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JEE Main Chemistry: Equilibrium questions with solutions

407 questions with worked solutions.

Questions

Q1. The solubility product constants of Ag2CrO4, AgCl, AgBr and AgI are 1.1 × 10⁻¹², 1.8 × 10⁻¹⁰, 5.0 × 10⁻¹³ and 8.3 × 10⁻¹⁷, respectively. If AgNO3 solution is added to a mixture containing equal amounts of NaCl, NaBr, NaI and Na2CrO4, which silver salt will begin to precipitate at the highest Ag+ concentration, i.e., the last one to form?

  1. AgCl
  2. AgBr
  3. Ag2CrO4
  4. AgI

Answer: Ag2CrO4

For equal anion concentrations the [Ag+] needed to start precipitation is highest for Ag2CrO4 (~1e-6) versus AgCl 1.8e-10, AgBr 5e-13, AgI 8.3e-17. AgI precipitates first (lowest [Ag+]); Ag2CrO4 precipitates last.

Q2. Two sparingly soluble salts, MY and NY3, each have the same solubility product constant, Ksp = 6.2 × 10⁻¹³, at room temperature. Which of the following statements is correct for these two salts?

  1. The molar solubilities of MY and NY3 in water are the same.
  2. The molar solubility of MY in water is lower than that of NY3.
  3. Both salts become more soluble in 0.5 M KY than they are in pure water.
  4. Adding KY to solutions of MY and NY3 does not change their solubilities.

Answer: The molar solubility of MY in water is lower than that of NY3.

The molar solubility of MY is lower than that of NY3 because MY dissociates into fewer ions compared to NY3, which produces more ions upon dissolution. Since Ksp is the same for both salts, the salt with more ions in solution (NY3) will have a higher molar solubility.

Q3. Given the equilibrium constants for these reactions: N2 + 3H2 ⇌ 2NH3, K1 N2 + O2 ⇌ 2NO, K2 H2 + 1/2 O2 ⇌ H2O, K3 What is the equilibrium constant K for the reaction 2NH3 + 5/2 O2 ⇌ 2NO + 3H2O ?

  1. K2K3³/K1
  2. K2K3/K1
  3. K2K3³/K1²
  4. K3K1³/K2

Answer: K2K3³/K1

The equilibrium constant for the desired reaction can be derived by manipulating the given reactions. By reversing the first reaction (which introduces a factor of 1/K1) and adjusting the stoichiometry of the other reactions, we can combine them to yield the correct expression for K, which results in K2K3³/K1.

Q4. In a saturated solution of Ag2C2O4, the concentration of Ag+ ions is 2.2 × 10⁻⁴ mol L⁻¹. The solubility product constant (Ksp) of Ag2C2O4 is:

  1. 2.66 × 10⁻⁸
  2. 4.5 × 10⁻¹¹
  3. 5.3 × 10⁻¹²
  4. 2.42 × 10⁻⁸

Answer: 5.3 × 10⁻¹²

[C2O4^2-] = 2.2e-4/2 = 1.1e-4; Ksp = (2.2e-4)^2 * (1.1e-4) = 5.3e-12. The stored 2.66e-8 is wrong.

Q5. For the gaseous equilibrium PCl₅ ⇌ PCl₃ + Cl₂, how does the degree of dissociation (α) depend on the equilibrium pressure (p)?

  1. α is inversely proportional to p⁴
  2. α is inversely proportional to √p
  3. α is inversely proportional to p²
  4. α is directly proportional to p

Answer: α is inversely proportional to √p

The degree of dissociation (α) for the reaction is influenced by the change in the number of moles of gas during the reaction. As pressure increases, the equilibrium shifts to favor the side with fewer moles of gas, which in this case means that α decreases, and the relationship is inversely proportional to the square root of the pressure.

Q6. A movable-piston vessel of volume 20 L at 400 K contains CO₂(g) at a pressure of 0.4 atm along with excess SrO (ignore the solid’s volume). The piston is pushed inward, reducing the container volume. What is the largest volume the vessel can have when the CO₂ pressure reaches its highest value? Given: SrCO₃(s) ⇌ SrO(s) + CO₂(g), Kp = 1.6 atm

  1. 10 litre
  2. 4 litre
  3. 2 litre
  4. 5 litre

Answer: 5 litre

Compressing isothermally: 0.4 atm * 20 L = 1.6 atm * V, so V = 5 L is the largest volume at which CO2 pressure reaches its maximum (Kp = 1.6 atm). Below 5 L the excess CO2 forms SrCO3. The stored 4 L is wrong.

