JEE Chemistry Ionic Equilibrium MCQs Set 12

Chemistry Objective Questions and Answers: Ionic Equilibrium

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Multiple Choice Questions

Question 1: The pH of a solution made by mixing 50.0 mL of 0.2 M \(\ce{NH4Cl}\) and 75.0 mL of 0.1 M \(\ce{NaOH}\) (\(K_b=1.8\times10^{-5}\)) is
(a) 4.27
(b) 9.26
(c) 9.73
(d) 8.78
Show Answer & Explanation

Answer: (c) 9.73

Explanation:
1. \(\ce{NH4+}=10\) mmol and \(\ce{NaOH}=7.5\) mmol, giving 7.5 mmol \(\ce{NH3}\) and 2.5 mmol \(\ce{NH4+}\).
2. \(\text{pOH}=4.74+\log(2.5/7.5)=4.27\).
3. \(\text{pH}=9.73\).

Teacher's Note:
1. Strong base converts ammonium into ammonia.
2. More base than salt gives pOH below pKb.

Question 2: A buffer contains 0.02 mol propionic acid and 0.015 mol sodium propionate in 1.00 L (\(K_a=1.34\times10^{-5}\)). Its pH is
(a) 4.87
(b) 4.75
(c) 4.60
(d) 5.00
Show Answer & Explanation

Answer: (b) 4.75

Explanation:
1. \(\text{p}K_a=4.873\).
2. \(\text{pH}=4.873+\log(0.015/0.020)=4.873-0.125\).
3. \(\text{pH}=4.75\).

Teacher's Note:
1. Salt is less than acid, so the pH is below pKa.
2. Use the Henderson equation.

Question 3: To 10 mL of the buffer in the previous problem (0.02 M acid, 0.015 M salt, \(K_a=1.34\times10^{-5}\)) \(1.0\times10^{-5}\) mol of \(\ce{HCl}\) is added. The new pH is
(a) 4.70
(b) 2.00
(c) 4.75
(d) 4.80
Show Answer & Explanation

Answer: (a) 4.70

Explanation:
1. Moles in 10 mL: acid \(=2.0\times10^{-4}\), salt \(=1.5\times10^{-4}\).
2. HCl converts salt to acid: acid \(=2.1\times10^{-4}\), salt \(=1.4\times10^{-4}\).
3. \(\text{pH}=4.873+\log(1.4/2.1)=4.70\).

Teacher's Note:
1. The buffer absorbs strong acid with only a small pH change.
2. Convert the concentrations to moles in the sample.

Question 4: To 10 mL of the same buffer (0.02 M propionic acid, 0.015 M sodium propionate, \(K_a=1.34\times10^{-5}\)) \(1.0\times10^{-5}\) mol of \(\ce{NaOH}\) is added. The new pH is
(a) 4.70
(b) 4.80
(c) 9.00
(d) 4.75
Show Answer & Explanation

Answer: (b) 4.80

Explanation:
1. Moles in 10 mL: acid \(=2.0\times10^{-4}\), salt \(=1.5\times10^{-4}\).
2. NaOH converts acid to salt: acid \(=1.9\times10^{-4}\), salt \(=1.6\times10^{-4}\).
3. \(\text{pH}=4.873+\log(1.6/1.9)=4.80\).

Teacher's Note:
1. Base raises the pH slightly.
2. A buffer resists change but does not stop it.

Question 5: The \([H^+]\) of a solution that is 0.01 M in chloroacetic acid and 0.002 M in sodium chloroacetate (\(K_a=1.5\times10^{-3}\)) is
(a) \(7.5\times10^{-3}\ \text{M}\)
(b) \(3.87\times10^{-3}\ \text{M}\)
(c) \(1.5\times10^{-3}\ \text{M}\)
(d) \(2.5\times10^{-3}\ \text{M}\)
Show Answer & Explanation

Answer: (d) \(2.5\times10^{-3}\ \text{M}\)

Explanation:
1. Let \(x=[H^+]\): \(\dfrac{x(0.002+x)}{0.01-x}=1.5\times10^{-3}\).
2. \(x^2+0.0035x-1.5\times10^{-5}=0\), so \(x=2.5\times10^{-3}\ \text{M}\).

