How do you calculate the pH of acetic acid?

Question

Luna Chen · Accepted Answer

Here's how you can do that.

Acetic acid, #"CH"_3"COOH"#, is a weak acid, meaning that it partially ionizes in aqueous solution to form hydronium cations, #"H"_3"O"^(+)#, and acetate anions, #"CH"_3"COO"^(-)#. #"CH"_ 3"COO"color(red)("H")_ ((aq)) + "H"_ 2"O"_ ((l)) rightleftharpoons "H"_ 3"O"_ ((aq))^(color(red)(+)) + "CH"_ 3"COO"_ ((aq))^(-)# The position of the ionization equilibrium is given by the acid dissociation constant, #K_a#, which for acetic acid is equal to #K_a = 1.8 * 10^(-5)# Table of Monoprotic Acids (https://tutor.hix.ai).html Now, let's assume that you want to find the pH of a solution of acetic acid that has a concentration of #c#. According to the balanced chemical equation that describes the ionization of the acid, every mole of acetic acid that ionizes will produce If you take #x# to be the concentration of acetic acid that ionizes, you can find the equilibrium concentration of the hydronium cations by using an ICE table #"CH"_ 3"COO"color(red)("H")_ ((aq)) + "H"_ 2"O"_ ((l)) rightleftharpoons "H"_ 3"O"_ ((aq))^(color(red)(+)) + "CH"_ 3"COO"_ ((aq))^(-)# #color(purple)("I")color(white)(aaaaaaacolor(black)(c)aaaaaaaaaaaaaaaaaaacolor(black)(0)aaaaaaaaaaaacolor(black)(0)# #color(purple)("C")color(white)(aaaacolor(black)((-x))aaaaaaaaaaaaaaaacolor(black)((+x))aaaaaaaacolor(black)((+x))# #color(purple)("E")color(white)(aaaaacolor(black)(c-x)aaaaaaaaaaaaaaaaaacolor(black)(x)aaaaaaaaaaacolor(black)(x)# It will be equal to the acid dissociation constant. #K_a = (["H"_3"O"^(+)] * ["CH"_3"COO"^(-)])/(["CH"_3"COOH"])# This will be the same as #K_(sp) = (x * x)/(c-x) = x^2/(c-x)# Now, as long as the initial concentration of the acetic acid, #c#, is significantly higher than the #K_(sp)# of the acid, you can use the approximation #c - x ~~ c -> # valid when #color(red)(ul(color(black)(c " >> " K_(sp)))# In this instance, the formula turns into #K_(sp) = x^2/c# which provides you with #x = sqrt(c * K_(sp))# Since #x# represents the equilibrium concentration of hydronium cations, you will have #["H"_3"O"^(+)] = sqrt(c * K_(sp))# Currently, the solution's pH is determined by #color(blue)(|bar(ul(color(white)(a/a)"pH" = - log(["H"_3"O"^(+)])color(white)(a/a)|)))# Integrate these two formulas to obtain #color(green)(|bar(ul(color(white)(a/a)color(black)("pH" = - log( sqrt(c * K_(sp)))color(white)(a/a)|)))# For example, the pH of a #"0.050 M"# acetic acid solution will be #"pH" = - log( 0.050 * 1.8 * 10^(-5))# #"pH" = 3.02#

Jeremiah Adams · Answer

undefined To calculate the pH of acetic acid, you can use the formula: pH = -log[H+]. For acetic acid, which is a weak acid, you also need to consider its dissociation constant (Ka), which is 1.8 x 10^-5. Use the equilibrium expression for the dissociation of acetic acid to find the concentration of hydronium ions, [H+], and then plug this value into the pH formula. The equilibrium expression is Ka = [H+][CH3COO-]/[CH3COOH]. Solving for [H+], you get [H+] = √(Ka * [CH3COOH]). Then, plug this value into the pH formula to find the pH of acetic acid.