a solution is made by dissolving 25 g NaCl in enough water to make 1.0 L solution. Assume that density of the solution is 1.0 g/mL. calculate the mass percent, molarity, molality, and mole fraction of NaCl.
To calculate the mass percent, molarity, molality, and mole fraction of NaCl, we need to understand the definitions and formulas for each of these terms.
1. Mass Percent (%):
The mass percent is the percentage of the total mass of the solution that is contributed by a specific component (in this case, NaCl). It is calculated using the formula:
Mass Percent = (Mass of NaCl / Mass of Solution) x 100
2. Molarity (M):
Molarity is a measure of the concentration of a solute in a solution, expressed in moles of solute per liter of solution. It is calculated using the formula:
Molarity (M) = (Number of moles of NaCl / Volume of Solution in liters)
3. Molality (m):
Molality is another measure of concentration, expressed in moles of solute per kilogram of solvent. It is calculated using the formula:
Molality (m) = (Number of moles of NaCl / Mass of Solvent in kilograms)
4. Mole fraction (χ):
The mole fraction is a dimensionless quantity used to express the ratio of the number of moles of a component to the total number of moles in a solution. It is calculated using the formula:
Mole fraction (χ) = (Number of moles of NaCl / Total Number of moles in solution)
Now, let's calculate each of these values:
1. Mass Percent (%):
The given mass of NaCl is 25 g, and the density of the solution is 1.0 g/mL. Since the volume of the solution is given as 1.0 L (which is equivalent to 1000 mL), we can calculate the mass of the solution:
Mass of Solution = Density x Volume = 1.0 g/mL x 1000 mL = 1000 g
Mass Percent = (25 g / 1000 g) x 100 = 2.5 %
2. Molarity (M):
To calculate the molarity, we first need to determine the number of moles of NaCl. We can use the formula:
Number of moles = Mass / Molar mass
The molar mass of NaCl (sodium chloride) is approximately 58.44 g/mol.
Number of moles of NaCl = 25 g / 58.44 g/mol ≈ 0.428 mol
Molarity (M) = 0.428 mol / 1.0 L = 0.428 M
3. Molality (m):
To calculate the molality, we need to know the mass of the solvent (water). The mass of the solution is 1000 g (as calculated earlier), and the mass of NaCl is 25 g.
Mass of Water = Mass of Solution - Mass of NaCl = 1000 g - 25 g = 975 g
Now we can calculate molality using the formula:
Molality (m) = 0.428 mol / 0.975 kg ≈ 0.439 m
4. Mole fraction (χ):
The total number of moles in the solution is the sum of the moles of NaCl and moles of water:
Total Number of moles = Number of moles of NaCl + Number of moles of Water
Number of moles of Water = Mass of Water / Molar mass of water
Molar mass of water is approximately 18.015 g/mol.
Number of moles of Water = 975 g / 18.015 g/mol ≈ 54.12 mol
Now, we can calculate the mole fraction of NaCl using the formula:
Mole fraction (χ) = 0.428 mol / (0.428 mol + 54.12 mol)
Mole fraction (χ) ≈ 0.0079
Therefore, the mass percent of NaCl is 2.5%, the molarity is 0.428 M, the molality is 0.439 m, and the mole fraction is 0.0079.