Small amount of freshly precipitated magnesium hydroxides are stirred vigorous

step 1 So we're taking a look at the ionization of NH3 in water, where we have KB is equal to the conce

Small amount of freshly precipitated magnesium ...

Small amount of freshly precipitated $\begin{array}{llll}\text { magnesium } & \text { hydroxides } & \text { are } & \text { stirred }\end{array}$ vigorously in a buffer solution containing $0.25 \mathrm{M}$ of $\mathrm{NH}_{4} \mathrm{Cl}$ and $0.05 \mathrm{M}$ of $\mathrm{NH}_{4} \mathrm{OH}$. $\left[\mathrm{Mg}^{2}\right]$ in the resulting solution is $\left(K_{\mathrm{b}}\right.$ for $\mathrm{NH}_{4} \mathrm{OH}=2.0 \times 10^{-5}$ and $K_{\mathrm{sp}}$ of $\mathrm{Mg}(\mathrm{OH})_{2}$ $\left.=8.0 \times 10^{-12}\right)$ (a) $4 \times 10^{-6} \mathrm{M}$ (b) $2 \times 10^{-6} \mathrm{M}$ (c) $0.5 \mathrm{M}$ (d) $2.0 \mathrm{M}$

Small amount of freshly precipitated $\begin{array}{llll}\text { magnesium } & \text { hydroxides } & \text { are } & \text { stirred }\end{array}$ vigorously in a buffer solution containing $0.25 \mathrm{M}$ of $\mathrm{NH}_{4} \mathrm{Cl}$ and $0.05 \mathrm{M}$ of $\mathrm{NH}_{4} \mathrm{OH}$.
$\left[\mathrm{Mg}^{2}\right]$ in the resulting solution is $\left(K_{\mathrm{b}}\right.$ for $\mathrm{NH}_{4} \mathrm{OH}=2.0 \times 10^{-5}$ and $K_{\mathrm{sp}}$ of $\mathrm{Mg}(\mathrm{OH})_{2}$
$\left.=8.0 \times 10^{-12}\right)$
(a) $4 \times 10^{-6} \mathrm{M}$
(b) $2 \times 10^{-6} \mathrm{M}$
(c) $0.5 \mathrm{M}$
(d) $2.0 \mathrm{M}$

Key Concepts

Equilibrium Constant for Weak Bases (Kb)

The equilibrium constant for a weak base quantifies the extent to which the base accepts a proton in an aqueous solution, forming its conjugate acid and hydroxide ion. This constant is crucial for determining the concentration of hydroxide ions in solutions containing weak bases and plays a vital role in the behavior of buffer solutions. It also provides insight into the balance between the undissociated weak base and the ions produced in solution.

Buffer Solutions

A buffer solution is one that resists changes in its pH when small amounts of acid or base are added. Buffers are typically composed of a weak acid and its conjugate base or a weak base and its conjugate acid, and they operate by neutralizing added protons or hydroxide ions. In equilibrium systems, a buffer can stabilize the concentration of reactive species, influencing the behavior of other equilibria, such as precipitation.

Solubility Product Constant (Ksp)

The solubility product constant is a measure of the extent to which a sparingly soluble salt can dissolve in solution. It is defined for a dissolving salt by the product of the molar concentrations of the constituent ions, each raised to the power of their stoichiometric coefficients, at equilibrium. This constant is essential for predicting whether a precipitate will form and determining the concentration of ions in a solution in the presence of a sparingly soluble compound.

Common Ion Effect

The common ion effect refers to the decrease in solubility of a solute when a solution already contains an ion in common with the solute. In precipitation and solubility equilibria, the presence of a common ion shifts the equilibrium position, reducing the concentration of the dissolved ionic species. This effect is particularly important in systems involving sparingly soluble salts, as the added common ion can significantly influence the solubility limit.

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