Teacher's Note:
1. The buffer formula fails because the acid is fairly strong.
2. Solve the quadratic including the dissociation of the acid.

Question 6: A solution has \([H^+]=4\times10^{-3}\) M. For thymol blue, pH is 2.0 when half of the indicator is in the unionised form. The percentage of indicator in the unionised form at this \([H^+]\) is
(a) 71.4%
(b) 50%
(c) 28.6%
(d) 10%
Show Answer & Explanation

Answer: (c) 28.6%

Explanation:
1. Half unionised at pH 2 means \(\text{p}K_{in}=2\), so \(K_{in}=10^{-2}\).
2. \(\dfrac{[In^-]}{[HIn]}=\dfrac{K_{in}}{[H^+]}=\dfrac{10^{-2}}{4\times10^{-3}}=2.5\).
3. Fraction unionised \(=1/(1+2.5)=28.6\%\).

Teacher's Note:
1. At half ionisation pH equals pKin.
2. Convert the ratio into a percentage of the total.

Question 7: An indicator is a weak acid with \(K_{in}=4\times10^{-4}\). For which of the neutralisations (a) NaOH + CH3COOH, (b) HCl + NH3, (c) HCl + NaOH would it be useful?
(a) only (b) and (c)
(b) only (a)
(c) only (a) and (b)
(d) all of (a), (b) and (c)
Show Answer & Explanation

Answer: (a) only (b) and (c)

Explanation:
1. The indicator changes colour near \(\text{p}K_{in}=3.4\), roughly pH 2.4 to 4.4.
2. (c) The jump for a strong acid and strong base covers pH 4 to 10, which includes 3.4 to 4.4. (b) The equivalence point of a strong acid with a weak base is acidic (about 5), and the steep part reaches down to pH 3 to 4.
3. (a) Weak acid with strong base ends in the basic region, where this indicator is already fully in one colour, so it is not useful.

Teacher's Note:
1. Choose an indicator whose range lies on the steep part of the titration curve.
2. Match acidic indicators to acidic equivalence points.

Question 8: Bromophenol blue is an indicator with \(K_a=6\times10^{-5}\). The percentage of this indicator in its basic form at pH 5 is
(a) 85.7%
(b) 50%
(c) 14.3%
(d) 60%
Show Answer & Explanation

Answer: (a) 85.7%

Explanation:
1. \(\dfrac{[In^-]}{[HIn]}=\dfrac{K_a}{[H^+]}=\dfrac{6\times10^{-5}}{10^{-5}}=6\).
2. Basic fraction \(=6/7=85.7\%\).

Teacher's Note:
1. The base-to-acid ratio equals Ka over [H+].
2. Basic form is the ionised form.

Question 9: An indicator has \(K_a=3\times10^{-5}\), with a red acid form and a blue basic form. By how much must the pH change to change the indicator from 75% red to 75% blue?
(a) 1.908
(b) 0.954
(c) 0.301
(d) 0.477
Show Answer & Explanation

Answer: (b) 0.954

Explanation:
1. \(\text{pH}=\text{p}K_a+\log\dfrac{[\text{blue}]}{[\text{red}]}\).
2. At 75% red the ratio is \(1/3\), and at 75% blue it is \(3\).
3. \(\Delta\text{pH}=\log3-\log(1/3)=2\log3=0.954\).

Teacher's Note:
1. Both ratios are symmetric around the pKa.
2. The change is independent of the actual Ka value.

