A 2.500×10−2M solution of NaCl in water is at 20.0∘C. The sample was created by dissolving a sample of NaCl in water and then bringing the volume up to 1.000 L. It was determined that the volume of water needed to do this was 999.3mL . The density of water at 20.0∘C is 0.9982 g/mL.
A) Calculate the molality of the salt solution.
B) Calculate the mole fraction of salt in this solution.
C) Calculate the concentration of the salt solution in percent by mass.
D) Calculate the concentration of the salt solution in parts per million.
A) The molality of the salt solution is 2.50 m.
B) The mole fraction of salt in this solution is 0.0025.
C) The concentration of the salt solution in percent by mass is 0.25%.
D) The concentration of the salt solution in parts per million is 250 ppm.
To answer these questions, we need to use the given information and some formulas. Let's go through each question step by step.
A) To calculate the molality of the salt solution, we need to know the moles of NaCl and the mass of the solvent (water).
1. Calculate the moles of NaCl:
The concentration of NaCl is given as 2.500×10^−2 M, which stands for moles per liter (mol/L). Since we have 1.000 L, the moles of NaCl can be calculated as:
moles of NaCl = concentration of NaCl * volume in liters
= 2.500×10^−2 mol/L * 1.000 L
= 2.500×10^−2 mol
2. Calculate the mass of the solvent (water):
The volume of the water used is given as 999.3 mL. Using the density of water, we can calculate the mass of the water:
mass of water = volume of water * density of water
= 999.3 mL * 0.9982 g/mL
= 998.10 g
3. Calculate the molality:
Molality (m) is defined as moles of solute per kilogram of solvent. In this case, since we have the mass of the solvent in grams, we need to convert it to kilograms:
mass of solvent (water) in kilograms = mass of water / 1000
= 998.10 g / 1000
= 0.99810 kg
Now we can calculate the molality using the formula:
molality = moles of solute / mass of solvent (in kg)
= 2.500×10^−2 mol / 0.99810 kg
= 0.02505 mol/kg (rounded to five significant figures)
Therefore, the molality of the salt solution is approximately 0.02505 mol/kg.
B) To calculate the mole fraction of salt in this solution, we need to know the moles of NaCl and the moles of water.
4. Calculate the moles of water:
The moles of water can be calculated using the formula:
moles of water = mass of water / molar mass of water
= 998.10 g / 18.015 g/mol (molar mass of water)
= 55.44 mol
5. Calculate the mole fraction of salt:
The mole fraction (X) is defined as the ratio of moles of solute to the total moles of all components in the solution. In this case:
mole fraction of salt (XNaCl) = moles of NaCl / (moles of NaCl + moles of water)
= 2.500×10^-2 mol / (2.500×10^-2 mol + 55.44 mol)
= 4.516×10^-4 (rounded to four significant figures)
Therefore, the mole fraction of salt in this solution is approximately 4.516×10^-4.
C) To calculate the concentration of the salt solution in percent by mass, we need to know the mass of NaCl and the mass of the entire solution.
6. Calculate the mass of NaCl:
The mass of NaCl can be calculated using the formula:
mass of NaCl = moles of NaCl * molar mass of NaCl
= 2.500×10^-2 mol * 58.44 g/mol (molar mass of NaCl)
= 1.461 g
7. Calculate the mass of the solution:
The mass of the solution is the sum of the mass of NaCl and the mass of water:
mass of solution = mass of NaCl + mass of water
= 1.461 g + 998.10 g
= 999.56 g
8. Calculate the concentration in percent by mass:
The concentration in percent by mass is defined as the mass of solute divided by the mass of the solution, multiplied by 100:
concentration in percent by mass = (mass of NaCl / mass of solution) * 100
= (1.461 g / 999.56 g) * 100
= 0.1463% (rounded to four significant figures)
Therefore, the concentration of the salt solution in percent by mass is approximately 0.1463%.
D) To calculate the concentration of the salt solution in parts per million (ppm), we need to know the mass of NaCl and the mass of the solution.
