Suppose 3.005 g of a nonvolatile solute is added to 20.02 g of water (the solvent), and the boiling point increases from 100.000 OC to 101.286 OC. Determine the TB, molality, moles, and molecular weight for the solute if kb for water is 0.512 OC/m. Report each value using the correct number of significant digits. Refer to Example 1.2 and pages 3-4 in the chapter 1 notes for general chemistry 1 to understand significant figures. Also, include all applicable units and conversion factors.

Whereas T2 accounts for the boiling point of the solution which is 101.286 °C, T1 the volume of pure water which is 100.000 °C, i the van't Hoff factor that for this problem is 1 due to the solute's non-volatility, m the molality of the solute and Kb the boiling point constant that is 0.512 °C/m. In such a way, the change in the temperature is:

[tex]\Delta T=T_2-T_1=101.286\°C-100.000\°C=1.286\°C[/tex]

The molality is computed from the boiling point raise:

[tex]m=\frac{T_2-T_1}{Kb}=\frac{1.286\°C}{0.512\°C/m}\\ \\m=2.51mol/kg[/tex]

The moles are computed by multiplying the molality by the kilograms of water as the solvent (0.02002g):

[tex]n=2.51mol/kg*0.02002kg\\\\n=0.0503mol[/tex]

And the molecular mass by dividing the mass of the solute by its moles:

[tex]M=\frac{3.005g}{0.0503mol}\\ \\M=59.8g/mol[/tex]

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