Question

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.

Answer 1

`\Delta T=1.286\°C`

`m=2.51mol/kg`

`n=0.0503mol`

`M=59.8g/mol`

Step-by-step explanation:

Hello,

In case, for the boiling point raise we can write:

`T_2-T_1=imK_b`

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:

`\Delta T=T_2-T_1=101.286\°C-100.000\°C=1.286\°C`

The molality is computed from the boiling point raise:

`m=(T_2-T_1)/(Kb)=(1.286\°C)/(0.512\°C/m)\\ \\m=2.51mol/kg`

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

`n=2.51mol/kg*0.02002kg\\\\n=0.0503mol`

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

`M=(3.005g)/(0.0503mol)\\ \\M=59.8g/mol`

Best regards.