Solutions Chapter-Wise Test 11

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the mole fraction of acetone (molar mass = 58 g/mol) in a solution containing 29 g of acetone and 54 g of water?

Moles of acetone = \( \frac{29}{58} = 0.5 \, \text{mol} \).

Moles of water = \( \frac{54}{18} = 3 \, \text{mol} \).

Total moles = \( 0.5 + 3 = 3.5 \).

Mole fraction = \( \frac{0.5}{3.5} \approx 0.143 \).

0.143
0.2
0.25
0.33
1

A solution of a non-volatile solute in water boils at 100.39°C at 1 atm. If the solute’s molality is 0.75 mol/kg, what is the value of \( K_b \) for water?

\( \Delta T_b = K_b \cdot m \).

\( 100.39 - 100 = 0.39 \).

\( 0.39 = K_b \times 0.75 \).

\( K_b = \frac{0.39}{0.75} = 0.52 \, \text{K kg mol}^{-1} \).

0.5 K kg mol\(^{-1}\)
0.48 K kg mol\(^{-1}\)
0.55 K kg mol\(^{-1}\)
0.52 K kg mol\(^{-1}\)
4

The vapor pressure of pure ethanol is 60 mm Hg. What is the vapor pressure of a solution with a solute mole fraction of 0.2?

Mole fraction of ethanol = \( 1 - 0.2 = 0.8 \).

Vapor pressure = \( 60 \times 0.8 = 48 \, \text{mm Hg} \).

48 mm Hg
50 mm Hg
45 mm Hg
55 mm Hg
1

A solution contains 25 g of a solute in 75 g of water. If the mass percentage of the solute is reduced to 20% by adding water, what is the total mass of the new solution?

Initial mass % = \( \frac{25}{25 + 75} \times 100 = 25\% \).

New mass % = \( 20\% = \frac{25}{25 + 75 + w} \times 100 \).

\( 0.2 (100 + w) = 25 \), \( 100 + w = 125 \), \( w = 25 \, \text{g} \).

Total mass = \( 100 + 25 = 125 \, \text{g} \).

125 g
150 g
100 g
130 g
1

A solution of two volatile liquids has vapor pressures of 200 mm Hg and 300 mm Hg for pure components. If the mole fraction of the first is 0.7, what is the total vapor pressure?

Mole fraction of second = \( 1 - 0.7 = 0.3 \).

Total vapor pressure = \( 200 \times 0.7 + 300 \times 0.3 = 140 + 90 = 230 \, \text{mm Hg} \).

220 mm Hg
230 mm Hg
240 mm Hg
250 mm Hg
2

A solution is made by mixing 30 g of a solute (molar mass = 60 g/mol) with water. If the molality is 0.5 mol/kg, what is the total mass of the solution?

Moles of solute = \( \frac{30}{60} = 0.5 \, \text{mol} \).

Molality = \( \frac{\text{Moles}}{\text{Mass of solvent in kg}} \), \( 0.5 = \frac{0.5}{w} \).

\( w = 1 \, \text{kg} = 1000 \, \text{g} \).

Total mass = \( 30 + 1000 = 1030 \, \text{g} \).

1000 g
1020 g
1030 g
1050 g
3

A solute dissociates into 2 ions with a van’t Hoff factor of 1.6. What is the degree of dissociation?

\( i = 1 + \alpha (n - 1) \), where \( n = 2 \).

\( 1.6 = 1 + \alpha \).

\( \alpha = 1.6 - 1 = 0.6 \).

0.4
0.5
0.7
0.6
4

A solution contains 20 g of a solute in 80 g of solvent. If the mass percentage is 20%, what is the mass of the solution?

Total mass = 20 g + 80 g = 100 g.

Mass % = \( \frac{20}{100} \times 100 = 20\% \), which matches the given value.

50 g
100 g
120 g
80 g
2

A solution contains 7 g of a solute (molar mass = 140 g/mol) in 350 mL of solution. What is the molarity?

Moles of solute = \( \frac{7}{140} = 0.05 \, \text{mol} \).

Volume = 350 mL = 0.35 L.

Molarity = \( \frac{0.05}{0.35} \approx 0.1429 \, \text{M} \).

0.13 M
0.1429 M
0.15 M
0.1 M
2

A 0.25 M solution of MgCl₂ (assuming complete dissociation) has an osmotic pressure of 1.845 atm at a certain temperature. What is the temperature? (\( R = 0.0821 \, \text{L atm mol}^{-1} \text{K}^{-1} \))

For MgCl₂, \( i = 3 \) (Mg²⁺ + 2Cl⁻).

\( \Pi = i \cdot M \cdot RT \).

\( 1.845 = 3 \times 0.25 \times 0.0821 \times T \).

\( T = \frac{1.845}{0.75 \times 0.0821} \approx 30 \, \text{K} \).

25 K
28 K
30 K
32 K
3

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