Solutions

• solution: homogeneous system containing multiple species
• examples
  • $C{H}_4(g)+H_{2}O(l)\to CO(g)+H_2(g)$
• $C{O}_2$ in $H_{2}O$
  • solute: $C{O}_2$
  • solvent: $H_{2}O$
• mole fraction: fraction of moles wrt total number of moles

$${\chi }_1=\frac{n_1}{n_1+n_2}{\chi }_2=\frac{n_2}{n_1+n_2}⟹{\chi }_1+{\chi }_2=1$$

• concentration: moles per unit volume
• molarity: $M=\frac{\text{moles}}{\text{liters}}=\frac{\text{mol}}{\text{L}}$
• molality: $\frac{\text{moles solute}}{\text{kg solvent}}$

Example Problem §

A $60835M$ $AcOH$ ($1M$) has a density of $1.0438\text{g}/\text{mL}$. What is the molality?

1. Assume $1\text{L}$ solution
2. Calculate total mass

$$P=\frac{M}{V}⟹M=VP=1\text{L}\left(\frac{1.0438\text{ g}}{\text{mL}}\right)\left(\frac{1000\text{ mL}}{\text{L}}\right)$$

3. Find mass of $AcOH$

$$6.0835\text{ mol}\left(\frac{60.052\text{ g}}{\text{mol}}\right)=365.33\text{ g}$$

4. Find molality

$$\frac{\text{moles solute}}{\text{kg solvent}}=\frac{6.0835\text{ mol}}{365.33\text{ g}}=8.96\text{ molal}$$

Preparing Solutions §

• //TODO

Nature of Dissolved Species §

• non-covalent interactions between solutes and solvents
• solution must replace solute-solute and solvent-solvent interactions with solvent-solute interactions

Reaction Stoichiometry §

$$Cl(\text{aq})+H\to HCl(\text{aq})$$

• all have $1M$ molarity
• to balance

$$MgC{l}_2(\text{aq})+2\text{HOTF}\to 2HCl+Mg\text{OTF}2$$

Titrations §

• quantify a reactive component of a solution
• given $2A+B\to A_{2}B$ and solution with $B$
• we can add solution $A$ until $B$ is consumed
• then calculate moles of $A$ to get $[B]$
• used to determine $[H^{+}],[H_3{O}^{+}]$
  • pH $=-\log [H^{+}]$
• aka acidity
• Arrhenius: $2H_{2}O\to H_3{O}^{+}+O{H}^{-}$
  • disproportionation reaction
  • $[H_3{O}^{+}]=[O{H}^{-}]=10^{-7}\text{ M}$
  • acid: increases $[H_{3}O]$
  • base: increases $[OH]$
  • example: phenolphthalein

Phase Equilibrium in Solution for Non-Volatile Solutes §

• vapor pressure of a solution changes with $\chi$
• ${\chi }_1=$ mole fraction of solvent
• $P_1^{\circ }=$ vapor pressure of pure solvent
• graph should look like

• Raoult’s Law: should be straight line
  • $P_1={\chi }_1{P}_1^{\circ }$
  • forms basis for

Colligative Properties §

Vapor Pressure lowering §

• for a 2-component solution

$$\begin{array}{c}{\chi }_1+{\chi }_2=1\\ \Delta P_1=P_1-P_1^{\circ }={\chi }_1{P}_1^{\circ }-P_1^{\circ }=(1-{\chi }_2)P_1^{\circ }-P_1^{\circ }=-{\chi }_2{P}_1^{\circ }\end{array}$$

Boiling Point Elevation §

• lower vapor pressure $⟹$ higher BP
• $\Delta T_b$: change in BP
• $K_b$: constant, table 11.2 in book
• $m$: molarity

$$\Delta T_b=K_{b}m$$

Freezing Point Depression §

$$\Delta T_f=K_{f}m$$

Osmotic Pressure §

• given semipermeable membrane in solution

$$\pi =\rho gh$$