what are the normal freezing points and boiling points of the following solutions: a. 21.1g NaCl in 135mL of water b. 15.4g urea in 66.7 mL water?
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To determine the freezing points and boiling points of solutions, we need to apply the concept of colligative properties. The freezing point depression and boiling point elevation are based on the concentration of solute particles rather than the specific identity of the solute.
For both solutions, we'll calculate the molality of the solution using the given mass of the solute and the mass of the solvent. Then, using the molality values, we can use the appropriate formulas to calculate the freezing point depression and boiling point elevation.
a. 21.1g NaCl in 135mL of water:
Step 1: Calculate the molality (mol/kg) of NaCl:
Molar mass of NaCl = 22.99 g/mol (sodium) + 35.45 g/mol (chlorine) = 58.44 g/mol
Number of moles of NaCl = mass of NaCl / molar mass of NaCl
Number of moles of NaCl = 21.1 g / 58.44 g/mol
Number of moles of NaCl = 0.361 mol
Mass of water = volume of water × density of water
Mass of water = 135 mL × 1 g/mL (since the density of water is approximately 1 g/mL)
Mass of water = 135 g
Molality of NaCl = moles of NaCl / mass of water (in kg)
Molality of NaCl = 0.361 mol / 0.135 kg
Molality of NaCl = 2.68 mol/kg
Step 2: Calculate the freezing point depression (∆Tf):
∆Tf = Kf × molality
Kf (molality freezing point depression constant of water) = 1.86 °C/m
∆Tf = 1.86 °C/m × 2.68 mol/kg
∆Tf = 4.99 °C
Step 3: Calculate the freezing point of the solution:
Freezing point of the solution = Freezing point of pure water - ∆Tf
Freezing point of pure water = 0 °C
Freezing point of the solution = 0 °C - 4.99 °C
Freezing point of the solution ≈ -4.99 °C
b. 15.4g urea in 66.7 mL water:
Step 1: Calculate the molality (mol/kg) of urea:
Molar mass of urea = 60.06 g/mol
Number of moles of urea = mass of urea / molar mass of urea
Number of moles of urea = 15.4 g / 60.06 g/mol
Number of moles of urea = 0.256 mol
Mass of water = 66.7 mL × 1 g/mL = 66.7 g
Molality of urea = moles of urea / mass of water (in kg)
Molality of urea = 0.256 mol / 0.0667 kg
Molality of urea = 3.84 mol/kg
Step 2: Calculate the boiling point elevation (∆Tb):
∆Tb = Kb × molality
Kb (molality boiling point elevation constant of water) = 0.512 °C/m
∆Tb = 0.512 °C/m × 3.84 mol/kg
∆Tb = 1.97 °C
Step 3: Calculate the boiling point of the solution:
Boiling point of the solution = Boiling point of pure water + ∆Tb
Boiling point of pure water = 100 °C
Boiling point of the solution = 100 °C + 1.97 °C
Boiling point of the solution ≈ 101.97 °C
Therefore, the freezing point of the 21.1g NaCl solution in 135mL of water is approximately -4.99 °C, and the boiling point of the 15.4g urea solution in 66.7 mL water is approximately 101.97 °C.