Science, Tech, Math Science How to Calculate the pH of a Weak Acid pH of a Weak Acid Worked Chemistry Problem Share Flipboard Email Print Determine the pH of a weak aid using the acid dissociation constant and quadratic equation. Glow Images, Inc / Getty Images Science Chemistry Basics Chemical Laws Molecules Periodic Table Projects & Experiments Scientific Method Biochemistry Physical Chemistry Medical Chemistry Chemistry in Everyday Life Famous Chemists Activities for Kids Abbreviations & Acronyms Biology Physics Geology Astronomy Weather & Climate by Todd Helmenstine Updated June 20, 2017 Calculating the pH of a weak acid is a bit more complicated than determining the pH of a strong acid because weak acids don't completely dissociate in water. Fortunately, the formula for calculating pH is simple. Here's what you do.pH of a Weak Acid ProblemWhat is the pH of a 0.01 M benzoic acid solution?Given: benzoic acid Ka= 6.5 x 10-5SolutionBenzoic acid dissociates in water asC6H5COOH → H+ + C6H5COO- The formula for Ka isKa = [H+][B-]/[HB]where[H+] = concentration of H+ ions[B-] = concentration of conjugate base ions[HB] = concentration of undissociated acid moleculesfor a reaction HB → H+ + B-Benzoic acid dissociates one H+ ion for every C6H5COO- ion, so [H+] = [C6H5COO-].Let x represent the concentration of H+ that dissociates from HB, then [HB] = C - x where C is the initial concentration.Enter these values into the Ka equationKa = x · x / (C -x)Ka = x²/(C - x)(C - x)Ka = x²x² = CKa - xKax² + Kax - CKa = 0Solve for x using the quadratic equationx = [-b ± (b² - 4ac)½]/2ax = [-Ka + (Ka² + 4CKa)½]/2**Note** Technically, there are two solutions for x. Since x represents a concentration of ions in solution, the value for x cannot be negative.Enter values for Ka and CKa = 6.5 x 10-5C = 0.01 Mx = {-6.5 x 10-5 + [(6.5 x 10-5)² + 4(0.01)(6.5 x 10-5)]½}/2x = (-6.5 x 10-5 + 1.6 x 10-3)/2x = (1.5 x 10-3)/2x = 7.7 x 10-4 Find pHpH = -log[H+]pH = -log(x)pH = -log(7.7 x 10-4)pH = -(-3.11)pH = 3.11AnswerThe pH of a 0.01 M benzoic acid solution is 3.11.Solution: Quick and Dirty Method to Find Weak Acid pHMost weak acids barely dissociate in solution. In this solution we found the acid only dissociated by 7.7 x 10-4 M. The original concentration was 1 x 10-2 or 770 times stronger than the dissociated ion concentration. Values for C - x then, would be very close to C to seem unchanged. If we substitute C for (C - x) in the Ka equation,Ka = x²/(C - x)Ka = x²/CWith this, there is no need to use the quadratic equation to solve for xx² = Ka·Cx² = (6.5 x 10-5)(0.01)x² = 6.5 x 10-7x = 8.06 x 10-4Find pHpH = -log[H+]pH = -log(x)pH = -log(8.06 x 10-4)pH = -(-3.09)pH = 3.09Note the two answers are nearly identical with only 0.02 difference. Also notice the difference between the first method's x and the second method's x is only 0.000036 M. For most laboratory situations, the second method is 'good enough' and much simpler. citecite this article Format mla apa chicago Your Citation Helmenstine, Todd. "How to Calculate the pH of a Weak Acid." ThoughtCo, Jun. 20, 2017, thoughtco.com/calculating-ph-of-a-weak-acid-problem-609589. Helmenstine, Todd. (2017, June 20). How to Calculate the pH of a Weak Acid. Retrieved from https://www.thoughtco.com/calculating-ph-of-a-weak-acid-problem-609589 Helmenstine, Todd. "How to Calculate the pH of a Weak Acid." ThoughtCo. https://www.thoughtco.com/calculating-ph-of-a-weak-acid-problem-609589 (accessed April 22, 2018). copy citation Continue Reading