Q7. An acid H₂A has first and second dissociation constants of 1.0 × 10⁻⁵ and 5.0 × 10⁻¹⁰, respectively. What is the overall dissociation constant of this acid?

  1. 0.2 × 10⁵
  2. 5.0 × 10⁵
  3. 5.0 × 10¹⁵
  4. 5.0 × 10⁻¹⁵

Answer: 5.0 × 10⁻¹⁵

Overall dissociation constant = (1.0e-5)(5.0e-10) = 5.0e-15. The stored 0.2e5 is wrong.

Q8. A 2.5 mL sample of a weak monobasic base of concentration (2/5) M, having Kb = 1 × 10⁻¹² at 25°C, is titrated with (2/15) M HCl in aqueous medium at 25°C. At the equivalence point, the hydrogen ion concentration is (Kw = 1 × 10⁻¹⁴ at 25°C):

  1. 3.7 × 10⁻¹⁴ M
  2. 3.2 × 10⁻⁷ M
  3. 3.2 × 10⁻² M
  4. 2.7 × 10⁻² M

Answer: 3.2 × 10⁻² M

Equivalence salt concentration = 1 mmol / 10 mL = 0.1 M; Ka(BH+) = 1e-14/1e-12 = 1e-2; [H+] = sqrt(1e-2 * 0.1) = 3.2e-2 M, not 3.2e-7.

Q9. A 1 mL sample of a 0.10 M weak monobasic base is diluted to a final volume of 100 mL at constant temperature. If the base dissociation constant, Kb, is 1 × 10⁻⁵, what is the pH of the resulting solution?

  1. 8
  2. 9
  3. 10
  4. 11

Answer: 10

After 100x dilution C = 1e-3 M; [OH-] = sqrt(1e-5 * 1e-3) = 1e-4, pOH = 4, pH = 10. The stored pH 9 is wrong.

Q10. A saturated solution of the sparingly soluble strong electrolyte AgIO₃ (molar mass = 283) is in equilibrium as AgIO₃(s) ⇌ Ag⁺(aq) + IO₃⁻(aq). If the solubility product constant, Ksp, of AgIO₃ at the stated temperature is 1.0 × 10⁻⁸, what mass of AgIO₃ is present in 100 mL of this saturated solution?

  1. 1.0 × 10⁻⁴ g
  2. 2.83 × 10⁻² g
  3. 2.83 × 10⁻³ g
  4. 1.0 × 10⁻⁷ g

Answer: 2.83 × 10⁻³ g

To find the mass of AgIO₃ in a saturated solution, we first determine the molarity of Ag⁺ and IO₃⁻ ions using the Ksp value. Given Ksp = [Ag⁺][IO₃⁻] = 1.0 × 10⁻⁸, and since the concentrations of Ag⁺ and IO₃⁻ are equal in a saturated solution, we can set both to 's'. Thus, s² = 1.0 × 10⁻⁸, leading to s = 1.0 × 10⁻⁴ M. In 100 mL, this corresponds to 1.0 × 10⁻⁴ moles, which converts to mass using the molar mass of AgIO₃ (283 g/mol), resulting in 2.83 × 10⁻³ g.

Q11. Which species can behave as both a Brønsted acid and a Brønsted base?

  1. HSO4−
  2. Na2CO3
  3. NH3
  4. OH−

Answer: HSO4−

HSO4− can donate a proton, acting as a Brønsted acid, and it can also accept a proton, behaving as a Brønsted base, making it amphiprotic.

Q12. Select the statement that is correct: Polyphosphates are used as water-softening agents because they

  1. form soluble complexes with anions
  2. cause cationic species to precipitate
  3. bring about precipitation of anionic species
  4. form soluble complexes with cations

Answer: form soluble complexes with cations

Polyphosphates soften water by forming soluble complexes (sequestering) with the Ca2+/Mg2+ cations, not by precipitating anionic species.

