is:

А) 3.016 ∙ 10−3 mol/L; B) 9.1 ∙ 10−6 mol/L; C) 2.08 ∙ 10−2 mol/L.

7 . 4 . З а д а н и я д л я с а м о к о н т р о л я

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6. Для реакции

2NO(г) + O2(г) 2NO2(г)

размерность константы равновесия:

А) моль л−1; Б) л моль−1; В) безразмерная; Г) л2 моль−2.

7. Для реакции

NH4Cl(к) NH3(г) + HCl(г)

размерность константы равновесия:

8. Если [H2] = 18.14 моль/л; [I2] = 0.41 моль/л; [HI] = 19.38 моль/л, то значение константы равновесия для реакции

2HI(г) H2(г) + I2(г)

9. Химическому равновесию

H2SO4(aq)  H+(aq) + HSO−4 (aq)

соответствует выражение константы:

10. Константа ионизации фосфорной кислоты по первой ступени:

А) Ka = 7.1 10−3; Б) Ka = 6.2 10−8; В) Ka = 5.0 10−13.

11.Наиболее сильной из кислот является:

А) H2Te, Ka1 = 2.3 ∙ 10−3;

Б) HCN, Ka = 1 ∙ 10−10; В) HBr, Ka = 1 ∙ 109; Г) HI, Ka = 1 ∙ 1011.

12.Наиболее слабой из кислот является:

А) HClO, Ka = 2.95 ∙ 10−8;

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Б) HClO2, Ka = 1.1 ∙ 10−2;

В) HClO3, Ka = 1 ∙ 103;

Г) HClO4, Ka = 1 ∙ 108.

13.C уменьшением растворимости соли в ряду AgCl – AgBr – AgI произведение растворимости соли:

А) не изменяется; Б) возрастает; В) уменьшается.

14.Произведение растворимости ПР(CaSO4) = 9.1∙10−6. Растворимость соли (моль/л ):

А) 3.016 ∙ 10−3 моль/л; Б) 9.1 ∙ 10−6 моль/л;

В) 2.08 ∙ 10−2 моль/л.

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8 . 2 . W o r k e d e x a m p l e s

Example 1. For the reaction

write the kinetic equations to determine reaction rate. Determine the units of the reaction rate constant, if the reaction order with respect to the A reactant is zero or one.

Answer

The rate of a chemical reaction at a constant volume is a change in the concentration of a reactant or product (in mol/L) per unit time (in s) and this gives units of rate as mol·L–1·s–1. The average reaction rate av in the time interval from t1 to t2 is determined by the relation

where C1, C2 are concentrations of a reactant or product (in mol/L) at times t1 and t2 respectively.

The rate of reaction can be expressed through a decrease in the concentration of the A reactant at a given time, and is written mathematically as the negative differential coefficient (derivative) of [A] with respect to time, t:

where the square brackets indicate the A reactant concentration in mol/L at a given time. The equation (8.3) characterizes the instantaneous rate of reaction. Since the concentrations of reactants always decrease at a given time, any rate expression involving a reactant includes a negative sign. When the instantaneous reaction rate is determined by the products B, C, the concentration of which increases, then for the reaction equation (8.1)

= − d[A]dt = + d[B]dt = + d[C]dt .

The general expression, which shows how the chemical reaction ratedepends on the concentrations of reactants, is called a rate law or the kinetic equation. For the reaction (8.1) the kinetic equation has form

= k[A]n,

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where n is the order of the reaction with respect to A and may be zero or have an integral or fractional value; the order is established experimentally and shows the exact dependence of the rate on [A] reactant. Parameter k is the rate constant for the reaction; the units of the rate constant depend on the reaction order.

For example, when a reaction is zero order with respect to a reactant A, the rate does not depend upon the concentration of A and the rate equation is:

= − d[A]dt = k[A]0.

Then

= k[A]0 = k,

so the units of k are mol L−1 s−1.

When a reaction is first order with respect to a reactant A, the rate depends upon the concentration of A according to the kinetic equation:

then the units of k are s−1.

Example 2. The temperature coefficient of the reaction rate is 2. How many times will the reaction rate increase with increasing temperature from 40 to 80 °C?

Answer

The empirical rule (Vant-Hoff rule) establishes the dependence of the reaction rate on temperature: a rise in temperature by 10 K leads to an increase in the reaction rate, , by about 2–4 times or mathematically:

(T2 − T1)

T2 = T1 10 ,

where T1 and T2 represent initial and final temperature respectively, is the temperature coefficient of the reaction rate, showing how many times the reaction rate will increase with a temperature increase of 10 K.

Then

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8 . 3 . T a s k s f o r s e l f - c o n t r o l

1. In a catalytic reaction the catalyst:

A.reduces the activation energy of the reaction;

B.changes the equilibrium constant of the reaction;

C.is changed during a chemical reaction;

D.does not change the reaction mechanism.

2. The effect of the catalyst on the reaction profile is shown in curve 2 of the figure:

3. The reaction rate increases by a factor of 16 for a rise in temperature from 60 to 80 °C. The temperature coefficient of the reaction rate is:

А) 8; B) 2; C) 4; D) 16.

4.The increase in the reaction rate after the addition of the catalyst is associated with:

А) a decrease in the activation energy of a new reaction pathway; B) an increase in the enthalpy of the system;

C) an increase in the activation energy of a new reaction pathway; D) an increase in pressure of the system.

5.If the rate constant of the first reaction (k') is greater than the rate constant of the second reaction (k"), then the ratio between the activation energies of these reactions is:

6. The Vant-Hoff rule on the temperature dependence of the reaction rate is:

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