NCERT solutions for Chemistry - Part 1 and 2 [English] Class 11 chapter 7 - Equilibrium [Latest edition]

A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.

What is the initial effect of the change on vapour pressure?

A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.

How do rates of evaporation and condensation change initially?

A liquid is in equilibrium with its vapour in a sealed container at a fixed temperature. The volume of the container is suddenly increased.

What happens when equilibrium is restored finally and what will be the final vapour pressure?

What is K_c for the following equilibrium when the equilibrium concentration of each substance is: [SO₂] = 0.60 M, [O₂] = 0.82 M and [SO₃] = 1.90 M?

\[\ce{2SO2(g) + O2(g) ⇌ 2SO3(g)}\]

At a certain temperature and total pressure of 10⁵ Pa, iodine vapour contains 40% by volume of I atoms

\[\ce{I2(g) <=> 2I(g)}\]

Calculate K_pfor the equilibrium.

Write the expression for the equilibrium constant, K_c for each of the following reactions:

\[\ce{2NOCl (g) ⇌ 2NO (g) + Cl2 (g)}\]

Write the expression for the equilibrium constant, Kc for the following reactions:

\[\ce{2Cu(NO3)2 (s) ⇌ 2CuO (s) + 4NO2 (g) + O2 (g)}\]

Write the expression for the equilibrium constant, K_c for the following reactions:

\[\ce{CH3COOC2H5(aq) + H2O(l) ⇌CH3COOH (aq) + C2H5OH (aq)}\]

Write the expression for the equilibrium constant, K_c for following reactions:

\[\ce{Fe^{3+}(aq) + 3OH^-(aq) ⇌ Fe(OH)3(s)}\]

Write the expression for the equilibrium constant, Kc for the following reactions

\[\ce{I2 (s) + 5F2 ⇌ 2IF5}\]

Find out the value of K_c for each of the following equilibria from the value of K_p:

\[\ce{2NOCl (g) ⇌ 2NO (g) + Cl2 (g)}\]; K_p= 1.8 × 10^-2 at 500 K

Find out the value of K_c for each of the following equilibria from the value of K_p:

\[\ce{CaCO3 (s) ⇌ CaO(s) + CO2(g)}\]; K_p= 167 at 1073 K

For the following equilibrium, K_c = 6.3 × 10¹⁴ at 1000 K

\[\ce{NO (g) + O3 (g) ⇌ NO2 (g) + O2 (g)}\]

Both the forward and reverse reactions in the equilibrium are elementary bimolecular reactions. What is K_c, for the reverse reaction?

Explain why pure liquids and solids can be ignored while writing the equilibrium constant expression?

A reaction between N₂ and O₂ takes place as follows:

\[\ce{2N2 (g) + O2 (g) ⇌ 2N2O (g)}\]

If a mixture of 0.482 mol of N₂ and 0.933 mol of O₂ is placed in a 10 L reaction vessel and allowed to form N₂O at a temperature for which K_c = 2.0 × 10^-37, determine the composition of equilibrium mixture.

Nitric oxide reacts with Br₂ and gives nitrosyl bromide as per reaction given below:

\[\ce{2NO(g) + Br2 (g) ⇌ 2NOBr (g)}\]

When 0.087 mol of NO and 0.0437 mol of Br₂ are mixed in a closed container at the constant temperature, 0.0518 mol of NOBr is obtained at equilibrium. Calculate the equilibrium amount of NO and Br₂.

At 450 K, K_p= 2.0 × 10¹⁰/bar for the given reaction at equilibrium.

\[\ce{2SO2(g) + O2(g) ⇌2SO3 (g)}\]

What is K_c at this temperature?

A sample of HI(g) is placed in flask at a pressure of 0.2 atm. At equilibrium, the partial pressure of HI(g) is 0.04 atm. What is Kp for the given equilibrium?

\[\ce{2HI (g) ⇌ H2 (g) + I2 (g)}\]

A mixture of 1.57 mol of N₂, 1.92 mol of H₂ and 8.13 mol of NH₃ is introduced into a 20 L reaction vessel at 500 K. At this temperature, the equilibrium constant, K_c for the reaction 

\[\ce{N2 (g) + 3H2 (g)⇌2NH3 (g)}\] is 1.7 × 10²

Is the reaction mixture at equilibrium? If not, what is the direction of the net reaction?