Q13. Which of the following substances, when dissolved in water, gives the poorest conduction of electric current?

  1. Ethanoic acid, C2H4O2
  2. Hydrogen chloride, HCl
  3. Ammonia, NH3
  4. Fructose, C6H12O6

Answer: Fructose, C6H12O6

Fructose is a non-electrolyte, meaning it does not dissociate into ions when dissolved in water, resulting in poor conductivity of electric current compared to the other options, which are electrolytes that ionize.

Q14. Which expression correctly represents the law of independent migration of ions and Ostwald’s dilution law?

  1. Λm = Λm° - BC¹/2
  2. Λ° = F(u+ + u-)
  3. Λm° = v+λ+ + v-λ-
  4. Λ°m / Λm = 1/Λm° + 1/Ka (Λm°)²

Answer: Λm° = v+λ+ + v-λ-

This expression accurately reflects the law of independent migration of ions, where the molar conductivity of an electrolyte at infinite dilution (Λm°) is the sum of the contributions from each ion, represented by their respective velocities (v) and molar conductivities (λ).

Q15. Which of the following statements is incorrect?

  1. The equilibrium constant of a reaction changes when a catalyst is present at equilibrium
  2. Enzymes mainly catalyse biochemical reactions
  3. Coenzymes enhance the catalytic activity of enzymes
  4. A catalyst does not initiate any reaction

Answer: The equilibrium constant of a reaction changes when a catalyst is present at equilibrium

A catalyst speeds up forward and reverse reactions equally and does not change the equilibrium constant Kc. So 'the equilibrium constant changes when a catalyst is present' is the incorrect statement. The other three statements are correct.

Q16. Hydrogen chloride in the gaseous state conducts electricity very poorly, whereas its water solution conducts well. This is because

  1. water itself is a good conductor of electricity
  2. a gas cannot conduct electricity, but a liquid can
  3. HCl gas does not follow Ohm's law, while its solution does
  4. HCl dissociates into ions in aqueous solution

Answer: HCl dissociates into ions in aqueous solution

In aqueous solution, hydrogen chloride dissociates into hydrogen ions (H+) and chloride ions (Cl-), which are charged particles that facilitate the flow of electricity, unlike in its gaseous state where it remains as neutral molecules.

Q17. For the equilibrium dissociation of phosphorus pentachloride, PCl₅ ⇌ PCl₃ + Cl₂, if the degree of dissociation is α and the total pressure is P, which expression gives the equilibrium constant Kₚ?

  1. Kₚ = α²P/(1 - α²)
  2. Kₚ = αP/(1 - α)
  3. Kₚ = α²P/(1 + α²)
  4. Kₚ = αP/(1 + α)

Answer: Kₚ = α²P/(1 - α²)

For PCl5 -> PCl3 + Cl2 starting with 1 mol, equilibrium moles are (1-a), a, a with total (1+a). Mole fractions times P give partial pressures, so Kp = [aP/(1+a)][aP/(1+a)] / [(1-a)P/(1+a)] = a^2 P/(1-a^2).

Q18. A weak monobasic base is represented as BOH. During its titration with hydrochloric acid, which reaction takes place?

  1. N₁V₁ = N₂V₂
  2. BOH + HCl ⇌ BCl + H₂O
  3. B⁺ + H₂O ⇌ BOH + H⁺
  4. 2/15 × V₁ = 2.5 × 2/5

Answer: BOH + HCl ⇌ BCl + H₂O

The correct option describes the neutralization reaction between the weak base BOH and hydrochloric acid (HCl), resulting in the formation of the salt BCl and water, which is characteristic of acid-base reactions.

Q19. A saturated solution of the silver salt of a monobasic acid HA has pH 9. If the acid dissociation constant of HA is 10⁻¹⁰, what is the solubility product constant of the sparingly soluble salt AgAs?

  1. 1.1 × 10⁻⁹
  2. 1.1 × 10⁻¹⁰
  3. 1.1 × 10⁻¹¹
  4. 10⁻¹²

Answer: 1.1 × 10⁻¹¹

The solubility product constant (Ksp) can be determined using the pH to find the concentration of hydroxide ions, which helps in calculating the concentration of the silver ions and the corresponding dissociation of the acid. Given the pH of 9, the concentration of hydroxide ions is 10⁻⁵ M, leading to the conclusion that the Ksp for the silver salt is 1.1 × 10⁻¹¹.