Question 10: In the titration of a weak acid HX with NaOH, the pH is 5.8 after 10.0 mL of NaOH and 6.402 after 20.0 mL. The \(\text{p}K_a\) of HX is
(a) 7.00
(b) 5.80
(c) 6.40
(d) 6.10
Show Answer & Explanation

Answer: (d) 6.10

Explanation:
1. With equivalence volume \(V_e\): \(\text{pH}=\text{p}K_a+\log\dfrac{V}{V_e-V}\).
2. Subtracting the two equations: \(0.602=\log\dfrac{2(V_e-10)}{V_e-20}\), so \(4=\dfrac{2(V_e-10)}{V_e-20}\) and \(V_e=30\) mL.
3. \(\text{p}K_a=5.8-\log(10/20)=6.10\), so \(K_a=7.9\times10^{-7}\).

Teacher's Note:
1. The unknown equivalence volume can be eliminated using two points.
2. pKa is the pH at half equivalence, 15 mL here.

Question 11: 0.515 g of phenol (\(\ce{C6H5OH}\), molar mass 94) is dissolved in exactly 100 mL of water and titrated with 0.123 M NaOH (\(K_a=1.3\times10^{-10}\)). The pH at the equivalence point is
(a) 7.00
(b) 11.22
(c) 8.73
(d) 5.28
Show Answer & Explanation

Answer: (b) 11.22

Explanation:
1. Moles of phenol \(=0.515/94=5.48\) mmol, so the volume of NaOH needed is \(44.5\) mL and the final volume is \(144.5\) mL.
2. \([\text{C}_6\text{H}_5\text{O}^-]=5.48/144.5=0.0379\ \text{M}\) and \(K_h=K_w/K_a=7.7\times10^{-5}\). Solving \(\dfrac{x^2}{0.0379-x}=7.7\times10^{-5}\) gives \([OH^-]=1.67\times10^{-3}\ \text{M}\).
3. \(\text{pOH}=2.78\), so \(\text{pH}=11.22\) and \([Na^+]=0.0379\ \text{M}\).

Teacher's Note:
1. Phenoxide is a much stronger base than acetate because phenol is a weaker acid.
2. Equivalence point of a weak acid with strong base is above 7.

Question 12: A weak acid (50.0 mL) is titrated with 0.1 M NaOH. The pH is 4.16 after 10.0 mL and 4.76 after 25.0 mL of base. The \(K_a\) of the acid and the pH at the equivalence point are
(a) \(K_a=5.7\times10^{-10}\) and pH \(=8.73\)
(b) \(K_a=1.74\times10^{-5}\) and pH \(=7.00\)
(c) \(K_a=1.74\times10^{-5}\) and pH \(=8.73\)
(d) \(K_a=1.74\times10^{-5}\) and pH \(=5.27\)
Show Answer & Explanation

Answer: (c) \(K_a=1.74\times10^{-5}\) and pH \(=8.73\)

Explanation:
1. Half way point at 25 mL (equivalence at 50 mL) gives \(\text{p}K_a=4.76\), so \(K_a=1.74\times10^{-5}\).
2. Salt concentration at equivalence \(=0.05\ \text{M}\).
3. \([OH^-]=\sqrt{\dfrac{K_w}{K_a}C}=5.36\times10^{-6}\ \text{M}\), so \(\text{pOH}=5.27\) and \(\text{pH}=8.73\).

Teacher's Note:
1. pH at half neutralisation equals pKa.
2. The 10 mL point is consistent: 4.76 + log(10/40) = 4.16.

Question 13: 50 mL of 0.1 M acetic acid (\(K_a=2\times10^-5\)) is titrated with 0.1 M NaOH. The pH after adding 20 mL of NaOH is
(a) 4.52
(b) 3.52
(c) 5.30
(d) 4.70
Show Answer & Explanation

Answer: (a) 4.52

Explanation:
1. \(\ce{CH3COOH}=5\) mmol and \(\ce{NaOH}=2\) mmol, leaving 3 mmol acid and 2 mmol acetate.
2. \(\text{pH}=4.70+\log(2/3)=4.52\).

Teacher's Note:
1. Identify the stage of titration before choosing a formula.
2. Buffer region uses the Henderson equation; equivalence uses salt hydrolysis.

