(Solved): Colligative Properties - Freezing-Point Depression and Boiling-Point Elevation Learning Outcomes: 1 ...

Colligative Properties - Freezing-Point Depression and Boiling-Point Elevation Learning Outcomes: 1) Define a colligative property. 2) Define the van't Hoff factor for a solute, and determine the theoretical van't Hoff factor for a solute. 3) Define freezing-point depression and boiling-point elevation. 4) Use the Colligative Property Law to calculate the freezing-point and boiling-point of a solution. 5) Use the freezing-point depression and boiling-point elevation of a solution to determine the molar mass of a nonelectrolytic solute that is added to a pure solvent. Colligative Properties: When a solute is dissolved in a solvent, the resulting solution will have physical properties that are different than those of the pure solute and solvent themselves. A colligative property is a physical property of a solution that depends only on the amount (moles) of solute present in the solution, but not on the identity of the solute. Thus, colligative properties depend on the concentration of the solution only and not on the identity of the solute. Electrolytic Solutes: Solutes are classified based on their extent to dissociate into ions when dissolved into a solution. Solutes that are covalent (molecular) compounds do not dissociate into ions and are known as nonelectrolytes. Solutes that are ionic compounds may dissociate into ions and are known as electrolytes. However, the extent of dissociation of electrolytic solutes may not always be complete, and this often depends on the ionic charges, with solutes with larger ionic charges dissociating less fully. The extent of dissociation of solutes in solution is expressed by the van't Hoff factor (i), which is the ratio of the number of particles formed in the solution from one formula unit of solute. \[ i=\frac{\text { number of particles in solution }}{\text { formula unit of solute }} \] For nonelectrolytes, the van't Hoff factor is 1. For strong electrolytes which completely dissociate, the van't Hoff factor can be approximated as the number of ions in the formula unit. For dissociation, the van't Hoff factor is greater than \( 1 . \) In some cases, solute particles may associate into larger particles. For example, two solute molecules may be attracted together by hydrogen bonding to form a single larger particle, known as a dimer. If three solute molecules do this, then the resulting particle is known as a trimer. For association, the van't Hoff factor is less than 1 . Identify whether the following solutes are electrolytes or nonelectrolytes and determine the theoretical van't Hoff factor (f). assumine complete dissociation. Freezing-Point Depression: When a solute is added to a solvent, the resulting solution will have a freezing-point that is lower than that of the pure solvent. This lowering of the freezing-point is known as a freezing-point depression \( \left(\Delta T_{f p}\right) \). The magnitude of the freezing-point depression is a colligative property and only depends on the concentration of the solute, but not on the identity of the solute. The Colligative Property Law expresses the freezing-point depression to the molality \( (m) \) of the solute in the solution and a property of the solvent, known as its molal freezing-point depression constant \( \left(K_{f_{p}}\right) \) : \[ \Delta T_{f p}=i K_{f p} m \] The van't Hoff factor is included to account for dissociation of electrolytic solute. The freezingpoint \( \left(T_{f p}\right) \) of the solution will be lower than that of the pure solvent \( \left(T_{f p}^{0}\right) \) : \[ T_{f p}=T_{f p}^{p}-\Delta T_{f p} \] Calculate the freezing-point \( \left({ }^{\circ} \mathrm{C}\right) \) of the solution prepared by dissolving \( 4.285 \mathrm{~g} \) of sodium sulfate \( \left(\mathrm{Na}_{2} \mathrm{SO}_{4}, \mathrm{FW}=142.042 \mathrm{~g} / \mathrm{mol}\right) \) into \( 50.000 \mathrm{~g} \) of water. The normal freezing-point of pure water is \( 0.00^{\circ} \mathrm{C} \), and its molal freezing-point depression constant \( \left(K_{f p}\right) \) is \( 1.86 \frac{\mathrm{C}}{\mathrm{m}} \). Assume complete dissociation. a. What is the mass (in grams) of solute? b. What is the moles of solute? Show your work: c. What is the mass (in grams) of solvent? d. What is the mass (in kilograms) of solvent? Show your work: e. What is the molality \( (m) \) of the solution? Show your work: f. What is the van't Hoff factor (i) of the solute? 