Q20. For the equilibrium NH4HS ⇌ NH3(g) + H2S(g) at a fixed temperature, if the total equilibrium pressure is X bar, what is the value of ΔG°?

  1. −2RT ln X
  2. −RT ln (X − ln 2)
  3. −2RT ln (X − ln 2)
  4. None of these

Answer: None of these

For NH4HS -> NH3 + H2S the gases form in equal amounts, so P(NH3) = P(H2S) = X/2 and Kp = (X/2)(X/2) = X^2/4. Then dG-standard = -RT ln Kp = -RT ln(X^2/4) = -2RT ln X + RT ln 4. None of the given expressions equal this, so the answer is 'None of these'.

Q21. For the equilibrium A(g) + 2B(g) ⇌ C(g) + D(g), the equilibrium constant is Kc = 10¹². In a 1 L container, the initial amounts of A, B, C, and D are 0.5 mol, 1 mol, 0.5 mol, and 3.5 mol, respectively. What will be the equilibrium concentration of B?

  1. 10⁻⁴
  2. 2 × 10⁻⁴
  3. 4 × 10⁻⁴
  4. 8 × 10⁻⁴

Answer: 2 × 10⁻⁴

The equilibrium constant Kc indicates that the reaction heavily favors the products, meaning that as the reaction proceeds towards equilibrium, the concentration of reactants will decrease significantly. Given the initial concentrations and the large value of Kc, the change in concentration of B will be small, leading to an equilibrium concentration of 2 × 10⁻⁴ mol/L.

Q22. A salt of the type AB2 is only slightly soluble in water. If its molar solubility is 1.0 × 10−5 mol L−1, what is the value of its solubility product?

  1. 4 × 10−10
  2. 1 × 10−15
  3. 1 × 10−10
  4. 4 × 10−15

Answer: 4 × 10−15

The solubility product (Ksp) for a salt AB2 can be calculated using the formula Ksp = [A⁺][B^−]². Given the molar solubility of AB2 is 1.0 × 10−5 mol L−1, the concentration of A⁺ is 1.0 × 10−5 mol L−1 and the concentration of B^− is 2 × 1.0 × 10−5 mol L−1. Therefore, Ksp = (1.0 × 10−5)(2 × 1.0 × 10−5)² = 4 × 10−15.

Q23. For the equilibrium process N2O4(g) ⇌ 2NO2(g), the equilibrium concentrations of N2O4 and NO2 are 4.8 × 10−2 mol L−1 and 1.2 × 10−2 mol L−1, respectively. What is the value of Kc for this reaction?

  1. 3 × 10−1 mol L−1
  2. 3 × 10−3 mol L−1
  3. 3 × 10³ mol L−1
  4. 3.3 × 10² mol L−1

Answer: 3 × 10−3 mol L−1

The equilibrium constant Kc is calculated using the formula Kc = [NO2]² / [N2O4]. Substituting the given concentrations, Kc = (1.2 × 10−2)² / (4.8 × 10−2) results in a value of 3 × 10−3 mol L−1, confirming option B as correct.

Q24. For the equilibrium 2 SO2(g) + O2(g) ⇌ 2 SO3(g), with ΔH° = −198 kJ, which set of conditions will shift the equilibrium in favour of product formation according to Le Chatelier’s principle?

  1. Raise the temperature and also raise the pressure
  2. Decrease the temperature and increase the pressure
  3. Any temperature and pressure conditions
  4. Decrease both the temperature and the pressure

Answer: Decrease the temperature and increase the pressure

Decreasing the temperature favors the exothermic reaction, which produces more SO3, while increasing the pressure shifts the equilibrium towards the side with fewer moles of gas, thus promoting product formation.

Q25. Which species is formed when H2PO4− loses one proton?

  1. H3PO4
  2. P2O5
  3. PO43−
  4. HPO42−

Answer: HPO42−

When H2PO4− loses one proton (H+), it becomes HPO42−, which is the next species in the dissociation of phosphoric acid. This process reflects the stepwise deprotonation of the phosphate ion.

