Weak Acid Mixtures

Basic Concept

This module calculates the pH of a solution containing two weak acids of very different strengths.

If a solution contains two weak acids of very different strengths, its pH can be calculated this way:

In the solution containing 1.00M HCN (K_a = 6.2 x 10^-10) and 5.00M  HNO₂ (K_a = 4.0 x 10^-4), there are three equilibriums existed in the solution:

            HCN (aq) =     H⁺ (aq) +     CN^- (aq)        K_a = 6.2 x 10^-10

            HNO₂ (aq) =     H⁺ (aq) +     NO₂^- (aq)     K_a = 4.0 x 10^-4

            H₂O (l) =    H⁺ (aq) +     OH^- (aq)            K_w = 1.0 x 10^-14

Because the K_a of HNO₂ is much larger than that of HCN, it is assumed to be the dominant producer of H⁺, and the equilibrium expression is:

            K_a = 4.0 x 10^-4 = [H⁺][NO₂^-] / [HNO₂]

 The ICE table of the equilibrium is:

                HNO₂ (aq)  =     H⁺ (aq) +     NO₂^- (aq)

Initial:         5.00                        0                  0

Change:       -x                          x                   x

Equilibrium: 5.00 - x                  x                   x 

            K_a = 4.0 x 10^-4 = (x)(x) / (5.00 -x) x² / 5.00

            x 4.5 x 10^-2

The equilibrium concentration of cyanide ion in this solution can be calculated based on the equilibrium below:

            HCN (aq)  =     H⁺ (aq) +     CN^- (aq)

            K_a = 6.2 x 10^-10 = [H⁺][CN^-] / [HCN] = (4.5 x 10^-2 +x) (x) / (1.00 -x) 4.5 x 10^-2 x 

            [CN^-] = x = 1.4 x 10^-8 M

The concentration of proton produced in the dissociation of HCN is same as that of cyanide ion (1.4 x 10^-8 M). It is negligible comparison with the concentration of [H⁺] produced by HNO₂ at equilibrium (4.5 x 10^-2). Therefore, the pH of the solution is:

            pH = -log(4.5 x 10^-2) = 1.35 

User Instructions

For the above example,in the solution containing 1.00M HCN (K_a = 6.2 x 10^-10) and 5.00M  HNO₂ (K_a = 4.0 x 10^-4),calculate pH.

This is one step process, enter the known data and press Calculate to output the unknowns.

1. Select Weak Acid Mixtures link from the front page or Weak Acid Mixtures tab from the Acid, Baseand Salt module. The Input and Output screen appears.

2. In the Input area, enter the known quantities with a proper significant figure.

3. Click Calculate to output the answer.

 

4. The Show Work area on the right shows you step-by-step how your problem has been solved.

To start a new problem, click Reset. All Input fields will be cleared. Follow Step 1-3 again.