Example 50. Calculate normality of the mixture obtained by mixing 100ml of 0.1N HCl and 50ml of 0.25N NaOH solution.
(a) 0.0467 N
(b) 0.0367 N
(c) 0.0267 N
(d) 0.0167 N
Ans. (d)
Solution.
Molal eq. of HCl = 100 × 0.1 = 10
Molal eq. of NaOH = 50 × 0.25 = 12.5
HCl and NaOH neutralize each other with equal eq.
Eq. of NaOH left = 12.5  10 = 2.5
Volume of new solution = 100 + 50 = 150 ml.
Hence normality of the mixture obtained is 0.0167 N
Example 51. 300 ml 0.1 M HCl and 200 ml of 0.03M H_{2}SO_{4} are mixed. Calculate the normality of the resulting mixture
(a) 0.084 N
(b) 0.84 N
(c) 2.04 N
(d) 2.84 N
Ans. (a)
Solution.
For HCl For H_{2}SO_{4}
V_{1} = 300 ml V_{2} = 200 ml
N_{1} = M × Basicity N_{2} = M × Basicity
= 0.1 × 1 = 0.1 = 0.03 × 2 = 0.06
Normality of the mixture
= 0.084 N
Example 52. In what ratio should a 6.5 N HNO_{3} be diluted with water to get 3.5 N HNO_{3}?
(a) 6 : 7
(b) 7 : 6
(c) 5 : 6
(d) 6 : 5
Ans. (b)
Solution.
N_{1}V_{1} = N_{2}V_{2}
6.5 V_{1} = 3.5 (V_{1} x)
6.5 V_{1} = 3.5 V_{1} 3.5 x
3 V_{1} = 3.5 x
_{ }
Example 53. Calculate the amount of each in the following solutions 
(i) 150 ml of N/7 H_{2}SO_{4}
(ii) 250 ml of 0.2M NaHCO_{3}
(iii) 400 ml of N/10 Na_{2}CO_{3}
(iv) 1052 g of 1 m KOH.
(a) 52g, 2.12g, 4.2g, 1.05g
(b) 1.05g, 4.2g, 2.12g, 52g
(c) 1.05g, 2.12g, 52g, 4.2g
(d) 4.2g, 2.12g, 1.05g, 52g
Ans. (b)
Solution.
(i) Eq. wt. of H_{2}SO_{4}
Amount of H_{2}SO_{4} per litre (strength) = Normality × Eq. wt. = × 49 = 7 g/litre
Amount in 150 ml
(ii) Molecular wt. of
NaHCO_{3} = 23 1 12 48 = 84
Amount of NaHCO_{3} required to produce 1000 c.c. of one molar solution = 84 g
Amount present per litre in 0.2 M solution = 84 × 0.2 = 16.8 g
Amount present in 250 c.c.
= 4.2 g
(iii) Equivalent weight of
= 53
Amount of Na_{2}CO_{3} = Normality × Eq. wt. = × 53 = 5.3 g/litre
Amount present in 400 c.c.
= 2.12 g
(iv) We know that 1 molal solution of a substance contains 1000 g of solvent.
Wt. of KOH in 1052 g of 1 m KOH solution = 1052  1000 = 52 g
Example 54. How many kilograms of wet NaOH containing 12% water are required to prepare 60 litres of 0.50 N solution ?
(a) 1.36 kg
(b) 1.50 kg
(c) 2.40 gm
(d) 3.16 kg
Ans. (a)
Solution.
One litre of 0.50 N NaOH contains = 0.50 × 40g = 20 g = 0.020 kg
60 litres of 0.50 N NaOH contain
= 0.020 × 60 kg = 1.20 kg NaOH
Since the given NaOH contains 12% water, the amount of pure NaOH in 100 kg of the given NaOH = 100  12 = 88 kg
Thus 88 kg of pure NaOH is present in 100 kg wet NaOH
1.20 kg of pure NaOH is present in
= 1.36 kg wet NaOH
Example 55. Calculate the vapour pressure of a solution at 100^{0}C containing 3g of cane sugar in 33g of water. (At wt. C = 12 , H = 1 , O = 16)
(a) 760 mm
(b) 756.90 mm
(c) 758.30 mm
(d) None
Ans. (b)
Solution.
Vapour pressure of pure water (solvent) at 1000C, p° = 760 mm.
Vapour pressure of solution, p = ?
Wt. of solvent, W = 33g
Wt. of solute, w = 3g
Mol. wt. of water (H_{2}O), M = 18
Mol. wt. of sugar (C_{12}H_{22}O_{11}),
m = (12 × 12) + (22 × 1) + (11 × 16) = 342
According to Raoult's law,
(pº^{ }for H_{2}O = 760 mm)
= 760  3.19 = 756.90 mm
Example 56. Osmotic pressure of a sugar solution at 24°C is 2.5 atmospheres. Determine the concentration of the solution in gm mole per litre.