Q26. What is the equilibrium expression for the reaction P4(s) + 5O2(g) ⇌ P4O10(s) ?

  1. Kc = [O2]⁵
  2. Kc = [P4O10]/5[P4][O2]
  3. Kc = [P4O10]/[P4][O2]⁵
  4. Kc = 1/[O2]⁵

Answer: Kc = 1/[O2]⁵

The equilibrium expression for a reaction only includes the concentrations of gaseous and aqueous species, while solids and liquids are omitted. In this case, since P4 and P4O10 are solids, the expression focuses on the gaseous reactant O2, leading to the correct form of Kc as the inverse of its concentration raised to the power of its stoichiometric coefficient.

Q27. For the reaction CO(g) + Cl2(g) ⇌ COCl2(g) the Kp/Kc is equal to

  1. √RT
  2. RT
  3. 1/RT
  4. 1.0

Answer: 1/RT

The relationship between Kp and Kc is given by the equation Kp = Kc(RT)^(Δn), where Δn is the change in the number of moles of gas. In this reaction, Δn is negative, leading to Kp being equal to Kc divided by RT, hence Kp/Kc equals 1/RT.

Q28. At temperature T, the equilibrium constant for N2(g) + O2(g) ⇌ 2NO(g) is 4 × 10⁻⁴. What is the value of Kc for the reaction NO(g) ⇌ 1/2 N2(g) + 1/2 O2(g) at the same temperature?

  1. 4 × 10⁻⁴
  2. 50
  3. 2.5 × 10²
  4. 0.02

Answer: 50

The equilibrium constant for the reverse reaction is the reciprocal of the original reaction's equilibrium constant. Since the new reaction involves taking the square root of the original reaction's equilibrium constant (because of the coefficients being halved), we find that Kc = 1 / (4 × 10⁻⁴)^(1/2) = 50.

Q29. The molar solubility (in mol L⁻¹) of a sparingly soluble salt MX4 is 's'. The corresponding solubility product is Ksp. 's' is given in term of Ksp by the relation

  1. s = (256 Ksp)^(1/5)
  2. s = (128 Ksp)^(1/4)
  3. s = (Ksp/128)^(1/4)
  4. s = (Ksp/256)^(1/5)

Answer: s = (Ksp/256)^(1/5)

The correct option relates the molar solubility 's' of the salt MX4 to its solubility product Ksp by recognizing that the dissolution of MX4 produces one mole of M and four moles of X, leading to the expression Ksp = [M][X]⁴. By substituting the concentrations in terms of 's', we derive the relationship s = (Ksp/256)^(1/5), which accurately reflects the stoichiometry of the dissolution process.

Q30. The solubility product of a salt having general formula MX2, in water, is 4 × 10⁻¹². The concentration of M2+ ions in the aqueous solution of the salt is

  1. 4.0 × 10⁻¹⁰ M
  2. 1.6 × 10⁻⁴ M
  3. 1.0 × 10⁻⁴ M
  4. 2.0 × 10⁻⁶ M

Answer: 1.0 × 10⁻⁴ M

The solubility product (Ksp) expression for the salt MX2 is Ksp = [M2+][X-]². Given Ksp = 4 × 10⁻¹², if we let the solubility of MX2 be 's', then [M2+] = s and [X-] = 2s. Substituting these into the Ksp expression gives 4 × 10⁻¹² = s(2s)² = 4s³, leading to s = 1.0 × 10⁻⁴ M for [M2+].

Q31. The exothermic formation of ClF3 is represented by the equation: Cl2(g) + 3F2(g) ⇌ 2ClF3(g); ΔH = -329 kJ. Which of the following will increase the quantity of ClF3 in an equilibrium mixture of Cl2, F2 and ClF3 ?

  1. Adding F2
  2. Increasing the volume of the container
  3. Removing Cl2
  4. Increasing the temperature

Answer: Adding F2

Adding F2 shifts the equilibrium to the right according to Le Chatelier's principle, as the system responds to the increased concentration of reactants by producing more ClF3.

