3) A solution is prepared by dissolving 20.2 ml of methanol in 100.0 mL of water

Question

3) A solution is prepared by dissolving 20.2 ml of methanol in 100.0 mL of water. The final volume of the solution is 118 ml. The densities of methanol and water are 0.782 g/mL and 1.00 g/ml, respectively. For this solution, calculate molarity, molality, mass percent and mole fraction. Be careful with "solution" vs. "solvent" for this problem. (Hint: the mass of the solution is the mass of the solute + the mass of the solvent.) (12 pts). Molarity: Molality: Mass %: Mole fraction: Hint! Start by figuring out: Volume of Solvent: Mass of Solvent: Moles of solvent: Volume of Solute: Mass of Solute: Moles of Solute: Volume of Solution: Mass of Solution:

Explanation / Answer

Part 1: Calculate moles of solvent

Volume of solvent (water) is 100.0 mL. Density of water is 1.00 g/mL. Calculate mass of water as follows:

Mass = Volume x Density

Mass = 100.0 mL x 1.00 g/mL

Mass = 100.0 g

Molar mass of water is 18.015 g/mol. Calcualte number of moles in 100.0 g of water as follows:

Moles of water = Mass / molar mass

Moles of water = (100.0 g) / (18.015 g/mol)

Moles of water = 5.55 mol

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Part 2: Calculate moles of solute

Volume of solute (methanol) is 20.2 mL. Density of methanol is 0.782 g/mL. Calculate mass of methanol as follows:

Mass = Volume x Density

Mass = 20.2 mL   x 0.782 g/mL

Mass = 15.8 g

Molar mass of methanol is 32.04 g/mol. Calcuate number of moles in 15.8 g of methanol as follows:

Moles of methanol = Mass / molar mass

Moles of methanol = (15.8 g) / (32.04 g/mol)

Moles of methanol = 0.49 mol

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Part 3: Calculate mass of solution

Volume of solution is 118 mL. Calcualte mass of solution by addition of mass of methanol and water.

Mass of solution = mass of water + mass of methanol

Mass of solution = 100.0 g + 15.8 g

Mass of solution = 115.8 g

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Part 4: Calculate molarity of the solution

Calculate molarity of the solution as follows:

Molarity = moles of solute / volume of solution in liter

Convert volume of solution from mL to L using conversion factor (1L / 1000 mL)

Molarity = 0.49 mol / 118 mL x (1L / 1000 mL)

Molarity = 4.15 M

Therefore, molarity of given solution of methanol in water is 4.15 M

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Part 5: Calculate molality of the solution

Calculate molality of the solution as follows:

Molality = moles of solute / mass of solution in kg

Convert mass of solution from g to kg using conversion factor (1kg / 1000 g)

Molality = 0.49 mol / 115.8 g x (1kg / 1000 g)

Molality = 4.23 molal

Therefore, molality of given solution of methanol in water is 4.23 molal

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Part 6: Calculate mass percent of the solution

Calculate mass percent of the solution as follows:

Mass percent = (Mass of solute / mass of solution) x 100

Mass percent = (15.8 g / 115.8 g) x 100

Mass percent = 13.64 %

Therefore, mass percent of methanol in given solution is 13.64 %

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Part 7 : Calculate mole fraction of the solution

Calculate mole fraction of the solution as follows:

Mole fraction = moles of solute / (moles of solute + moles of solvent)

Mole fraction = 0.49 mol / (0.49 mol + 5.55 mol)

Mole fraction = 0.49 mol / 6.04 mol

Mole fraction = 0.081

Therefore, mole fraction of methanol in given solution is 0.081

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