pH of Weak Acids and ICE Chart Calculations

pH of Weak Acids

Introduction to Weak Acids

Weak acids are substances that only partially dissociate into ions in aqueous solution. Understanding their behavior is essential for calculating pH and equilibrium concentrations in solution.

• Weak acids are electrolytes that do not fully ionize in water.

• They require the use of an ICE Chart (Initial, Change, Equilibrium) to calculate equilibrium amounts.

• The units of an ICE Chart should be in molarity (mol/L) and use "x" to represent changes.

ICE Chart Method for Weak Acids

The ICE Chart is a systematic way to organize and solve equilibrium problems involving weak acids.

1. Write the balanced equation for the weak acid dissociation.

2. Set up the ICE Chart with initial concentrations, changes (using x), and equilibrium concentrations.

3. Apply the acid dissociation constant ($K_a$) expression to solve for x.

Example: Calculating [H+] for a Weak Acid

Calculate the hydronium ion concentration for 0.30 M HCN. The acid dissociation constant, $K_a$, for HCN is $4.9 \times 10^{-10}$.

	HCN (aq)	H3O+ (aq)	CN- (aq)
Initial	0.30	0	0
Change	-x	+x	+x
Equilibrium	0.30-x	x	x

Set up the equilibrium expression:

$K_a = \frac{[H_3O^+][CN^-]}{[HCN]} = \frac{x^2}{0.30-x}$

ICE Chart Shortcut

For quadratic equations, use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Where the equation is in the form $ax^2 + bx + c = 0$.

Calculating pH

The pH of a weak acid can be calculated once the equilibrium concentration of $[H^+]$ is found.

• Use the equilibrium value of x from the ICE Chart as $[H^+]$.

• Calculate pH using:

$pH = -\log[H^+]$

Example: pH of a Weak Acid Solution

What is the pH of a 0.174 M nitrous acid, HNO2, solution? $K_a$ for HNO2 is $4.4 \times 10^{-4}$.

	HNO2 (aq)	H3O+ (aq)	NO2- (aq)
Initial	0.174	0	0
Change	-x	+x	+x
Equilibrium	0.174-x	x	x

$K_a = \frac{x^2}{0.174-x}$

Percent Ionization/Dissociation

Percent ionization measures the fraction of a weak acid that ionizes in solution.

• It is calculated using the equilibrium concentration of $[H^+]$ and the initial acid concentration.

Percent Ionization Formula:

$\%\ \text{Ionization} = \frac{[H^+]_{eq}}{[HA]_{initial}} \times 100$

Example: Percent Dissociation

Calculate the percent dissociation of 4.0 × 10-3 M acetic acid, HC2H3O2. $K_a$ value is $1.8 \times 10^{-5}$.

	HC2H3O2 (aq)	H3O+ (aq)	C2H3O2- (aq)
Initial	4.0 \times 10^{-3}	0	0
Change	-x	+x	+x
Equilibrium	4.0 \times 10^{-3} - x	x	x

$K_a = \frac{x^2}{4.0 \times 10^{-3} - x}$

Calculate x, then use the percent ionization formula above.

Practice Problems

• Calculate the pH of a 0.50 M solution of methylammonium bromide, CH3NH3Br. $K_a$ of methylamine, CH3NH2, is $4.4 \times 10^{-4}$.

• An unknown weak acid has an initial concentration of 0.55 M. What is the pH if the acid has a pKa of 5.57?

Summary Table: ICE Chart Steps for Weak Acids

Step	Description
1	Write the balanced equation for the weak acid dissociation.
2	Set up the ICE Chart with initial concentrations, changes (x), and equilibrium concentrations.
3	Write the $K_a$ expression and substitute equilibrium values.
4	Solve for x (use quadratic formula if necessary).
5	Calculate pH or percent ionization as required.

Additional info: The ICE Chart method is widely used for all weak acid and weak base equilibrium problems in general chemistry. Approximations can sometimes be used if x is much smaller than the initial concentration, but always check if the approximation is valid (usually if $K_a$ is very small and initial concentration is relatively large).