Chapter 13

Write the equation relating osmotic pressure to the concentration of a solution. Define all the terms and give their units.

What does it mean when we say that the osmotic pressure of a sample of seawater is \(25 \mathrm{~atm}\) at a certain temperature?

Explain why molality is used for boiling-point elevation and freezing-point depression calculations and molarity is used in osmotic pressure calculations.

Describe how you would use the freezing-point depression and osmotic pressure measurements to determine the molar mass of a compound. Why is the boiling- point elevation phenomenon normally not used for this purpose?

Explain why it is essential that fluids used in intravenous injections have approximately the same osmotic pressure as blood.

The molar mass of benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) determined by measuring the freezing-point depression in benzene is twice that expected for the molecular formula, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2}\). Explain this apparent anomaly.

The vapor pressures of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and 1 -propanol \(\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\right)\) at \(35^{\circ} \mathrm{C}\) are \(100 \mathrm{mmHg}\) and \(37.6 \mathrm{mmHg},\) respectively. Assume ideal behavior and calculate the partial pressures of ethanol and 1 -propanol at \(35^{\circ} \mathrm{C}\) over a solution of ethanol in I-propanol, in which the mole fraction of ethanol is 0.300

The vapor pressure of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) at \(20^{\circ} \mathrm{C}\) is \(44 \mathrm{mmHg},\) and the vapor pressure of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) at the same temperature is \(94 \mathrm{mmHg}\). A mixture of \(30.0 \mathrm{~g}\) of methanol and \(45.0 \mathrm{~g}\) of ethanol is prepared (and may be assumed to behave as an ideal solution). (a) Calculate the vapor pressure of methanol and ethanol above this solution at \(20^{\circ} \mathrm{C}\). (b) Calculate the mole fraction of methanol and ethanol in the vapor above this solution at \(20^{\circ} \mathrm{C}\).

Pheromones are compounds secreted by the females of many insect species to attract males. One of these compounds contains \(80.78 \%\) C, \(13.56 \% \mathrm{H}\), and \(5.66 \%\) O. A solution of \(1.00 \mathrm{~g}\) of this pheromone in \(8.50 \mathrm{~g}\) of benzene freezes at \(3.37^{\circ} \mathrm{C}\). What are the molecular formula and molar mass of the compound? (The normal freezing point of pure benzene is \(5.50^{\circ} \mathrm{C}\) ).

A solution of \(2.50 \mathrm{~g}\) of a compound of empirical formula \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{P}\) in \(25.0 \mathrm{~g}\) of benzene is observed to freeze at \(4.3^{\circ} \mathrm{C}\). Calculate the molar mass of the solute and its molecular formula.