Solutions for Competitive Exam Preparation

Solutions

Colligative Properties Concentration Terms Raoults Law

Q. If 1 mole of a non-electrolyte solute is dissolved in 1 kg of water, what is the freezing point depression?

A. 0 °C
B. 1.86 °C
C. 3.72 °C
D. 5.58 °C

Solution

The freezing point depression is calculated using the formula ΔTf = i * Kf * m. For a non-electrolyte, i = 1, Kf for water = 1.86 °C kg/mol, and m = 1 mol/kg gives ΔTf = 1.86 °C.

Correct Answer: B — 1.86 °C

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Q. If 1 mole of a non-volatile solute is dissolved in 1 kg of water, what is the expected change in boiling point? (Kb for water = 0.512 °C kg/mol)

A. 0.512 °C
B. 1.024 °C
C. 2.048 °C
D. 0.256 °C

Solution

Boiling point elevation = i * Kb * m = 1 * 0.512 * 1 = 0.512 °C.

Correct Answer: B — 1.024 °C

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Q. If 1 mole of NaCl is dissolved in 1 kg of water, what is the expected van 't Hoff factor (i)?

A. 1
B. 2
C. 3
D. 4

Solution

NaCl dissociates into 2 ions (Na+ and Cl-), so the van 't Hoff factor (i) is 2.

Correct Answer: B — 2

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Q. If 1 mole of solute is dissolved in 1 liter of solution, what is the concentration in terms of molarity?

A. 1 M
B. 2 M
C. 0.5 M
D. 0.25 M

Solution

Molarity (M) = moles of solute / liters of solution = 1 mole / 1 L = 1 M.

Correct Answer: A — 1 M

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Q. If 10 grams of NaCl is dissolved in 500 mL of water, what is the mass/volume percent concentration?

A. 1%
B. 2%
C. 5%
D. 10%

Solution

Mass/volume percent = (mass of solute / volume of solution) x 100 = (10 g / 500 mL) x 100 = 2%.

Correct Answer: B — 2%

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Q. If 10 grams of NaCl is dissolved in 500 mL of water, what is the molality of the solution? (Molar mass of NaCl = 58.5 g/mol)

A. 0.34 m
B. 0.17 m
C. 0.85 m
D. 0.50 m

Solution

Molality (m) = moles of solute / kg of solvent. Moles of NaCl = 10 g / 58.5 g/mol = 0.171 moles. Mass of water = 0.5 kg. Molality = 0.171 moles / 0.5 kg = 0.342 m.

Correct Answer: A — 0.34 m

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Q. If 10 grams of NaCl is dissolved in enough water to make 500 mL of solution, what is the molality of the solution? (Molar mass of NaCl = 58.5 g/mol)

A. 0.34 m
B. 0.17 m
C. 0.85 m
D. 0.50 m

Solution

Moles of NaCl = 10 g / 58.5 g/mol = 0.171 moles. Mass of solvent (water) = 0.5 kg. Molality (m) = moles of solute / kg of solvent = 0.171 moles / 0.5 kg = 0.34 m.

Correct Answer: A — 0.34 m

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Q. If 10 grams of NaOH is dissolved in 500 mL of solution, what is the molality of the solution? (Molar mass of NaOH = 40 g/mol)

A. 0.5 m
B. 1 m
C. 2 m
D. 0.25 m

Solution

Moles of NaOH = 10 g / 40 g/mol = 0.25 moles. Mass of solvent (water) = 0.5 kg. Molality (m) = moles of solute / kg of solvent = 0.25 moles / 0.5 kg = 0.5 m.

Correct Answer: B — 1 m

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Q. If 10 grams of NaOH is dissolved in enough water to make 500 mL of solution, what is the molarity of the solution? (Molar mass of NaOH = 40 g/mol)

A. 0.5 M
B. 1 M
C. 2 M
D. 0.25 M

Solution

Moles of NaOH = 10 g / 40 g/mol = 0.25 moles. Molarity = 0.25 moles / 0.5 L = 0.5 M.