Question 14: 50 mL of 0.1 M acetic acid (\(K_a=2\times10^-5\)) is titrated with 0.1 M NaOH. The pH after adding 40 mL of NaOH is
(a) 5.30
(b) 4.10
(c) 5.00
(d) 4.70
Show Answer & Explanation

Answer: (a) 5.30

Explanation:
1. \(\ce{CH3COOH}=5\) mmol and \(\ce{NaOH}=4\) mmol, leaving 1 mmol acid and 4 mmol acetate.
2. \(\text{pH}=4.70+\log4=5.30\).

Teacher's Note:
1. Identify the stage of titration before choosing a formula.
2. Buffer region uses the Henderson equation; equivalence uses salt hydrolysis.

Question 15: 50 mL of 0.1 M acetic acid (\(K_a=2\times10^-5\)) is titrated with 0.1 M NaOH. The pH after adding 50 mL of NaOH is
(a) 5.30
(b) 7.00
(c) 9.30
(d) 8.70
Show Answer & Explanation

Answer: (d) 8.70

Explanation:
1. Equivalence: 5 mmol of acetate in 100 mL, so \(C=0.05\ \text{M}\).
2. \([OH^-]=\sqrt{\dfrac{10^{-14}}{2\times10^{-5}}\times0.05}=5\times10^{-6}\ \text{M}\), so \(\text{pOH}=5.30\) and \(\text{pH}=8.70\).

Teacher's Note:
1. Identify the stage of titration before choosing a formula.
2. Buffer region uses the Henderson equation; equivalence uses salt hydrolysis.

Question 16: The salts MX and \(\ce{QX2}\) each have \(K_{sp}=4.0\times10^{-18}\). Which is more soluble and what are the solubilities?
(a) MX is more soluble: \(2\times10^{-9}\ \text{M}\) against \(10^{-6}\ \text{M}\)
(b) \(\ce{QX2}\) is more soluble: \(2\times10^{-9}\ \text{M}\) against \(10^{-6}\ \text{M}\)
(c) \(\ce{QX2}\) is more soluble: \(10^{-6}\ \text{M}\) against \(2\times10^{-9}\ \text{M}\)
(d) both are equally soluble at \(2\times10^{-9}\ \text{M}\)
Show Answer & Explanation

Answer: (c) \(\ce{QX2}\) is more soluble: \(10^{-6}\ \text{M}\) against \(2\times10^{-9}\ \text{M}\)

Explanation:
1. For MX, \(S=\sqrt{K_{sp}}=2\times10^{-9}\ \text{M}\).
2. For \(\ce{QX2}\), \(K_{sp}=4S^3\), so \(S=(10^{-18})^{1/3}=10^{-6}\ \text{M}\).
3. \(\ce{QX2}\) is more soluble.

Teacher's Note:
1. Salts of different types cannot be compared by Ksp alone.
2. Calculate the molar solubility of each.

Question 17: The solubility of \(\ce{PbSO4}\) in water is 0.038 g/L (molar mass 303). Its solubility product is
(a) \(1.6\times10^{-4}\)
(b) \(1.25\times10^{-4}\)
(c) \(1.6\times10^{-8}\)
(d) \(3.2\times10^{-8}\)
Show Answer & Explanation

Answer: (c) \(1.6\times10^{-8}\)

Explanation:
1. \(S=0.038/303=1.25\times10^{-4}\ \text{mol L}^{-1}\).
2. \(K_{sp}=S^2=1.57\times10^{-8}\approx1.6\times10^{-8}\).

Teacher's Note:
1. For a 1:1 salt Ksp is the square of the solubility.
2. Convert g per L into mol per L first.