Q32. For the reaction: 2NO2(g) ⇌ 2NO(g) + O2(g), (Kc = 1.8 × 10⁻⁶ at 184°C) [R = 0.0831 kJ/(mol.K)] When Kp and Kc are compared at 184°C, it is found that

  1. Whether Kp is greater than, less than, or equal to Kc depends upon the total gas pressure
  2. Kp = Kc
  3. Kp is less than Kc
  4. Kp is greater than Kc

Answer: Kp is greater than Kc

Kp is greater than Kc because the reaction produces more moles of gas on the product side than on the reactant side, leading to a higher partial pressure of products compared to the reactants, which increases Kp relative to Kc.

Q33. Hydrogen ion concentration in mol/L in a solution of pH = 5.4 will be:

  1. 3.98 × 10⁻⁶
  2. 3.68 × 10⁻⁶
  3. 3.88 × 10⁶
  4. 3.98 × 10⁶

Answer: 3.98 × 10⁻⁶

The hydrogen ion concentration can be calculated using the formula [H+] = 10^(-pH). For a pH of 5.4, this results in a concentration of approximately 3.98 × 10⁻⁶ mol/L, confirming option A as the correct answer.

Q34. What is the conjugate base of OH⁻ ?

  1. O2⁻
  2. O⁻
  3. H2O
  4. O2

Answer: O2⁻

The conjugate base of OH⁻ is formed when it donates a proton (H+), resulting in O2⁻, which is the hydroxide ion's corresponding base.

Q35. An amount of solid NH4HS is placed in a flask already containing ammonia gas at a certain temperature and 0.50 atm pressure. Ammonium hydrogen sulphide decomposes to yield NH3 and H2S gases in the flask. When the decomposition reaction reaches equilibrium, the total pressure in the flask rises to 0.84 atm? The equilibrium constant for NH4HS decomposition at this temperature is

  1. 0.11
  2. 0.17
  3. 0.18
  4. 0.30

Answer: 0.11

The equilibrium constant is calculated using the partial pressures of the gases at equilibrium. Given that the total pressure increased to 0.84 atm and the initial pressure of NH3 was 0.50 atm, the change in pressure due to the decomposition of NH4HS allows us to derive the equilibrium constant, which is found to be 0.11.

Q36. For the equilibrium SO3(g) ⇌ SO2(g) + 1/2 O2(g), the equilibrium constant is Kc = 4.9 × 10⁻². What is the value of Kc for the reaction 2SO2(g) + O2(g) ⇌ 2SO3(g)?

  1. 9.8 × 10⁻²
  2. 4.9 × 10⁻²
  3. 416
  4. 2.40 × 10⁻³

Answer: 416

The equilibrium constant for a reaction is related to the equilibrium constant of its reverse reaction by taking the reciprocal and raising it to the power of the stoichiometric coefficients. Since the given reaction is the reverse of the original and involves doubling the coefficients, the new equilibrium constant is Kc = (1/Kc_original)², which results in 416.

Q37. An acid H2A has first and second dissociation constants of 1.0 × 10⁻⁵ and 5.0 × 10⁻¹⁰, respectively. What is the overall dissociation constant of this acid?

  1. 0.2 × 10⁻⁵
  2. 5.0 × 10⁻⁵
  3. 5.0 × 10¹⁵
  4. 5.0 × 10⁻¹⁵

Answer: 5.0 × 10⁻¹⁵

The overall dissociation constant for a polyprotic acid is calculated by multiplying its individual dissociation constants. In this case, the overall dissociation constant is found by multiplying 1.0 × 10⁻⁵ (first dissociation) by 5.0 × 10⁻¹⁰ (second dissociation), resulting in 5.0 × 10⁻¹⁵.

Q38. A weak acid HA has a pKa of 4.5. What is the pH of an aqueous buffer containing HA when 50% of the acid molecules are ionized?

  1. 7.0
  2. 4.5
  3. 2.5
  4. 9.5

Answer: 4.5

By Henderson-Hasselbalch, pH = pKa + log([A-]/[HA]). At 50% ionization [A-] = [HA], so log term = 0 and pH = pKa = 4.5.

Q39. A saturated solution of the sparingly soluble strong electrolyte AgIO3 is in equilibrium with its solid phase as AgIO3(s) ⇌ Ag+(aq) + IO3−(aq). If the solubility product constant of AgIO3 at a certain temperature is 1.0 × 10⁻⁸, what mass of AgIO3 is present in 100 mL of the saturated solution?