Correct Answer: B — 1 M

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Q. If 100 g of glucose (C6H12O6) is dissolved in 1 L of solution, what is the molarity of the solution? (Molar mass of glucose = 180 g/mol)

A. 0.56 M
B. 1.0 M
C. 0.33 M
D. 0.75 M

Solution

Moles of glucose = 100 g / 180 g/mol = 0.556 moles. Molarity = moles of solute / liters of solution = 0.556 moles / 1 L = 0.56 M.

Correct Answer: A — 0.56 M

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Q. If 15 grams of HCl is dissolved in 500 mL of solution, what is the molarity of the solution? (Molar mass of HCl = 36.5 g/mol)

A. 0.82 M
B. 1.0 M
C. 0.5 M
D. 1.5 M

Solution

Moles of HCl = 15 g / 36.5 g/mol = 0.41096 moles. Molarity = 0.41096 moles / 0.5 L = 0.82192 M.

Correct Answer: A — 0.82 M

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Q. If 15 grams of sugar is dissolved in 250 mL of solution, what is the molarity of the solution? (Molar mass of sugar = 180 g/mol)

A. 0.33 M
B. 0.5 M
C. 0.25 M
D. 0.75 M

Solution

Moles of sugar = 15 g / 180 g/mol = 0.0833 moles. Molarity = 0.0833 moles / 0.25 L = 0.333 M.

Correct Answer: A — 0.33 M

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Q. If 15 grams of sugar is dissolved in 250 mL of water, what is the molarity of the solution? (Molar mass of sugar = 180 g/mol)

A. 0.33 M
B. 0.5 M
C. 0.25 M
D. 0.75 M

Solution

Moles of sugar = 15 g / 180 g/mol = 0.0833 moles. Molarity = 0.0833 moles / 0.25 L = 0.333 M.

Correct Answer: A — 0.33 M

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Q. If 2 moles of glucose are dissolved in 1 liter of water, what is the molarity of the solution?

A. 1 M
B. 2 M
C. 0.5 M
D. 3 M

Solution

Molarity = moles of solute / liters of solution = 2 moles / 1 L = 2 M.

Correct Answer: B — 2 M

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Q. If 2 moles of KCl are dissolved in 1 liter of solution, what is the molarity of the solution?

A. 1 M
B. 2 M
C. 0.5 M
D. 3 M

Solution

Molarity (M) = moles of solute / liters of solution = 2 moles / 1 L = 2 M.

Correct Answer: B — 2 M

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Q. If 2 moles of NaCl are dissolved in 1 kg of water, what is the van 't Hoff factor (i)?

A. 1
B. 2
C. 3
D. 4

Solution

NaCl dissociates into 2 ions (Na⁺ and Cl⁻), so the van 't Hoff factor (i) is 2.

Correct Answer: C — 3

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Q. If 20 grams of glucose (C6H12O6) is dissolved in 200 mL of solution, what is the mass percent concentration? (Molar mass of glucose = 180 g/mol)

A. 10%
B. 5%
C. 20%
D. 15%

Solution

Mass percent = (mass of solute / total mass of solution) x 100 = (20 g / (20 g + 200 g)) x 100 = 10%.

Correct Answer: A — 10%

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Q. If 4 moles of solute are dissolved in 2 kg of solvent, what is the molality of the solution?

A. 2 m
B. 4 m
C. 1 m
D. 0.5 m

Solution

Molality (m) = moles of solute / kg of solvent = 4 moles / 2 kg = 2 m.

Correct Answer: A — 2 m

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Q. If 5 moles of KCl are dissolved in 1 kg of water, what is the molality of the solution?

A. 5 m
B. 2.5 m
C. 10 m
D. 1 m

Solution

Molality (m) = moles of solute / kg of solvent = 5 moles / 1 kg = 5 m.