3 Calculate the freezing-point \( \left({ }^{\circ} \mathrm{C}\right) \) of the solution prepared by dissolving \( 4.285 \mathrm{~g} \) of anthracene \( \left(C_{14} H_{10}, F W=178.234 \mathrm{~g} / \mathrm{mol}\right) \) into \( 26.320 \mathrm{~g} \) of benzene \( \left(C_{6} H_{6}, \mathrm{FW}=78.114 \mathrm{~g} / \mathrm{mol}\right) \). The normal freezing-point of pure benzene is \( 5.53{ }^{\circ} \mathrm{C} \), and its molal freezing-point depression constant \( \left(K_{f p}\right) \) is \( 5.12 \frac{\pi}{\mathrm{m}^{2}} \) Rank the following aqueous solutions in order of increasing freezing-points. Assume complete dissociation of any electrolytic solutes. Justify your answer by calculating the freezing-point of each solution. The normal freezing-point of pure water is \( 0.00^{\circ} \mathrm{C} \), and its molal freezing-point depression constant \( \left(K_{f p}\right) \) is \( 1.86 \) ?. \( 0.25 \mathrm{mNaCl}(a q) . \quad 0.60 \mathrm{mCH} \mathrm{CH}(a q) .0 .10 \mathrm{mBaCt}(a q) \cdot \quad 0.20 \mathrm{~m} \mathrm{Na} \mathrm{NO}_{4}(a q) \) Boiling-Point Elevation: When a solute is added to a solvent, the resulting solution will have a higher boiling-point than that of the pure solvent. This raising of the boiling-point is known as a boiling-point elevation \( \left(\Delta T_{b p}\right) \). The magnitude of the boiling-point elevation is a colligative property and only depends on the concentration of the solute, but not on the identity of the solute. The Colligative Property Law expresses boiling-point elevation to the molality \( (\mathrm{m}) \) of the solute in the solution and a property of the solvent, known as its molal boiling-point elevation constant \( \left(K_{b p}\right. \) ): \[ \Delta T_{b p}=i K_{b p} m \] The van't Hoff factor is included to account for dissociation of electrolytic solute. The boilingpoint \( \left(T_{b j}\right) \) of the solution will be higher than that of the pure solvent \( \left(T_{b \mathrm{p}}\right) \) : \[ T_{b p}=T_{b p}^{0}+\Delta T_{b p} \] Calculate the boiling-point \( \left({ }^{\circ} \mathrm{C}\right) \) of the solution prepared by dissolving \( 2.335 \mathrm{~g} \) of sodium fluoride ( \( \mathrm{NaF} \), FW \( =41.998 \mathrm{~g} / \mathrm{mol}) \) into \( 22.106 \mathrm{~g} \) of water. The normal boiling-point of pure water is \( 100.00^{\circ} \mathrm{C} \), and its molal boiling-point elevation constant \( \left(K_{b p}\right) \) is \( 0.512 \% \). Assume complete dissociation. a. What is the mass (in grams) of solute? b. What is the moles of solute? Show your work: c. What is the mass (in grams) of solvent? d. What is the mass (in kilograms) of solvent? Show your work: e. What is the molality \( (m) \) of the solution? Show your work: f. What is the van't Hoff factor (i) of the solute? g. What is the boiling-point elevation \( \left(\Delta T_{\text {ipp }}\right) \) ? Show your work: 6 Calculate the boiling-point \( \left({ }^{\circ} \mathrm{C}\right) \) of the solution prepared by dissolving \( 1.350 \mathrm{~g} \) of vanillin \( \left(\mathrm{C}_{\mathrm{g}} \mathrm{H}_{\mathrm{B}} \mathrm{O}_{3}, \mathrm{FW}=152.15 \mathrm{~g} / \mathrm{mol}\right) \) into \( 19.704 \mathrm{~g} \) of chloroform \( \left(\mathrm{CHCl}_{3}\right) \). The normal boiling-point of pure chloroform is \( 61.15^{\circ} \mathrm{C} \), and its molal boiling-point elevation constant \( \left(K_{b p}\right) \) is \( 3.88 \frac{\mathrm{c}}{\mathrm{m}} \) Rank the following aqueous solutions in order of increasing boiling-points. Assume complete dissociation of any electrolytic solutes. Justify your answer by calculating the bolling-point of each solution. The normal boiling-point of pure water is \( 100.00^{\circ} \mathrm{C} \), and its molal boilingpoint elevation constant \( \left(K_{b p}\right) \) is \( 0.512 \frac{*}{m} \). \( 0.25 \mathrm{mNaCl}(a q), \quad 0.60 \mathrm{mCH} \mathrm{OH}(a q), 0.10 \mathrm{mBaCl}(a q), \quad 0.20 \mathrm{mNa} \mathrm{NOO}_{4}(a q) \) Show your work: Determining the Molar Mass of a Nonelectrolytic Solute Using Freezing-Point Depression and Boiling-Point Elevation: If the freezing-point depression \( \left(\Delta T_{f p}\right) \) or boiling-point elevation \( \left(\Delta T_{b p}\right) \) caused by adding a known mass of a nonelectrolytic solute to a known mass of solvent is measured, then the molar mass of the solute \( \left(M_{\text {sotute }}\right) \) can be calculated. \[ M_{\text {solute }}=\frac{\text { mass of sofute }(g)}{\text { moles of sotute }} \] The moles of solute ( \( n_{\text {solute }} \) ) would be determined from the known mass of solvent ( \( m_{\text {solvent }} \) ) and the measured molality \( (m) \) of the solution. \[ n_{\text {solute }}=m_{\text {solvent }}(\mathrm{kg}) \times m\left(\frac{\mathrm{mot}}{\mathrm{kg}}\right) \] A \( 1.705 \mathrm{~g} \) sample of an unknown nondissociating solute is dissolved in \( 28.230 \mathrm{~g} \) of g. What is the moles of solute? Show your work: h. What is the molar mass (MC) of the solute \( (\mathrm{g} / \mathrm{mol}) \) ? Show your work: 10 A \( 1.180 \mathrm{~g} \) sample of an unknown nondissociating solute is dissolved in \( 19.704 \mathrm{~g} \) of carbon tetrachloride \( \left(\mathrm{CCl}_{4}\right) \), and the boiling-point of the resulting solution was measured to be 78. \( 06^{\circ} \mathrm{C} \). Calculate the molar mass of the solute. The normal boiling-point of pure carbon tetrachloride is \( 76.72{ }^{\circ} \mathrm{C} \), and its molal boiling-point elevation constant \( \left(K_{b p}\right) \) is \( 5.03 \frac{{ }^{C}}{\ldots} \). a. What is the molar mass \( (M) \) of the solute \( (\mathrm{g} / \mathrm{mol}) \) ?