Chapter I: Solutions and the Phenomenon of Solubilization

Flashcards covering Chapter I: Solutions and the phenomenon of solubilization, including concentration expressions, normality, electrolytes, and the Debye–Hückel model.

What is an aqueous solution, and how are its components defined?

An aqueous solution is a homogeneous mixture formed by dissolving a solute (solid, liquid, or gas) in water, which acts as the solvent.

How is molar concentration ($C$) defined and mathematically expressed?

Molar concentration is the ratio of the number of moles of solute ($n$) to the volume of solution ($V$) in liters: $C = \frac{n}{V}$. It is expressed in $\text{mol}\cdot\text{L}^{-1}$.

What is mass concentration ($C_m$), and what is its unit?

Mass concentration is the ratio of the mass of solute to the volume of the solution ($C_m = \frac{m}{V}$), expressed in $\text{g}\cdot\text{L}^{-1}$.

What is the mass concentration of a solution prepared by dissolving $250\,\text{g}$ of sodium chloride in water to obtain $400\,\text{mL}$ of solution?

$$C_m = \frac{m}{V} = \frac{250\,\text{g}}{0.4\,\text{L}} = 625.0\,\text{g}\cdot\text{L}^{-1}$$

How is molality ($b$) defined, and what is its formula?

Molality is the ratio of the number of moles of solute to the mass of solvent expressed in kilograms: $b = \frac{n_{\text{solute}}}{m_{\text{solvent}}(\text{kg})}$.

When dissolving $0.585\,\text{g}$ of $\text{NaCl}$ in $100\,\text{mL}$ of a solution with a density of $2.17\,\text{g}\cdot\text{cm}^{-3}$, what is the mass of the water (solvent)?

$\text{Mass of water} = \text{Mass of solution} - \text{Mass of solute} = 217\,\text{g} - 0.585\,\text{g} = 216.415\,\text{g}$ (or $0.216415\,\text{kg}$).

What is the relationship between normality ($N$) and molar concentration ($C$)?

$N = \frac{n(\text{éqg})}{V} = \frac{n \cdot eq}{V} = C \cdot eq$, where $eq$ is the equivalence factor (number of equivalents per mole).

How is a gram-equivalent ($\text{eqg}$) determined for an acid?

It is based on the number of $H^+$ ions the acid can donate upon complete dissociation (e.g., $1\,\text{mol}$ of $\text{HCl}$ corresponds to $1\,\text{eqg}$, and $1\,\text{mol}$ of $\text{H}_2\text{SO}_4$ corresponds to $2\,\text{eqg}$).

According to Brønsted's definition, how many gram-equivalents correspond to $1\,\text{mole}$ of hydrazine ($\text{H}_2\text{N–NH}_2$)?

$2\,\text{eqg}$, because $1\,\text{mole}$ of $\text{H}_2\text{N–NH}_2$ accepts $2\,\text{moles}$ of $H^+$ through complete protonation.

How is one equivalent gram ($\text{eqg}$) defined for a salt?

One mole of positive (or negative) charges corresponds to $1\,\text{eqg}$ of salt upon complete dissociation (e.g., $1\,\text{mol}$ of $\text{Na}_2\text{SO}_4$ yields $2\,\text{mol}$ of positive charges, corresponding to $2\,\text{eqg}$).

How is one equivalent gram ($\text{eqg}$) defined for oxidizing and reducing agents?

One mole of electrons exchanged corresponds to $1\,\text{eqg}$ of oxidizing or reducing agent (e.g., when $1\,\text{mol}$ of $\text{Al}$ loses $3\,\text{mol}$ of electrons, it corresponds to $3\,\text{eqg}$).

What is the normality of a solution containing $98\,\text{g}$ of phosphoric acid ($\text{H}_3\text{PO}_4$, $M = 98\,\text{g}\cdot\text{mol}^{-1}$) dissolved in $500\,\text{mL}$ of solution?

$N = 6\,\text{N}$ (since $n = 1\,\text{mol}$, and as a triprotic acid, $n_{eq} = 1 \times 3 = 3\,\text{equivalents}$, giving $N = \frac{3}{0.500\,\text{L}} = 6\,\text{N}$).

What is the formula for the mass percentage ($\% m/m$) of a solution?

$$\% m/m = \frac{m_1\,\text{solute}(\text{g})}{m_2\,\text{solution}(\text{g})} \times 100$$

What volume of pure hydrogen peroxide is present in $400\,\text{mL}$ of a $30\%\,(v/v)$ solution?

$$v_1 = \frac{30 \times 400\,\text{mL}}{100} = 120\,\text{mL}$$

What are molar fraction ($X_i$) and mass fraction ($W_i$), and what is the sum of fractions in a mixture?

Molar fraction is $X_i = \frac{n_i}{\sum_i n_i}$ and mass fraction is $W_i = \frac{m_i}{\sum_i m_i}$. Both are dimensionless, and their respective sums equal $1$ ($\sum_i X_i = 1$ and $\sum_i W_i = 1$).

In aqueous solutions, what rule of thumb relates milligrams and liters to parts per million (ppm)?

$1\,\text{mg}$ of solute dissolved in $1\,\text{L}$ of water $\approx 1\,\text{ppm}$, because $1\,\text{L}$ of water $\approx 1\,\text{kg} = 1{,}000{,}000\,\text{mg}$.

How does the degree of dissociation ($\alpha$) distinguish strong electrolytes from weak electrolytes?

$\alpha = \frac{\text{Number of moles dissociated at equilibrium}}{\text{Number of moles initially dissolved}}$; $\alpha = 1$ for a strong electrolyte, and $0 < \alpha < 1$ for a weak electrolyte.

Under what condition does an electrolyte solution exhibit ideal behavior rather than real (non-ideal) behavior?

A solution behaves ideally when it is very dilute, meaning solvation is complete, inter-ionic distances are large, and ion interactions are negligible. In concentrated solutions, interactions are non-negligible, causing real behavior.

According to the Debye–Hückel model (1923), what is the formula for $\log(\gamma_i)$ when the ionic strength is $I < 0.02\,\text{M}$?

$\log(\gamma_i) = -0.509 Z_i^2 \sqrt{I}$, where $Z_i$ is the charge of ion $i$ and $I = \frac{1}{2} \sum Z_i^2 C_i$.

Why is the mean activity coefficient ($\gamma_{\pm}$) introduced, and what is its formula for an electrolyte $A_m B_n \rightarrow m A^{n+} + n B^{m-}$?

It is introduced because individual ion activity coefficients cannot be measured experimentally. It is defined as $\gamma_{\pm} = \sqrt[m+n]{\gamma_{A^{n+}}^m \times \gamma_{B^{m-}}^n}$.