The equilibrium constant expression for a gas reaction is,

`"K"_"c" = (["NH"_3]^4["O"_2]^5)/(["NO"]^4["H"_2"O"]^6)`

One mole of H₂O and one mole of CO are taken in 10 L vessel and heated to 725 K. At equilibrium, 40% of water (by mass) reacts with CO according to the equation, 

\[\ce{H2O (g) + CO (g) ⇌ H2 (g) + CO2 (g)}\] 

Calculate the equilibrium constant for the reaction.

At 700 K, the equilibrium constant for the reaction

\[\ce{H_{2(g)} + I_{2(g)} ↔ 2HI_{(g)}}\] 

is 54.8. If 0.5 molL^–1 of HI_(g) is present at equilibrium at 700 K, what are the concentration of H_2(g) and I_2(g) assuming that we initially started with HI_(g) and allowed it to reach equilibrium at 700 K?

What is the equilibrium concentration of each of the substances in the equilibrium when the initial concentration of ICl was 0.78 M?

\[\ce{2 ICl(g) ⇌  I2(g) + Cl2(g)}\]; K_C = 0.14

K_p = 0.04 atm at 899 K for the equilibrium shown below. What is the equilibrium concentration of C₂H₆ when it is placed in a flask at 4.0 atm pressure and allowed to come to equilibrium?

\[\ce{C2H6 (g) ⇌ C2H4 (g) + H2 (g)}\]

Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:

\[\ce{CH3COOH (l) + C2H5OH (l) ⇌ CH3COOC2H5 (l) + H2O (l)}\]

Write the concentration ratio (reaction quotient), Qc, for this reaction (note: water is not in excess and is not a solvent in this reaction).

Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:

\[\ce{CH3COOH (l) + C2H5OH (l) ⇌ CH3COOC2H5 (l) + H2O (l)}\]

At 293 K, if one starts with 1.00 mol of acetic acid and 0.18 mol of ethanol, there is 0.171 mol of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant.

Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:

\[\ce{CH3COOH (l) + C2H5OH (l) ⇌ CH3COOC2H5 (l) + H2O (l)}\]

Starting with 0.5 mol of ethanol and 1.0 mol of acetic acid and maintaining it at 293 K, 0.214 mol of ethyl acetate is found after sometime. Has equilibrium been reached?

A sample of pure PCl₅ was introduced into an evacuated vessel at 473 K. After equilibrium was attained, the concentration of PCl₅ was found to be 0.5 × 10^–1 mol L^–1. If the value of K_c is 8.3 × 10^–3, what are the concentrations of PCl₃ and Cl₂ at equilibrium?

\[\ce{PCl5 (g) ⇌ PCl3 (g) + Cl2(g)}\]

One of the reactions that takes place in producing steel from iron ore is the reduction of iron (II) oxide by carbon monoxide to give iron metal and CO₂.

\[\ce{FeO (s) + CO (g) ↔ Fe (s) + CO2 (g)}\]; K_p= 0.265 at 1050 K.

What are the equilibrium partial pressures of CO and CO₂ at 1050 K if the initial partial pressures are: p_CO = 1.4 atm and `"p"_("co"_2)`= 0.80 atm?

Equilibrium constant, K_c for the reaction 

\[\ce{N2 (g) + 3H2 (g) ⇌ 2NH3 (g)}\] at 500 K is 0.061.

At a particular time, the analysis shows that composition of the reaction mixture is 3.0 mol L^–1 N₂, 2.0 mol L^–1 H₂ and 0.5 mol L^–1 NH₃. Is the reaction at equilibrium? If not in which direction does the reaction tend to proceed to reach equilibrium?

Bromine monochloride, BrCl decomposes into bromine and chlorine and reaches the equilibrium:

\[\ce{2BrCl (g) ⇌ Br2 (g) + Cl2 (g)}\]

for which K_c= 32 at 500 K. If initially pure BrCl is present at a concentration of 3.3 × 10^–3 molL^–1, what is its molar concentration in the mixture at equilibrium?

At 1127 K and 1 atm pressure, a gaseous mixture of CO and CO₂ in equilibrium with solid carbon has 90.55% CO by mass

\[\ce{C (s) + CO2 (g) ⇌ 2CO (g)}\]

Calculate K_c for this reaction at the above temperature.