(a) 0.0821 moles/litre
(b) 1.082 moles/litre
(c) 0.1025 moles/litre
(d) 0.0827 moles/litre
Ans. (c)
Solution.
Here it is given that
p = 2.5 atm, T = 24 273 = 297K, S = 0.0821 lit. atm. deg^{1} mol^{1}, C = ?
We know that p = CST
or
= 0.1025 moles/litre
Example 57. Twenty grams of a substance were dissolved in 500 ml. of water and the osmotic pressure of the solution was found to be 600 mm of mercury at 15ºC. Determine the molecular weight of the substance
(a) 1120
(b) 1198
(c) 1200
(d) None of these
Ans. (c)
Solution.
Here it is given that
w = 20 gm ; V = 500 ml.
= 500/1000 = 0.5 litre
p = 600 mm = 600/760 atm;
T = 15 273 = 288^{0}A
m = ?
According to Van't Hoff equation,
pV = nST pV
= 1198
Example 58. Blood plasma has the following composition (milliequivalents per litre). Calculate its osmotic pressure at 37^{0}C.
Na^{ } = 138 , Ca^{2 } = 5.2, K^{ } = 4.5, Mg^{2 } = 2.0 , Cl¯ = 105, HCO_{3}¯ = 25, PO_{4}^{3}= 2.2 , SO_{4}^{2}= 0.5,
Proteins = 16, Others = 1.0
(a) 7.47 atm
(b) 7.30 atm
(c) 7.29 atm
(d) 7.40 atm
Ans. (a)
Solution.
Since for calculating osmotic pressure we require millimoles/litre therefore
Na^{+}= 138 Ca^{2+ }= 5.2/2 = 2.6, K^{ }= 4.5,
Mg^{2+ }= 2.0/2 = 1.0 , Cl¯ = 105,
HCO_{3}¯ = 24,PO_{4}^{3}^{}= 2.2/3 = 0.73,
SO_{4}^{2}^{}= 0.5/2 = 0.25 , Proteins = 16,
others = 1.0
Total = 294.18 millimoles/litre = 294.18/1000
= 0.294 moles/litre
Now since p = CST
= 0.294 × 0.0821 × .310 = 7.47 atm
Example 59. 0.15g of a substance dissolved in 15g of solvent boiled at a temperature higher by 0.216^{0}C than that of the pure solvent. Calculate the molecular weight of the substance. Molal elevation constant for the solvent is 2.16^{0}C.
(a) 216
(b) 100
(c) 178
(d) None of these
Ans. (b)
Solution.
Here it is given that
w = 0.15 g, DT_{b} = 0.216^{0}C
W = 15g K_{b} = 2.16^{0}C
m = ?
Substituting values in the expression,
= 100
Example 60. A solution of 0.450 gm of urea (mol. wt 60) in 22.5 g of water showed 0.170^{0}C of elevation in boiling point. Calculate the molal elevation constant of water
(a) 0.17ºC
(b) 0.45ºC
(c) 0.51ºC
(d) 0.30ºC
Ans. (c)
Solution.Fig: Structure of urea
Wt. of solute, w = 0.450 g
Wt. of solvent, W = 22.5 g
Mol. wt of solute, m = 60
Molal elevation constant K_{b} = ?
Boiling point elevation, DT_{b} = 0.170^{0}C
Substituting these values in the equation
=
= 0.51^{0}C
Example 61. Calculate the boiling point of a solution containing 0.45g of camphor (mol. wt. 152) dissolved in 35.4g of acetone (b.p. 56.3^{0}C); K_{b} per 100 gm of acetone is 17.2^{0}C.
(a) 56.446°C
(b) 52.401°C
(c) 56.146°C
(d) 50.464°C
Ans. (a)
Solution.
Here it is given that
w = 0.45 g, W = 35.4, m = 152,
Kb = 17.2 per 100gm
Now we know that ΔT_{b}
(Note that this is expression when K_{b} is given per 100g of the solvent)
Substituting the values in the above expression.
= 0.146^{0}C
Now we know that
B.P. of solution (T)  B.P. of solvent (T_{0}) = DT
B.P. of solution (T) = B.P. of solvent(T_{0}) DT
Hence B.P. of solution = 56.3 0.146
= 56.446^{0}C
Example 62. The freezing point of 0.2 molal K_{2}SO_{4} is _1.1ºC. Calculate Van't Haff factor and percentage degree of dissociation of K_{2}SO_{4}. K_{f} for water is 1.86º
(a) 97.5
(b) 90.75
(c) 105.5
(d) 85.75
Ans. (a)
Solution.
ΔT_{f} = freezing point of water freezing point of solution = 0º C  (1.1º C) = 1.1º
We know that,
ΔT_{f} = i × K_{f} × m
1.1 = i × 1.86 × 0.2
But we know
i = 1 (n  1) a
2.95 = 1 (3  1) a = 1 2a
a = 0.975
Van't Haff factor (i) = 2.95
Degree of dissociation = 0.975
Percentage degree of dissociation = 97.5

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