A certain substance X has a normal boiling point of 101.6°C and a molal boiling point elevation constant =Kb·2.26°C·kgmol−1. A solution is prepared by dissolving some urea NH22CO in 350.g of X. This solution boils at 105.3°C. Calculate the mass of urea that was dissolved.Round your answer to 2 significant digits.
Question
A certain substance X has a normal boiling point of 101.6°C and a molal boiling point elevation constant =Kb·2.26°C·kgmol−1. A solution is prepared by dissolving some urea NH22CO in 350.g of X. This solution boils at 105.3°C. Calculate the mass of urea that was dissolved.Round your answer to 2 significant digits.
Solution
To solve this problem, we need to use the formula for boiling point elevation, which is ΔTb = Kb·m, where ΔTb is the change in boiling point, Kb is the boiling point elevation constant, and m is the molality of the solution.
Step 1: Calculate the change in boiling point (ΔTb) ΔTb = Tb (solution) - Tb (pure solvent) ΔTb = 105.3°C - 101.6°C = 3.7°C
Step 2: Calculate the molality (m) using the formula ΔTb = Kb·m Rearrange the formula to solve for m: m = ΔTb / Kb m = 3.7°C / 2.26°C·kgmol−1 = 1.64 mol/kg
Step 3: Calculate the mass of urea (NH22CO) We know that molality (m) = moles of solute / mass of solvent (in kg) Rearrange the formula to solve for moles of solute: moles of solute = m * mass of solvent moles of solute = 1.64 mol/kg * 0.350 kg = 0.574 mol
The molar mass of urea (NH22CO) is approximately 60 g/mol, so the mass of urea is: mass of urea = moles of solute * molar mass of solute mass of urea = 0.574 mol * 60 g/mol = 34.44 g
So, the mass of urea that was dissolved is approximately 34.44 g. Rounded to two significant digits, the mass of urea is 34 g.
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