Calculate a) ΔG°and b) the equilibrium constant for the formation of NO₂ from NO and O₂ at 298 K

\[\ce{NO(g) + 1/2 O_2 (g) <=> NO_2(g)}\]

where Δ_fG^⊝ (NO₂) = 52.0 kJ/mol

Δ_fG^⊝ (NO) = 87.0 kJ/mol

Δ_fG^⊝ (O₂) = 0 kJ/mol

Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?

\[\ce{PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)}\]

Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?

\[\ce{CaO (s) + CO2 (g) ⇌ CaCO3 (s)}\]

Does the number of moles of reaction products increase, decrease or remain same when each of the following equilibria is subjected to a decrease in pressure by increasing the volume?

\[\ce{3Fe (s) + 4H2O (g) ⇌ Fe3O4 (s) + 4H2 (g)}\]

Which of the following reactions will get affected by increasing the pressure? Also, mention whether change will cause the reaction to go into forward or backward direction.

1. \[\ce{COCl2 (g) ⇌ CO (g) + Cl2 (g)}\]
2. \[\ce{CH4 (g) + 2S2 (g) ⇌ CS2 (g) + 2H2S (g)}\]
3. \[\ce{CO2 (g) + C (s) ⇌ 2CO (g)}\]
4. \[\ce{2H2 (g) + CO (g) ⇌ CH3OH (g)}\]
5. \[\ce{CaCO3 (s) ⇌ CaO (s) + CO2 (g)}\]
6. \[\ce{4 NH3 (g) + 5O2 (g) ⇌ 4NO (g) + 6H2O(g)}\]

The equilibrium constant for the following reaction is 1.6 ×10⁵ at 1024K

\[\ce{H2(g) + Br2(g) ⇌ 2HBr(g)}\]

Find the equilibrium pressure of all gases if 10.0 bar of HBr is introduced into a sealed container at 1024K.

Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per following endothermic reaction:

\[\ce{CH4 (g) + H2O (g) ⇌ CO (g) + 3H2 (g)}\]

Write as the expression for K_p for the above reaction.

Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per following endothermic reaction:

\[\ce{CH4 (g) + H2O (g) ⇌ CO (g) + 3H2 (g)}\]

How will the values of Kp and composition of equilibrium mixture be affected by

1. increasing the pressure
2. increasing the temperature
3. using a catalyst?

Describe the effect of addition of H₂  on the equilibrium of the reaction: 

\[\ce{2H2(g) + CO (g) ⇌ CH3OH (g)}\]

Describe the effect of Addition of CH₃OH  on the equilibrium of the reaction: 

\[\ce{2H2(g) + CO (g) ⇌ CH3OH (g)}\]

Describe the effect of Removal of CO on the equilibrium of the reaction: 

\[\ce{2H2(g) + CO (g) ⇌ CH3OH (g)}\]

Describe the effect of Removal of CH₃OH on the equilibrium of the reaction:

\[\ce{2H2(g) + CO (g) ⇌ CH3OH (g)}\]

At 473 K, equilibrium constant K_c for decomposition of phosphorus pentachloride, PCl₅is 8.3 ×10^-3. If decomposition is depicted as,

\[\ce{PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)}\]  Δ_rH° = 124.0 kJmol^–1

Write an expression for K_c for the reaction.

At 473 K, equilibrium constant K_c for decomposition of phosphorus pentachloride, PCl₅is 8.3 ×10^-3. If decomposition is depicted as,

\[\ce{PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)}\]  Δ_rH° = 124.0 kJmol^–1

What is the value of K_c for the reverse reaction at the same temperature?

At 473 K, equilibrium constant K_c for decomposition of phosphorus pentachloride, PCl₅ is 8.3 ×10^-3. If decomposition is depicted as,

\[\ce{PCl5 (g) ⇌ PCl3 (g) + Cl2 (g)}\]  Δ_rH° = 124.0 kJmol^–1

What would be the effect on K_c if

1. more PCl₅ is added
2. pressure is increased?
3. The temperature is increased?

Dihydrogen gas used in Haber’s process is produced by reacting methane from natural gas with high-temperature steam. The first stage of two-stage reaction involves the formation of CO and H₂. In the second stage, CO formed in the first stage is reacted with more steam in water gas shift reaction,

\[\ce{CO (g) + H2O (g) ⇌ CO2 (g) + H2 (g)}\]

If a reaction vessel at 400°C is charged with an equimolar mixture of CO and steam such that `"p"_"CO" = "p"_("H"_2"O")` = 4.0 bar, what will be the partial pressure of H₂ at equilibrium? K_p = 10.1 at 400°C.

