Q: A solution contains 0.050 M NaF saturated with CaF$_2$. The ionic strength is 0.050 M. If the activity coefficients are $y_{Ca^{2+}} = 0.485$ and $y_{F^-} = 0.81$, what is the equilibrium concentration of Ca$^{2+}$ given $K_{sp} = 3.2 \times 10^{-11}$? $ K_{sp} = [Ca^{2+}] y_{Ca^{2+}} [F^-]^2 y_{F^-}^2 $

$[Ca^{2+}] = 4.0 \times 10^{-7}$ M

Question 1

Which of the following best explains why adding an inert salt like KNO$_3$ to a solution containing Fe$^{3+}$ and SCN$^-$ causes the red color of Fe(SCN)$^{2+}$ to fade?

Accepted Answer

The increased ionic strength decreases the activity coefficients, shifting the equilibrium toward dissociation of Fe(SCN)$^{2+}$.

Question 2

What is the ionic strength ($	ext{I}$) of a solution prepared by dissolving 0.010 M Na$_2$SO$_4$ in water?

Accepted Answer

$	ext{I} = 0.030$ M

Question 3

Which statement about activity coefficients ($	ext{y}$) is correct?

Accepted Answer

Activity coefficients measure the deviation from ideal behavior and depend on ionic strength.

Question 4

Given the Debye-Hückel equation for activity coefficients:
$
\log y = -0.51 \frac{z^2 \sqrt{I}}{1 + a \sqrt{I}/305}
$
Which variable most strongly affects the magnitude of the activity coefficient for an ion?

Accepted Answer

The charge ($z$) of the ion

Question 5

A solution contains 0.050 M NaF saturated with CaF$_2$. The ionic strength is 0.050 M. If the activity coefficients are $y_{Ca^{2+}} = 0.485$ and $y_{F^-} = 0.81$, what is the equilibrium concentration of Ca$^{2+}$ given $K_{sp} = 3.2 	imes 10^{-11}$?
$
K_{sp} = [Ca^{2+}] y_{Ca^{2+}} [F^-]^2 y_{F^-}^2
$

Accepted Answer

$[Ca^{2+}] = 4.0 	imes 10^{-7}$ M

Question 6

Which of the following is the correct charge balance equation for an aqueous solution containing CaCl$_2$?

Accepted Answer

$2[Ca^{2+}] + [H^+] = [OH^-] + 2[Cl^-]$

Question 7

Why do activity corrections become more important for ions with higher charge and smaller size?

Accepted Answer

Because their deviation from ideality is greater due to stronger electrostatic interactions.

Question 8

Which of the following is true regarding the activity of a pure solid or liquid in equilibrium calculations?

Accepted Answer

It is always set to unity (1).

Question 9

A solution contains 0.0100 mol NH$_3$ in 1.000 L. The relevant equilibria are:
$
NH_3 + H_2O ightleftharpoons NH_4^+ + OH^- \qquad K_b = 1.76 	imes 10^{-5}
$
$
H_2O ightleftharpoons H^+ + OH^- \qquad K_w = 1.0 	imes 10^{-14}
$
Ignoring activities, which set of equations would you use to solve for all species concentrations?

Accepted Answer

Mass balance, charge balance, and both equilibrium expressions

Question 10

Which of the following best describes the effect of increasing ionic strength on the solubility of a sparingly soluble salt like CaSO$_4$?

Accepted Answer

It increases the solubility by decreasing the attraction between ions.

Question 11

Which equation correctly defines the activity ($a_C$) of a solute C in solution?

Accepted Answer

$a_C = [C] \cdot y_C$

Question 12

When measuring pH with a pH meter, what is actually being measured?

Accepted Answer

The negative logarithm of the hydrogen ion activity

Question 13

Which of the following is a correct mass balance equation for a solution containing 0.1 M Na$_2$S?

Accepted Answer

$0.1 = [S^{2-}] + [HS^-] + [H_2S]$

Question 14

Which of the following statements about neutral molecules in solution is correct?

Accepted Answer

Their activity coefficients are approximately 1 at ionic strengths below 0.1 M.

Question 15

A solution contains 1 mM CaCl$_2$. What is the ionic strength ($I$) of the solution?

Accepted Answer

$I = 3$ mM

Question 16

Which of the following is NOT a step in the systematic treatment of equilibrium?

Accepted Answer

Ignoring the conservation of matter

Question 17

For the equilibrium $Fe^{3+} + SCN^- \rightleftharpoons Fe(SCN)^{2+}$, which expression represents the thermodynamic equilibrium constant ($K$) including activities?

Accepted Answer

$K = \frac{[Fe(SCN)^{2+}] y_{Fe(SCN)^{2+}}}{[Fe^{3+}] y_{Fe^{3+}} [SCN^-] y_{SCN^-}}$

Question 18

Which factor does NOT affect the activity coefficient of an ion in solution?

Accepted Answer

Color of the ion

Question 19

In a solution containing Mg$^{2+}$ and OH$^-$, which charge balance equation is correct?

Accepted Answer

$[Mg^{2+}] + [MgOH^+] + [H^+] = [OH^-]$

Chapter 8: Activity and the Systematic Treatment of Equilibrium

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