Question 18: The solubility of \(\ce{Mg(OH)2}\) in water (\(K_{sp}=1.2\times10^{-11}\)) is
(a) \(3.46\times10^{-6}\ \text{M}\)
(b) \(1.2\times10^{-11}\ \text{M}\)
(c) \(2.29\times10^{-4}\ \text{M}\)
(d) \(1.44\times10^{-4}\ \text{M}\)
Show Answer & Explanation

Answer: (d) \(1.44\times10^{-4}\ \text{M}\)

Explanation:
1. \(K_{sp}=4S^3\).
2. \(S=(1.2\times10^{-11}/4)^{1/3}=(3\times10^{-12})^{1/3}=1.44\times10^{-4}\ \text{M}\).

Teacher's Note:
1. Mg(OH)2 gives one Mg2+ and two OH-.
2. Cube root, not square root.

Question 19: The number of moles of \(\ce{CuI}\) (\(K_{sp}=5\times10^{-12}\)) that dissolve in 1.0 L of 0.10 M \(\ce{NaI}\) is
(a) \(5\times10^{-11}\)
(b) \(5\times10^{-12}\)
(c) \(2.24\times10^{-6}\)
(d) \(5\times10^{-13}\)
Show Answer & Explanation

Answer: (a) \(5\times10^{-11}\)

Explanation:
1. \([I^-]\approx0.10\ \text{M}\) from NaI.
2. \(S=[Cu^+]=K_{sp}/[I^-]=5\times10^{-12}/0.10=5\times10^{-11}\ \text{mol L}^{-1}\).

Teacher's Note:
1. Common ion greatly lowers the solubility.
2. The iodide from the sparingly soluble salt is negligible.

Question 20: A saturated solution of \(\ce{CaF2}\) contains \(4.1\times10^{-4}\) M fluoride ion. Its \(K_{sp}\) (neglecting hydrolysis) is
(a) \(1.7\times10^{-7}\)
(b) \(1.7\times10^{-10}\)
(c) \(6.9\times10^{-11}\)
(d) \(3.45\times10^{-11}\)
Show Answer & Explanation

Answer: (d) \(3.45\times10^{-11}\)

Explanation:
1. \([Ca^{2+}]=\tfrac12[F^-]=2.05\times10^{-4}\ \text{M}\).
2. \(K_{sp}=[Ca^{2+}][F^-]^2=2.05\times10^{-4}\times(4.1\times10^{-4})^2=3.45\times10^{-11}\).

Teacher's Note:
1. Do not set the calcium concentration equal to the fluoride concentration.
2. Square the fluoride concentration.

Question 21: The solubility of \(\ce{Fe(OH)3}\) (\(K_{sp}=1.0\times10^{-36}\)) in a solution of pH 8.0 is
(a) \(1\times10^{-18}\ \text{M}\)
(b) \(1\times10^{-36}\ \text{M}\)
(c) \(1\times10^{-24}\ \text{M}\)
(d) \(1\times10^{-30}\ \text{M}\)
Show Answer & Explanation

Answer: (a) \(1\times10^{-18}\ \text{M}\)

Explanation:
1. \([OH^-]=10^{-6}\ \text{M}\) at pH 8.
2. \(S=K_{sp}/[OH^-]^3=10^{-36}/10^{-18}=10^{-18}\ \text{M}\).

Teacher's Note:
1. pH fixes the hydroxide concentration.
2. Cube the hydroxide concentration.

Question 22: The solubility of \(\ce{Ag2CrO4}\) in water is 0.044 g/L (molar mass 332). Its \(K_{sp}\) is
(a) \(1.3\times10^{-4}\)
(b) \(1.7\times10^{-8}\)
(c) \(9.3\times10^{-12}\)
(d) \(3.1\times10^{-12}\)
Show Answer & Explanation

Answer: (c) \(9.3\times10^{-12}\)

Explanation:
1. \(S=0.044/332=1.33\times10^{-4}\ \text{M}\).
2. \(K_{sp}=4S^3=4\times(1.33\times10^{-4})^3=9.3\times10^{-12}\).

Teacher's Note:
1. Silver chromate is a 2:1 salt.
2. Ksp = 4 S cubed.

