Question at position 27 Dimethylglyoxime, DMG, is a nonelectrolyte compound. A solution prepared by dissolving 65.0 g of DMG in 375 g of ethanol boils at 80.3 °C. What is the molar mass of DMG? Kb = 1.22 °C/m, boiling point of pure ethanol = 78.5 °C 132 g/mol 65.8 g/mol 553 g/mol 117 g/mol 44.1 g/molSingle choice
A
132 g/mol
B
65.8 g/mol
C
553 g/mol
D
117 g/mol
E
44.1 g/mol

Question

Question at position 27 Dimethylglyoxime, DMG, is a nonelectrolyte compound. A solution prepared by dissolving 65.0 g of DMG in 375 g of ethanol boils at 80.3 °C. What is the molar mass of DMG? Kb = 1.22 °C/m, boiling point of pure ethanol = 78.5 °C 132 g/mol 65.8 g/mol 553 g/mol 117 g/mol 44.1 g/molSingle choice

A

132 g/mol

B

65.8 g/mol

C

553 g/mol

D

117 g/mol

E

44.1 g/mol

BlackTom AI · Accepted Answer

ΔTb = Kb · m (with van ’t Hoff factor i = 1 for a nonelectrolyte), so use ΔTb = 1 · Kb · m.

Relevant concepts:
- Boiling-point elevation is a colligative property: ΔTb = i Kb m.
- Molality m = moles solute / kilograms solvent.
- DMG is a nonelectrolyte, so i = 1.

Step-by-step reasoning and calculations:
1. Calculate the boiling-point elevation:
   ΔTb = T_solution − T_pure = 80.3 °C − 78.5 °C = 1.8 °C.
2. Use ΔTb = i Kb m with i = 1:
   m = ΔTb / Kb = 1.8 °C / 1.22 °C·kg/mol = 1.475409836... mol/kg.
3. Convert solvent mass to kilograms: 375 g = 0.375 kg.
4. Find moles of DMG:
   moles = m · kg solvent = 1.475409836 mol/kg × 0.375 kg = 0.5532786885 mol.
5. Compute molar mass (M = mass / moles):
   M = 65.0 g / 0.5532786885 mol = 117.515... g/mol ≈ 117 g/mol (to appropriate significant figures).

Why this answer is correct:
- The calculation uses the correct form of the boiling-point elevation law with i = 1 (nonelectrolyte).
- All unit conversions and intermediate steps are consistent; the computed molar mass (≈117.5 g/mol) rounds to 117 g/mol, matching the provided choice.

Why the other choices are incorrect:
- 132 g/mol and 65.8 g/mol do not match the derived value from the colligative calculation.
- 553 g/mol and 44.1 g/mol are far from the calculated ~117.5 g/mol and thus inconsistent with the measured ΔTb.

Conclusion: The molar mass of DMG is 117 g/mol, which agrees with the provided correct answer.

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