Mole concept and molar mass

Correct answer: B. 0.10 mol

Molarity is moles of solute per litre of solution, so use n = M × V with volume in litres. Convert 400 mL to 0.400 L. Then n = 0.25 mol L⁻¹ × 0.400 L = 0.100 mol. Thus option B is correct. The value 0.25 ignores the volume, while using 400 without conversion would create a factor-of-1000 error.

Correct answer: C. 0.4 M

Molarity is the amount of solute in moles divided by the volume of the complete solution in litres: M = n/V. Convert 500 mL to 0.500 L, then calculate M = 0.2/0.500 = 0.40 mol L−1, or 0.4 M. Thus option C is correct. Option B ignores the volume conversion, while option D reverses the division and gives litres per mole rather than moles per litre.

Correct answer: C. 0.4 mol kg⁻¹

Molality is calculated using the mass of solvent, not the total mass or volume of the solution. First convert 500 g of solvent into kilograms: 500 g = 0.500 kg. Then apply m = moles of solute / kilograms of solvent. Thus m = 0.2/0.5 = 0.4 mol kg⁻¹. Therefore, option C is correct. The solute amount is already given in moles, so no further conversion is required.

Correct answer: D. 100 g mol⁻¹

Use the definition of molar mass: M = mass/amount in moles. The given mass is 3 g and the amount is 0.03 mol. Thus, M = 3/0.03 = 100 g mol⁻¹. Therefore, option D is correct. A useful check is that 0.03 × 100 = 3, which reproduces the stated mass. The answer must have the unit grams per mole, not grams alone or moles per gram.

Correct answer: C. 180 g mol⁻¹

Molar mass is obtained from M = m/n. Substituting the given values, M = 18 g / 0.1 mol = 180 g mol⁻¹. Thus, option C is correct. This result means that one mole of the substance would have a mass of 180 g, assuming the sample represents the same pure substance. Option A incorrectly uses the sample mass without accounting for the fact that the sample contains only 0.1 mol.

Correct answer: C. 180 g mol⁻¹

Molar mass is the mass of one mole of a substance and is calculated using M = m/n, where m is mass in grams and n is amount in moles. Here, M = 1.8 g ÷ 0.01 mol = 180 g mol⁻¹. Dividing by 0.01 is equivalent to multiplying by 100. Hence, the correct answer is option C, and the unit confirms that the result is a molar mass.

Correct answer: C. 100 g mol⁻¹

Molar mass is calculated by dividing the mass of a substance by its amount in moles: M = m/n. Here the mass is 1 g and the amount is 0.01 mol. Thus, M = 1 g ÷ 0.01 mol = 100 g mol⁻¹. The answer must have units of grams per mole because grams are divided by moles. Therefore, option C is correct. This is a basic mole-concept calculation.

Correct answer: C. 100 g mol⁻¹

The molar mass formula is M = mass ÷ amount in moles. Substituting the given values gives M = 5 g ÷ 0.050 mol = 100 g mol⁻¹. Therefore, option C is correct. The decimal 0.050 equals 5 hundredths of a mole, so dividing 5 by 0.05 gives 100 rather than 0.25 or 50. The unit is grams per mole.

Correct answer: C. 180 g mol⁻¹

Molarity gives moles per litre of solution. Therefore, the moles of solute are n = M × V = 0.010 mol L⁻¹ × 1 L = 0.010 mol. The molar mass is then mass ÷ moles = 1.8 g ÷ 0.010 mol = 180 g mol⁻¹. Thus, option C is correct. The volume must be expressed in litres because the concentration is given in mol L⁻¹.

Correct answer: A. 0.1 mol

The number of moles is obtained by dividing the given mass by the molar mass: n = m/M. Substituting the values gives n = 18 g ÷ (180 g mol⁻¹) = 0.1 mol. The gram units cancel, leaving the unit mol. Therefore, 18 g of glucose represents one-tenth of a mole, and option A is correct.

Correct answer: C. 100 g mol^-1

Molality is defined as moles of solute per kilogram of solvent. Therefore, the number of solute moles is n = 0.25 mol kg^-1 × 0.2 kg = 0.05 mol. Molar mass is the mass of solute divided by the number of moles, so M = 5 g/0.05 mol = 100 g mol^-1. The non-dissociation condition confirms that the given molality corresponds directly to the solute formula units. Thus, option C is correct.

Correct answer: C. 200 g mol^-1

Molar mass is defined as the mass of a substance divided by the amount of substance in moles: M = m/n. Here, m = 2 g and n = 0.01 mol. Therefore, M = 2/0.01 = 200 g mol^-1. The statement that the solute is non-dissociated is not needed for this direct calculation because the actual number of moles is already provided. Therefore, option C is correct.

Correct answer: B. \(40\,\mathrm{g\,mol^{-1}}\)

Molar mass is the mass of one mole and is calculated using \(M=m/n\), where \(m\) is the sample mass and \(n\) is the amount in moles. Substituting the given values gives \(M=5\,\mathrm{g}/0.125\,\mathrm{mol}=40\,\mathrm{g\,mol^{-1}}\). The units are grams per mole, as required. Therefore, option B is correct.

Correct answer: C. 60 g mol⁻¹

Molar mass is the mass of one mole of a substance and is calculated using M = m/n, where m is the given mass and n is the amount in moles. Substituting the data gives M = 12 g ÷ 0.2 mol = 60 g mol⁻¹. Therefore, option C is correct. The answer 120 g mol⁻¹ would result from incorrectly treating the amount as 0.1 mol.