The density of 3M solution of NaCl is 1.25 g/mL. Calculate the molality of the solution.
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To calculate the molality of the solution, we need to know the molar mass of sodium chloride (NaCl). The molar mass of NaCl is 58.44 g/mol.
Molality (m) is defined as the number of moles of solute (in this case, NaCl) per kilogram of solvent (in this case, water).
Step 1: Calculate the mass of 1 liter (1000 mL) of the solution.
Given that the density of the solution is 1.25 g/mL, the mass of 1 liter of the solution can be calculated as follows:
Mass of 1 liter solution = Density * Volume
Mass of 1 liter solution = 1.25 g/mL * 1000 mL
Mass of 1 liter solution = 1250 g
Step 2: Calculate the number of moles of NaCl in the solution.
To find the number of moles, we first need to find the mass of NaCl in the solution. This can be calculated as follows:
Mass of NaCl = Mass of solution * Fraction of NaCl in solution
Mass of NaCl = 1250 g * (3/1000) [3M means 3 moles of NaCl in 1 liter of solution]
Mass of NaCl = 3.75 g
Next, calculate the number of moles using the formula:
Number of moles = Mass of NaCl / Molar mass of NaCl
Number of moles = 3.75 g / 58.44 g/mol
Number of moles = 0.064 moles
Step 3: Calculate the mass of the water in kilograms.
As molality is defined as the number of moles per kilogram of water, we need to convert the mass of water from grams to kilograms:
Mass of water = Mass of solution - Mass of NaCl
Mass of water = 1250 g - 3.75 g
Mass of water = 1246.25 g
Mass of water in kg = 1246.25 g / 1000
Mass of water in kg = 1.24625 kg
Step 4: Calculate the molality.
Now, we have the number of moles of solute (NaCl) and the mass of the solvent (water). We can use these values to calculate the molality using the formula:
Molality (m) = Number of moles / Mass of water in kg
Molality (m) = 0.064 moles / 1.24625 kg
Molality (m) ≈ 0.0514 mol/kg
Therefore, the molality of the 3M NaCl solution is approximately 0.0514 mol/kg.