Finding the pH

Very strong acids and bases will dissociate almost completely. This means that the HA or BOH concentration (for the acid and base respectively) will be nearly zero. Since division by zero is impossible, for such acids and bases, there is no Ka or Kh. Surprisingly, this fact makes it easier to find the pH of strong acid and strong base solutions. Since the entire concentration of acid or base is assumed to dissociate, the concentration of H or OH is the same as the original concentration of acid or base. For instance, a 0.01 molar solution of HC1 will have 0.01 mol L 1 of H+ ions. Since 0.01 = 10 2, and -log(10 2) = 2, the pH of the solution will be 2. Likewise, in a 0.01 molar solution of NaOH, we will have 0.01 mol L 1 of OH ions. (Be careful here ) The pOH will equal 2 so the pH will equal 12. You can avoid a mistake here by remembering that an acid has a pH below 7 and a base has a pH above 7. 

Weak acids and bases can be a little trickier. Doing a sample problem is the best way to learn. For example, in order to find the pH of a 0.01 molar solution of HCN, we do the following  

If we add 0.01 moles of HCN to one liter of pure water, then x amount of that HCN will dissociate. Thus, we will have V mol L 1 of H+ ions and V mol L 1 of CN ions. The concentration of undissociated I lf N will be whatever is left, or 0.01 - x. Plugging these values into the equation above, we have  

If we solve for x, we have a quadratic equation. Forget it You don t need this for the MCAT. We make an assumption that x is less than 5% of 0.01, and we will check it when we are done. Throwing out the x in the denominator, we have  

x is approximately 2.5 x 10 6. This is much smaller than 0.01, so our assumption was valid, x is the concentration of H+ ions. The pH of the solution is between 5 and 6. This is close enough for the MCAT. [-log(2.5 x 10 6) = 5.6] Just to make sure, we ask ourselves, Is 5.6 a reasonable pH for a dilute weak acid The answer is yes. 

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This same approach can be extended to find the pH of a monoprotic weak base, replacing with Kb, Chf with the weak base s concentration, and solving for the [OH ] in place of [H3O+]. 

A more challenging problem is to find the pH of a solution prepared from a polyprotic acid or one of its conjugate species. As an example, we will use the amino acid alanine whose structure and acid dissociation constants are shown in Figure 6.11. 

Find the pH and pOH of solutions with die following [H+]. Classify each as acidic or basic. 

EXAMPLE 10.14 Sample exercise Finding the pH of a very dilute aqueous solution of a strong acid... 

Autoprotolysis also contributes to the pH of very dilute solutions of weak acids. In fact, some acids, such as hypoiodous acid, HIO, are so weak and undergo so little deprotonation that the autoprotolysis of water almost always contributes significantly to the pH. To find the pH of these solutions, we must take into account the autoprotolysis of water. 

In aqueous solutions of very weak acids, the autoprotolysis of water must be taken into account if the hydronium ion concentration is less than 10 6 mol-L The expressions for Kw and Ka are combined with the equations for charge balance and material balance to find the pH. 

Find the pH of an aqueous solution of strong acid or base that is so dilute that the autoprotolysis of water significantly affects the pH (Example 10.14). 

STRATEGY First, identify the weak acid and its conjugate base. Then, write the proton transfer equilibrium between them, rearrange the expression for Ka to give [H30+], and find the pH, by using the approximation that the equilibrium concentrations of the acid and its conjugate base are essentially the same as the initial concentrations. 

Step 5 If acid is in excess, take the negative logarithm of the H3Oa molarity to find the pH. If base is in excess, find the pOH, and then convert pOH into pH by using the relation pH + pOH = p Kw. 

SOLUTION For (a) we use the procedure in Toolbox 10.1. For (b) we expect a pH slightly greater than that of the pure acid, due to the added base, and find the pH using the procedure in Toolbox 11.2. 

To find the pH of a solution, first compute [H3 O ] or [OH ] and then apply Equation or. Sodium hydroxide is a strong base, and the water equilibrium provides the link between hydroxide and hydronium ion concentrations. 

C17-0062. For a 1.50 M aqueous solution of hydrazoic acid, HN3, do the following (a) Identify the major and minor species, (b) Compute concentrations of all species present, (c) Find the pH. (d) Draw a molecular picture illustrating the equilibrium reaction that determines the pH. 

You may wonder why we did not use the titration curve to determine the pH at the stoichiometric point of the ephedrine titration, as we did to find the pH at the midpoint. Notice from Figure 18-6 that near the stoichiometric point, the pH changes very rapidly with added H3 O. At the stoichiometric point, the curve is nearly vertical. Thus, there Is much uncertainty in reading a graph to determine the pH at the stoichiometric point. In contrast, a titration curve is nearly fiat in the vicinity of the midpoint, minimizing uncertainty caused by errors in graph reading. 

The exponent (or power) to which the base number (10) has to be raised is the logarithm. To find the pH of a substance, the negative of the logarithm of the hydrogen ion concentration must be taken. 

Using Appendix B, what is the approximate pH of the solution What two indicators would you use to find the pH more precisely and why ... 

Refer to the volume of NaOH on your graph (from question 2). Calculate half this volume. On your graph, find the pH when the solution was half-neutralized. 

You can find the pH range of differenf indicators on p. 20 of the SQA Data Bookiet. 

An acid-base titration is a method that allows quantitative analysis of the concentration of an unknown acid or base solution. In an acid-base titration, the base will react with the weak acid and form a solution that contains the weak acid and its conjugate base until the acid is completely neutralized. The following equation is used frequently when trying to find the pH of buffer solutions. 

The problem is to find the pH of a solution of the weak acid HA, given the formal concentration of HA and the value of Ka.4 Let s call the formal concentration F and use the systematic treatment of equilibrium ... 

When faced with finding the pH of a weak acid, you should immediately realize that [H+] = [A = x and proceed to set up and solve the equation... 

Assuming that what we mixed stays in the same form, we plug these concentrations into the Henderson-Hasselbalch equation to find the pH ... 

F. Find the pH of 0.050 M sodium butanoate (the sodium salt of butanoic acid, also called butyric acid). 

BH CIO4 is a salt formed from the base B (Kh = 1.00 X 10-4) and perchloric acid. It dissociates into BH1, a weak acid, and Cl04, which is neither an acid nor a base. Find the pH of 0.100M BH Cl04. 

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