Question 23: The solubility of \(\ce{A2X3}\) in pure water (\(K_{sp}=1.1\times10^{-23}\)), assuming no reaction of the ions with water, is
(a) \(3.3\times10^{-8}\ \text{M}\)
(b) \(1\times10^{-4}\ \text{M}\)
(c) \(1\times10^{-5}\ \text{M}\)
(d) \(1.1\times10^{-5}\ \text{M}\)
Show Answer & Explanation

Answer: (c) \(1\times10^{-5}\ \text{M}\)

Explanation:
1. \(K_{sp}=(2S)^2(3S)^3=108S^5\).
2. \(S=(1.1\times10^{-23}/108)^{1/5}=(1.02\times10^{-25})^{1/5}\approx1.0\times10^{-5}\ \text{M}\).

Teacher's Note:
1. A2X3 gives 2 A and 3 X ions per formula unit.
2. Take the fifth root.

Question 24: The solubility of \(\ce{AgCl}\) (\(K_{sp}=1\times10^{-10}\)) in 0.1 M \(\ce{BaCl2}\) is
(a) \(1\times10^{-9}\ \text{M}\)
(b) \(1\times10^{-5}\ \text{M}\)
(c) \(2.5\times10^{-10}\ \text{M}\)
(d) \(5\times10^{-10}\ \text{M}\)
Show Answer & Explanation

Answer: (d) \(5\times10^{-10}\ \text{M}\)

Explanation:
1. \([Cl^-]=2\times0.1=0.2\ \text{M}\).
2. \(S=[Ag^+]=K_{sp}/[Cl^-]=10^{-10}/0.2=5\times10^{-10}\ \text{M}\).

Teacher's Note:
1. Barium chloride provides two chloride ions per formula unit.
2. Common ion effect.

Question 25: A solution has \([Mg^{2+}]=0.0010\ \text{M}\) and \(K_{sp}\) of \(\ce{Mg(OH)2}=1.2\times10^{-11}\). Will \(\ce{Mg(OH)2}\) precipitate if \([OH^-]\) is (i) \(10^{-5}\) M and (ii) \(10^{-3}\) M?
(a) precipitate in (i), no precipitate in (ii)
(b) no precipitate in (i), precipitate in (ii)
(c) no precipitate in either
(d) precipitate in both
Show Answer & Explanation

Answer: (b) no precipitate in (i), precipitate in (ii)

Explanation:
1. (i) \(Q=10^{-3}\times(10^{-5})^2=10^{-13}<1.2\times10^{-11}\), so no precipitate.
2. (ii) \(Q=10^{-3}\times(10^{-3})^2=10^{-9}>1.2\times10^{-11}\), so it precipitates.

Teacher's Note:
1. Compare the ionic product with Ksp.
2. A precipitate forms only if Q exceeds Ksp.

Question 26: The solubility of \(\ce{AgCN}\) (\(K_{sp}=4\times10^{-16}\)) in a buffer of pH 3 is (take \(K_a\) of HCN \(=9\times10^{-10}\))
(a) \(4\times10^{-3}\ \text{M}\)
(b) \(2\times10^{-8}\ \text{M}\)
(c) \(2.1\times10^{-5}\ \text{M}\)
(d) \(2\times10^{-9}\ \text{M}\)
Show Answer & Explanation

Answer: (c) \(2.1\times10^{-5}\ \text{M}\)

Explanation:
1. The cyanide formed combines with \(\ce{H+}\): \(S=[Ag^+]=[CN^-]+[HCN]=[CN^-](1+[H^+]/K_a)\).
2. \(1+10^{-3}/9\times10^{-10}=1.11\times10^{6}\), so \(K_{sp}=[Ag^+][CN^-]\) gives \(S^2=K_{sp}\times1.11\times10^{6}=4.44\times10^{-10}\).
3. \(S=2.1\times10^{-5}\ \text{M}\).

Teacher's Note:
1. The salt of a weak acid is more soluble in acid.
2. Include the protonated cyanide in the total solubility.

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