  1. 1.0 × 10⁻⁴ g
  2. 28.3 × 10⁻² g
  3. 2.83 × 10⁻³ g
  4. 1.0 × 10⁻⁷ g

Answer: 2.83 × 10⁻³ g

The solubility product constant (Ksp) relates the concentrations of the ions in a saturated solution. Given Ksp = 1.0 × 10⁻⁸, we can set up the equation Ksp = [Ag+][IO3−]. Since the stoichiometry is 1:1, if 's' is the solubility in mol/L, then Ksp = s². Solving for 's' gives s = 1.0 × 10⁻⁴ mol/L. In 100 mL, this corresponds to 1.0 × 10⁻⁴ mol, which converts to 2.83 × 10⁻³ g of AgIO3, confirming option C as correct.

Q40. For the equilibria X ⇌ 2Y and Z ⇌ P + Q, the equilibrium constants Kp1 and Kp2 are related as 1: 9. If X and Z have the same degree of dissociation, what is the ratio of the total pressures at the two equilibria?

  1. 1:36
  2. 1:1
  3. 1:3
  4. 1:9

Answer: 1:36

The ratio of the total pressures at the two equilibria can be derived from the relationship between the equilibrium constants and the stoichiometry of the reactions. Given that Kp1 and Kp2 are in the ratio of 1:9 and both reactions have the same degree of dissociation, the total pressure ratio is determined by the changes in moles of gas, leading to a final ratio of 1:36.

Q41. For the reactions below, the equilibrium constants are K1, K2 and K3 respectively: (i) CO(g) + H2O(g) ⇌ CO2(g) + H2(g) (ii) CH4(g) + H2O(g) ⇌ CO(g) + 3H2(g) (iii) CH4(g) + 2H2O(g) ⇌ CO2(g) + 4H2(g) Which relation is true?

  1. K1√K2 = K3
  2. K2K3 = K1
  3. K3 = K1K2
  4. K3² = K1²

Answer: K3 = K1K2

The correct option K3 = K1K2 is derived from the principle of combining equilibrium constants for sequential reactions. When the reactions are added together, the equilibrium constant for the overall reaction is the product of the equilibrium constants of the individual reactions.

Q42. A weak acid HA has pKa = 4.80 and a weak base BOH has pKb = 4.78. What will be the pH of an aqueous solution of the salt BA formed from them?

  1. 9.58
  2. 4.79
  3. 7.01
  4. 9.22

Answer: 7.01

For salt BA: pH = 7 + 0.5(pKa - pKb) = 7 + 0.5(4.80 - 4.78) = 7 + 0.01 = 7.01. So the solution is essentially neutral, pH = 7.01.

Q43. Solid barium nitrate, Ba(NO3)2, is added slowly to a 1.0 × 10⁻⁴ M sodium carbonate solution. At what Ba2+ concentration will BaCO3 just start to precipitate? (Ksp of BaCO3 = 5.1 × 10⁻⁹)

  1. 5.1 × 10⁻⁵ M
  2. 8.1 × 10⁻⁸ M
  3. 8.1 × 10⁻⁷ M
  4. 4.1 × 10⁻⁵ M

Answer: 5.1 × 10⁻⁵ M

The correct option is right because the solubility product constant (Ksp) for BaCO3 indicates that the product of the concentrations of Ba2+ and CO3²- ions must equal 5.1 × 10⁻⁹ at equilibrium. Given the carbonate concentration of 1.0 × 10⁻⁴ M, the concentration of Ba2+ that leads to precipitation can be calculated using the Ksp expression, resulting in 5.1 × 10⁻⁵ M.

Q44. Consider the following three reactions involving dihydrogen phosphate ion: (i) H3PO4 + H2O → H3O+ + H2PO4− (ii) H2PO4− + H2O → HPO4²− + H3O+ (iii) H2PO4− + OH− → H3PO4 + O2− In which of these reactions does H2PO4− behave as an acid?

  1. (ii) only
  2. (i) and (ii)
  3. (iii) only
  4. (i) only

Answer: (ii) only

In (ii) H2PO4- -> HPO4^2- + H3O+, the dihydrogen phosphate donates a proton, so it acts as an acid. In (i) it is a product and in (iii) it gains H+ (acts as a base). Hence only (ii).