Predict which of the following reaction will have the appreciable concentration of reactants and products:

1. \[\ce{Cl2 (g) ⇌ 2Cl (g)}\] K_c = 5 ×10^–39
2. \[\ce{Cl2 (g) + 2NO (g) ⇌ 2NOCl (g)}\] K_c = 3.7 × 10⁸
3. \[\ce{Cl2 (g) + 2NO2 (g) ⇌ 2NO2Cl (g)}\] K_c = 1.8

The value of K_c for the reaction 3O₂ (g) ↔ 2O₃ (g) is 2.0 ×10^–50 at 25°C. If the equilibrium concentration of O₂ in the air at 25°C is 1.6 ×10^–2, what is the concentration of O₃?

The reaction, \[\ce{CO(g) + 3H2(g) ↔ CH4(g) + H2O(g)}\] is at equilibrium at 1300 K in a 1L flask. It also contains 0.30 mol of CO, 0.10 mol of H₂ and 0.02 mol of H₂O and an unknown amount of CH₄ in the flask. Determine the concentration of CH₄ in the mixture. The equilibrium constant, K_c for the reaction at the given temperature is 3.90.

What is meant by the conjugate acid-base pair? Find the conjugate acid/base for the following species:

HNO₂, CN^–, HClO₄, F^–, OH^–, `"CO"_3^(2-)`, and S^2–

Which of the followings are Lewis acids? H₂O, BF₃, H⁺, and `"NH"_4^(+)`?

What will be the conjugate bases for the following Bronsted acids:

HF, H₂SO₄ and \[\ce{HCO^-_3}\]? 

Write the conjugate acids for the following Brönsted bases: NH₂^–, NH₃ and HCOO^–.

The species: H₂O,`"HCO"_3^(-)`,`"HSO"_4^(-)` and NH₃ can act both as Brönsted acids and bases. For each case give the corresponding conjugate acid and base.

Classify the following species into Lewis acids and Lewis bases and show how these act as Lewis acid/base: 

`"OH"^(-)`

Classify the following species into Lewis acids and Lewis bases and show how these act as Lewis acid/base:  

F^–

Classify the following species into Lewis acids and Lewis bases and show how these act as Lewis acid/base: 

H⁺ 

Classify the following species into Lewis acids and Lewis bases and show how these act as Lewis acid/base:

BCl₃

The concentration of hydrogen ion in a sample of soft drink is 3.8 × 10^–3 M. what is its pH?

The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it.

The ionization constant of HF, HCOOH and HCN at 298K are 6.8 × 10^–4, 1.8 × 10^–4 and 4.8 × 10^–9 respectively. Calculate the ionization constants of the corresponding conjugate base.

The ionization constant of phenol is 1.0 × 10^–10. What is the concentration of phenolate ion in 0.05 M solution of phenol? What will be its degree of ionization if the solution is also 0.01M in sodium phenolate?

The first ionization constant of H_2­­S is 9.1 × 10^–8. Calculate the concentration of HS^–ion in its 0.1 M solution. How will this concentration be affected if the solution is 0.1 M in HCl also? If the second dissociation constant of H₂S is 1.2 × 10^–13, calculate the concentration of S^2– under both conditions.

The ionization constant of acetic acid is 1.74 × 10^–5. Calculate the degree of dissociation of acetic acid in its 0.05 M solution. Calculate the concentration of acetate ion in the solution and its pH.

It has been found that the pH of a 0.01M solution of an organic acid is 4.15. Calculate the concentration of the anion, the ionization constant of the acid and its pK_a.

Assuming complete dissociation, calculate the pH of the following solution:

0.003 M HCl

Assuming complete dissociation, calculate the pH of the following solution:

0.005 M NaOH 

Assuming complete dissociation, calculate the pH of the following solution:

0.002 M HBr

Assuming complete dissociation, calculate the pH of the following solution:

0.002 M KOH

Calculate the pH of the following solution: 

2 g of TlOH dissolved in water to give 2 litre of solution.

Calculate the pH of the following solutions:

0.3 g of Ca(OH)₂ dissolved in water to give 500 mL of solution.

