What is the boiling point of a solution containing 2.33 g of caffeine, #C_8H_10N_4O_2#, dissolved in 15.0 g of benzene? The boiling point of pure benzene is 80.1 °C and the boiling point elevation constant, Kbp, is 2.53 °C/m.

The boiling point elevation formulas are

where

Finding the solution's molality is our first task.

We now compute the elevation of the boiling point.

We compute the new boiling point at the end.

The first step is to calculate the molality ((m)) of the solution using the given mass of solute (caffeine) and solvent (benzene):

[ m = \frac{n_{\text{solute}}}{m_{\text{solvent}}} ]

Next, we calculate the boiling point elevation (( \Delta T_b )) of the solution using the formula:

[ \Delta T_b = K_{\text{bp}} \times m ]

where ( K_{\text{bp}} ) is the boiling point elevation constant.

Then, we use the boiling point elevation to find the boiling point of the solution:

[ T_{\text{solution}} = T_{\text{pure}} + \Delta T_b ]

where ( T_{\text{pure}} ) is the boiling point of the pure solvent.

Given:

• Mass of caffeine (( C_8H_{10}N_{4}O_{2} )) = 2.33 g
• Mass of benzene (( C_6H_{6} )) = 15.0 g
• Boiling point of pure benzene (( T_{\text{pure}} )) = 80.1 °C
• Boiling point elevation constant (( K_{\text{bp}} )) = 2.53 °C/m

First, calculate the molality (( m )): [ m = \frac{2.33 , \text{g}}{78.12 , \text{g/mol}} \div \frac{15.0 , \text{g}}{78.12 , \text{g/mol}} ]

Next, calculate the boiling point elevation (( \Delta T_b )): [ \Delta T_b = 2.53 , \text{°C/m} \times m ]

Finally, calculate the boiling point of the solution (( T_{\text{solution}} )): [ T_{\text{solution}} = 80.1 , \text{°C} + \Delta T_b ]

By substituting the values and solving the equations, we can find the boiling point of the solution containing the given amounts of caffeine and benzene.