3.0 molal NaOH solution has a density of 1.110g/ml. The molarity of th...
3.0 molal NaOH solution has a density of 1.110g/ml. The molarity of th...
Solution:
Given:
Molality (m) = 3.0 mol/kg
Density = 1.110 g/mL
To find:
Molarity (M) of the solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent.
Molality (m) = moles of solute / mass of solvent in kg
We know that the molar mass of NaOH is 40 g/mol.
Step 1: Calculation of mass of solute (NaOH)
The molality is given as 3.0 mol/kg. Let's assume the mass of the solvent is 1 kg.
Therefore, the moles of solute (NaOH) = molality x mass of solvent = 3.0 mol/kg x 1 kg = 3.0 mol
Step 2: Calculation of volume of solution
The density is given as 1.110 g/mL. Let's assume the volume of the solution is V mL.
Therefore, the mass of the solution = density x volume of solution = 1.110 g/mL x V mL = 1.110V g
Since the mass of the solution is equal to the mass of the solute plus the mass of the solvent, we can write:
mass of the solution = mass of solute (NaOH) + mass of solvent
1.110V g = 3.0 mol x 40 g/mol + mass of solvent
Step 3: Calculation of mass of solvent
Rearranging the equation, we get:
mass of solvent = 1.110V g - 3.0 mol x 40 g/mol
Step 4: Calculation of molarity
Molarity (M) is defined as the number of moles of solute per liter of solution.
Molarity (M) = moles of solute / volume of solution in L
Since the volume of the solution is given in mL, we need to convert it to L.
1 L = 1000 mL
Therefore, volume of solution in L = V mL / 1000 = V/1000 L
Using the equation for molarity, we can substitute the values we calculated:
Molarity (M) = 3.0 mol / (V/1000 L)
Since the answer choices are given in 3 decimal places, we need to round the molarity to the nearest thousandth.
Therefore, the molarity of the solution is given by option (D) 2.973 M.
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.