Calculate the pH of the following solution:  

0.3 g of NaOH dissolved in water to give 200 mL of solution.

Calculate the pH of the following solution:

1mL of 13.6 M HCl is diluted with water to give 1 litre of solution.

The degree of ionization of a 0.1M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the pK_a of bromoacetic acid.

The pH of 0.005M codeine (C₁₈H₂₁NO₃) solution is 9.95. Calculate its ionization constant and pK_b.

What is the pH of 0.001 M aniline solution? The ionization constant of aniline can be taken from Table 7.7. Calculate the degree of ionization of aniline in the solution. Also calculate the ionization constant of the conjugate acid of aniline

Calculate the degree of ionization of 0.05M acetic acid if its pK_a value is 4.74.

How is the degree of dissociation affected when its solution also contains

1. 0.01 M
2. 0.1 M in HCl?

The ionization constant of dimethylamine is 5.4 × 10^–4. Calculate its degree of ionization in its 0.02 M solution. What percentage of dimethylamine is ionized if the solution is also 0.1 M in NaOH?

Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human muscle-fluid, 6.83

Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human stomach fluid, 1.2

Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human blood, 7.38

Calculate the hydrogen ion concentration in the following biological fluids whose pH are given below:

Human saliva, 6.4.

The pH of milk, black coffee, tomato juice, lemon juice and egg white are 6.8, 5.0, 4.2, 2.2 and 7.8 respectively. Calculate corresponding hydrogen ion concentration in each.

If 0.561 g of KOH is dissolved in water to give 200 mL of solution at 298 K. Calculate the concentrations of potassium, hydrogen and hydroxyl ions. What is its pH?

The solubility of Sr(OH)₂ at 298 K is 19.23 g/L of solution. Calculate the concentrations of strontium and hydroxyl ions and the pH of the solution.

The ionization constant of propanoic acid is 1.32 × 10^–5. Calculate the degree of ionization of the acid in its 0.05M solution and also its pH. What will be its degree of ionization if the solution is 0.01M in HCl also?

The pH of 0.1M solution of cyanic acid (HCNO) is 2.34. Calculate the ionization constant of the acid and its degree of ionization in the solution.

The ionization constant of nitrous acid is 4.5 × 10^–4. Calculate the pH of 0.04 M sodium nitrite solution and also its degree of hydrolysis.

A 0.02 M solution of pyridinium hydrochloride has pH = 3.44. Calculate the ionization constant of pyridine.

Predict if the solutions of the following salts are neutral, acidic or basic:

NaCl, KBr, NaCN, NH₄NO₃, NaNO₂ and KF

The ionization constant of chloroacetic acid is 1.35 × 10–3. What will be the pH of 0.1M acid and its 0.1M sodium salt solution?

Ionic product of water at 310 K is 2.7 × 10^–14. What is the pH of neutral water at this temperature?

Calculate the pH of the resultant mixtures: 10 mL of 0.2M Ca(OH)₂ + 25 mL of 0.1M HCl.

Calculate the pH of the resultant mixtures: 10 mL of 0.01M H₂SO₄ + 10 mL of 0.01M Ca(OH)₂.

Calculate the pH of the resultant mixtures: 10 mL of 0.1M H₂SO₄ + 10 mL of 0.1M KOH

Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at 298K from their solubility product constants. Determine also the molarities of individual ions.

The solubility product constant of Ag₂CrO₄ and AgBr are 1.1 × 10^–12 and 5.0 × 10^–13respectively. Calculate the ratio of the molarities of their saturated solutions.

Equal volumes of 0.002 M solutions of sodium iodate and cupric chlorate are mixed together. Will it lead to precipitation of copper iodate? (For cupric iodate K_sp = 7.4 × 10^–8).

What is the maximum concentration of equimolar solutions of ferrous sulphate and sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide? (For iron sulphide, K_sp = 6.3 × 10^–18).

What is the minimum volume of water required to dissolve 1g of calcium sulphate at 298 K? (For calcium sulphate, K_sp is 9.1 × 10^–6).

The concentration of sulphide ion in 0.1M HCl solution saturated with hydrogen sulphide is 1.0 × 10^–19 M. If 10 mL of this is added to 5 mL of 0.04 M solution of the following: FeSO₄, MnCl₂, ZnCl₂ and CdCl₂. in which of these solutions precipitation will take place?