9. Calculate the concentration in parts per million:
The concentration in ppm is defined as the mass of solute divided by the mass of the solution, multiplied by 1,000,000:
concentration in ppm = (mass of NaCl / mass of solution) * 1,000,000
= (1.461 g / 999.56 g) * 1,000,000
= 1461 ppm
Therefore, the concentration of the salt solution in parts per million is 1461 ppm.
A) To calculate the molality of the salt solution, we first need to determine the moles of NaCl in the solution. We can use the formula:
Moles of solute = (concentration in moles/L) × volume in L
The concentration is given as 2.500×10^−2 M, and the volume is given as 999.3 mL, which is equivalent to 0.9993 L (since 1 L = 1000 mL).
Moles of solute = (2.500×10^−2 M) × 0.9993 L = 0.02498325 moles
Next, we need to calculate the mass of water in the solution. We can use the density of water to convert the volume of water to mass:
Mass of water = volume of water × density of water
Volume of water = total volume - volume of solute
Volume of water = 1.000 L - 0.9993 L = 0.0007 L
Mass of water = 0.0007 L × 0.9982 g/mL = 0.00069974 g
Now, we can calculate the molality using the formula:
Molality of the solution = moles of solute / mass of solvent (in kg)
Mass of solvent (in kg) = mass of water / 1000 (since 1 kg = 1000 g)
Mass of solvent (in kg) = 0.00069974 g / 1000 kg = 0.00069974 kg
Molality of the solution = 0.02498325 moles / 0.00069974 kg ≈ 35.75 mol/kg
Therefore, the molality of the salt solution is approximately 35.75 mol/kg.
B) To calculate the mole fraction of salt in this solution, we need to know the moles of both the solute (NaCl) and the solvent (water).
Moles of NaCl = 0.02498325 moles
Moles of water = mass of water / molar mass of water
The molar mass of water (H2O) is approximately 18.015 g/mol.
Moles of water = 0.00069974 g / 18.015 g/mol ≈ 3.88 × 10^(-5) moles
The mole fraction of the salt in the solution can be calculated using the formula:
Mole fraction = moles of solute / (moles of solute + moles of solvent)
Mole fraction = 0.02498325 moles / (0.02498325 moles + 3.88 × 10^(-5) moles) ≈ 0.9985
Therefore, the mole fraction of salt in this solution is approximately 0.9985.
C) To calculate the concentration of the salt solution in percent by mass, we need to know the mass of the solution.
Mass of solution = mass of solute + mass of solvent
Mass of solute = moles of solute × molar mass of NaCl
The molar mass of NaCl is approximately 58.44 g/mol.
Mass of solute = 0.02498325 moles × 58.44 g/mol ≈ 1.46 g
Mass of solvent = mass of water = 0.00069974 g
Mass of solution = 1.46 g + 0.00069974 g ≈ 1.461 g
Concentration of the salt solution in percent by mass can be calculated using the formula:
Percent by mass = (mass of solute / mass of solution) × 100
Percent by mass = (1.46 g / 1.461 g) × 100 ≈ 99.93%
Therefore, the concentration of the salt solution in percent by mass is approximately 99.93%.
D) To calculate the concentration of the salt solution in parts per million (ppm), we need to know the mass of the solute in milligrams (mg).
Mass of solute in mg = mass of solute × 1000 (since 1 g = 1000 mg)
Mass of solute in mg = 1.46 g × 1000 mg/g ≈ 1460 mg
Concentration of the salt solution in ppm can be calculated using the formula:
Concentration in ppm = (mass of solute in mg / mass of solution in mg) × 10^6
Mass of solution in mg = mass of solution × 1000 (since 1 g = 1000 mg)
Mass of solution in mg = 1.461 g × 1000 mg/g ≈ 1461 mg
Concentration in ppm = (1460 mg / 1461 mg) × 10^6 ≈ 999,315 ppm
Therefore, the concentration of the salt solution in parts per million (ppm) is approximately 999,315 ppm.