Calculate the molal elevation boiling point constant of a solution containg 1.0gm of urea (M=60) in 75.0gm water and boils at 100.114C.

To find the molal elevation boiling point constant (Kb) of a solution, we first need to understand the relationship between the boiling point elevation, the molality of the solution, and the constant itself. The formula we use is:

ΔT_b = Kb * m

Where:

• ΔT_b is the boiling point elevation.
• Kb is the molal boiling point elevation constant.
• m is the molality of the solution.

Let's break down the problem step by step.

Step 1: Calculate the boiling point elevation (ΔT_b)

The normal boiling point of water is 100.0 °C. The solution boils at 100.114 °C, so:

ΔT_b = 100.114 °C - 100.0 °C = 0.114 °C

Step 2: Determine the molality (m) of the solution

Molality is defined as the number of moles of solute per kilogram of solvent. First, we need to calculate the number of moles of urea:

Number of moles of urea = mass (g) / molar mass (g/mol)

Given that the mass of urea is 1.0 g and its molar mass (M) is 60 g/mol:

Number of moles of urea = 1.0 g / 60 g/mol = 0.01667 moles

Next, we convert the mass of water from grams to kilograms:

Mass of water = 75.0 g = 0.075 kg

Now we can calculate the molality:

m = moles of solute / kg of solvent = 0.01667 moles / 0.075 kg = 0.2223 mol/kg

Step 3: Rearranging the formula to find Kb

Now that we have both ΔT_b and m, we can rearrange the formula to solve for Kb:

Kb = ΔT_b / m

Step 4: Plugging in the values

Substituting the values we calculated:

Kb = 0.114 °C / 0.2223 mol/kg ≈ 0.513 °C kg/mol

Final Result

The molal elevation boiling point constant (Kb) for the solution is approximately 0.513 °C kg/mol. This value indicates how much the boiling point of the solvent (water, in this case) is elevated per mole of solute added per kilogram of solvent.