Chemistry Objective Questions and Answers: Ionic Equilibrium
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Multiple Choice Questions
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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.
(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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