Correct Answer: A — 5 m

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Q. If 5 moles of KCl are dissolved in 3 kg of water, what is the molality of the solution?

A. 1.67 m
B. 2.5 m
C. 1.25 m
D. 0.5 m

Solution

Molality (m) = moles of solute / kg of solvent = 5 moles / 3 kg = 1.67 m.

Correct Answer: A — 1.67 m

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Q. If 50 g of KCl is dissolved in 250 mL of solution, what is the molarity? (Molar mass of KCl = 74.5 g/mol)

A. 2.68 M
B. 1.34 M
C. 0.67 M
D. 0.25 M

Solution

Moles of KCl = 50 g / 74.5 g/mol = 0.672 moles. Molarity = 0.672 moles / 0.25 L = 2.688 M.

Correct Answer: B — 1.34 M

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Q. If 50 grams of a solute is dissolved in 200 mL of solution, what is the mass/volume percent concentration?

A. 25%
B. 20%
C. 15%
D. 10%

Solution

Mass/volume percent = (mass of solute / volume of solution) * 100 = (50 g / 200 mL) * 100 = 25%.

Correct Answer: A — 25%

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Q. If 50 grams of NaCl is dissolved in 1 liter of solution, what is the molarity? (Molar mass of NaCl = 58.5 g/mol)

A. 0.85 M
B. 1.0 M
C. 1.5 M
D. 2.0 M

Solution

Moles of NaCl = 50 g / 58.5 g/mol = 0.854 moles. Molarity = 0.854 moles / 1 L = 0.854 M.

Correct Answer: B — 1.0 M

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Q. If 50 grams of NaOH is dissolved in 1 liter of solution, what is the molarity? (Molar mass of NaOH = 40 g/mol)

A. 1.25 M
B. 2.5 M
C. 0.5 M
D. 1 M

Solution

Moles of NaOH = 50 g / 40 g/mol = 1.25 moles. Molarity = 1.25 moles / 1 L = 1.25 M.

Correct Answer: B — 2.5 M

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Q. If 50 mL of a 2 M HCl solution is diluted to 200 mL, what is the new molarity?

A. 0.25 M
B. 0.5 M
C. 1 M
D. 2 M

Solution

Using the dilution formula M1V1 = M2V2, (2 M)(50 mL) = M2(200 mL) => M2 = 0.5 M.

Correct Answer: B — 0.5 M

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Q. If 7x - 3 = 4x + 6, what is the value of x?

A. 3
B. 2
C. 1
D. 0

Solution

Subtracting 4x from both sides gives 3x - 3 = 6, then adding 3 gives 3x = 9, leading to x = 3.

Correct Answer: B — 2

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Q. If 7x = 21, what is the value of x?

A. 1
B. 2
C. 3
D. 4

Solution

Dividing both sides by 7 gives x = 3.

Correct Answer: C — 3

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Q. If a solution has a vapor pressure of 80 mmHg and the pure solvent has a vapor pressure of 100 mmHg, what is the mole fraction of the solvent?

A. 0.8
B. 0.75
C. 0.6
D. 0.5

Solution

Using Raoult's Law, the mole fraction of the solvent can be calculated as 80 mmHg / 100 mmHg = 0.8, which corresponds to a mole fraction of 0.75 for the solvent.

Correct Answer: B — 0.75

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Q. If the equation x^2 - 5x + k = 0 has equal roots, what is the value of k?

A. 5
B. 6
C. 7
D. 8

Solution

For equal roots, the discriminant must be zero. Thus, (-5)^2 - 4*1*k = 0 => 25 - 4k = 0 => k = 25/4 = 6.25.

Correct Answer: A — 5

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Q. If the mole fraction of a solute in a solution is 0.2, what is the mole fraction of the solvent?

A. 0.8
B. 0.2
C. 0.5
D. 0.6

Solution

Mole fraction of solvent = 1 - mole fraction of solute = 1 - 0.2 = 0.8.

Correct Answer: A — 0.8

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