A student is evaluating whether the term can be neglected when calculating the molar…

CHEMISTRY · Single correct · AP · Chemistry · Equilibrium · Equilibrium

Problem

A student is evaluating whether the term

x

can be neglected when calculating the molar solubility of

\text{PbCl}_2

in a

0.10\,\text{M}

NaCl solution. The solubility–product constant for

\text{PbCl}_2

at the temperature of the experiment is

K_{sp}=1.6\times10^{-5}

. Which of the following statements provides the best justification for neglecting

x

? (a) Because NaCl is a strong electrolyte, its addition completely suppresses the solubility of

\text{PbCl}_2

, so the equilibrium value of

x

is exactly zero. (b) Since dissolving

\text{PbCl}_2

generates twice as much

\text{Cl}^-

\text{Pb}^{2+}

x

must be only one-half of the

0.10\,\text{M}

chloride already present and can therefore be neglected. (c) Because

[\text{Cl}^-]^2

is more than

10^{3}

times larger than

K_{sp}

, the calculated value of

x

will be several orders of magnitude smaller than

0.10\,\text{M}

and therefore negligible. (d) Since

K_{sp}=1.6\times10^{-5}

, the equilibrium concentration of

\text{Pb}^{2+}

cannot exceed

1.6\times10^{-5}\,\text{M}

, which is negligible compared with

0.10\,\text{M}

, so

x

may be ignored.