Q45. In water, carbonic acid has ionization constants K1 = 4.2 × 10⁻⁷ and K2 = 4.8 × 10⁻¹¹. For a saturated 0.034 M solution of carbonic acid, choose the correct statement.

  1. The concentration of CO3²− is 0.034 M.
  2. The concentration of CO3²− exceeds that of HCO3−.
  3. The concentrations of H+ and HCO3− are nearly the same.
  4. The concentration of H+ is twice the concentration of CO3²−.

Answer: The concentrations of H+ and HCO3− are nearly the same.

Carbonic acid ionizes mainly in its first step (K1 >> K2), giving roughly equal [H+] and [HCO3-]. [CO3^2-] ~ K2 is tiny, and the second ionization is negligible, so the concentrations of H+ and HCO3- are nearly the same.

Q46. Solubility product of silver bromide is 5.0 × 10⁻¹³. The quantity of potassium bromide (molar mass taken as 120 g mol⁻¹) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is

  1. 1.2 × 10⁻¹⁰ g
  2. 1.2 × 10⁻⁹ g
  3. 6.2 × 10⁻⁵ g
  4. 5.0 × 10⁻⁸ g

Answer: 1.2 × 10⁻⁹ g

The correct option is derived from the solubility product expression, where the concentration of bromide ions must reach a level that exceeds the solubility product of silver bromide (AgBr) to initiate precipitation. By calculating the required concentration of bromide ions and converting it to mass using the molar mass of potassium bromide, we find that 1.2 × 10⁻⁹ g is the precise amount needed to start the precipitation.

Q47. At 25 °C, the solubility product of Mg(OH)2 is 1.0 × 10⁻¹¹. At which pH, will Mg2+ ions start precipitating in the form of Mg(OH)2 from a solution of 0.001 M Mg2+ ions?

  1. 9
  2. 10
  3. 11
  4. 8

Answer: 10

The solubility product (Ksp) of Mg(OH)2 indicates that precipitation occurs when the product of the concentrations of Mg2+ and OH- ions exceeds Ksp. At a pH of 10, the concentration of OH- ions is sufficient to cause the product of Mg2+ and OH- concentrations to reach the Ksp value, leading to precipitation.

Q48. A monoprotic acid HA dissociates according to HA ⇌ H+ + A−. If a 1.0 M solution of this acid has pH 5, what is its dissociation constant?

  1. 5
  2. 5 × 10⁻⁸
  3. 1 × 10⁻⁵
  4. 1 × 10⁻¹⁰

Answer: 1 × 10⁻¹⁰

The dissociation constant (Ka) can be calculated using the concentration of hydrogen ions and the initial concentration of the acid. Given that the pH is 5, the concentration of H+ ions is 1 × 10⁻⁵ M, and using the formula Ka = [H+][A−]/[HA], we find that the dissociation constant is 1 × 10⁻¹⁰.

Q49. An aqueous solution contains an unknown concentration of Ba2+. When 50 mL of a 1 M solution of Na2SO4 is added, BaSO4 just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO4 is 1 × 10⁻¹⁰. What is the original concentration of Ba2+?

  1. 5 × 10⁻⁹ M
  2. 2 × 10⁻⁹ M
  3. 1.1 × 10⁻⁹ M
  4. 1.0 × 10⁻¹⁰ M

Answer: 1.1 × 10⁻⁹ M

The correct option is derived from the equilibrium condition for the precipitation of BaSO4, where the product of the concentrations of Ba2+ and SO4²- must equal the solubility product (Ksp). Given that the concentration of SO4²- from the Na2SO4 solution is 0.1 M after dilution, the concentration of Ba2+ that satisfies the Ksp condition is calculated to be approximately 1.1 × 10⁻⁹ M.

Q50. Which of the following salts is the most basic in aqueous solution?

  1. Al(CN)3
  2. CH3COOK
  3. FeCl3
  4. Pb(CH3COO)2

Answer: CH3COOK

CH3COOK is the salt of a strong base (KOH) and a weak acid (CH3COOH); its anion hydrolyses to make the solution basic. The others are either acidic (FeCl3) or weak-acid/weak-base salts that are far less basic.

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