pH and pKa

If you have ever tried lemon juice, then you and I can agree that lemon juice has a very acidic taste. Lemon juice is a type of weak acid, and to learn about the pH and pKof weak acids, we need to dive into the world of Ka, ICE tables and even percent ionization!

pH and pKa pH and pKa

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Contents
Table of contents
    • This article is about pH and PKa.
    • First, we will talk about definitions of pH and pKa
    • Then, we will look at calculations involving pH and pKa
    • Lastly, we will learn about percent ionization.

    Relationship between pH and pKa

    Before diving into pH and pKa, let's recall the definition of Bronsted-Lowry acids and bases, and also the meaning of conjugate acids and bases.

    Bronsted-Lowry acids are proton (H+) donors, whereas Bronsted-Lowry bases are proton (H+) acceptors. Let's look at the reaction between ammonia and water.

    pH and pKa Chemistry equation of the reaction between ammonia and water StudySmarterFig. 1: The reaction between ammonia and water, Isadora Santos - StudySmarter Originals.

    Conjugate acids are bases that gained a proton H+. On the other hand, Conjugate bases are acids that lost a proton H+. For example, when HCl is added to H2O, it dissociates to form H3O+ and Cl-. Water will gain a proton, and HCl will lose a proton.

    pH and pKa Conjugate pairs in a reaction between HCl and water StudySmarterFig. 2: Conjugate pairs in a reaction between HCl and Water, Isadora Santos - StudySmarter Originals.

    Some chemistry books use H+ instead of H3O+ to refer to hydrogen ions. However, these two terms can be used interchangeably.

    Now that those definitions are fresh in our minds, let's look at how pH and pKa are related. The first thing you need to know is that we can use pH and pKa to describe the relationship between weak acids in an aqueous solution.

    pH is a measurement of the [H+] ion concentration in a solution.

    You can learn more about pH by reading "pH Scale"!

    The definition of pKa can sound confusing, especially if you are not familiar with the acid dissociation constant, also known as Ka. So, let's talk about that!

    When it comes to weak acids and pH calculation, we need an extra piece of information, the acid dissociation constant (Ka). Ka is used to determine the strength of an acid and its ability to stabilize its conjugate base. It measures how fully an acid is able to dissociate in water. In general, the higher the Ka of an acid, the stronger the acid will be.

    Ka can also be called acid ionization constant, or acidity constant.

    The general formula for a monobasic acid can be written as:HA (aq) H+ (aq) A- (aq), where:

    • HA is the weak acid.

    • H+ is the hydrogen ions.

    • A- is the conjugate base.

    We can use the following formula for Ka:

    $$K_{a}=\frac{[products]}{[reactants]}=\frac{[H^{+}]\cdot [A^{-}]}{HA}=\frac{[H^{+}]^{2}}{HA}c$$

    Keep in mind that solids (s) and pure liquids (l) like H2O (l) should not be included when calculating Ka because they have constant concentrations. Let's look at an example!

    What would be the equilibrium expression for the following equation?

    $$CH_{3}COOH^{(aq)}\rightleftharpoons H^{+}_{(aq)}+CH_{3}COO^{-}_{(aq)}$$

    Using the formula for Ka, the equilibrium expression would be:

    $$K_{a}=\frac{[products]}{[reactants]}=\frac{[H^{+}\cdot [CH_{3}COO^{-}]]}{[CH_{3}CCOH]}$$

    For extra practice, try writing the equilibrium expression of: $$NH_{4\ (aq)}^{+}\rightleftharpoons H^{+}_{(aq)}+NH_{3\ (aq)}$$ !

    Now that we know what Ka means, we can define pKa. Don't worry about pKa calculations right now - we will deal with it in a little bit!

    pKa is referred to as the negative log of Ka.

    • pKa can be calculated using the equation: pKa = - log10 (Ka)

    Buffers are solutions that contain either a weak acid + its conjugate base or a weak base + its conjugate acid, and have the ability to resist changes in pH.

    When dealing with buffers, pH and pKa are related through the Henderson-Hasselbalch equation, which has the following formula:

    $$pH=pK_{a}+log\frac{[A^{-}]}{[HA]}$$

    Difference between pKa and pH

    The main difference between pH and pKa is that pKa is used to show the strength of an acid. On the other hand, pH is a measure of the acidity or alkalinity of an aqueous solution. Let's make a table comparing pH and pKa.

    pHpKa
    pH = -log10 [H+]pKa= -log10 [Ka]
    ↑ pH = basic↓ pH = acidic↑ pKa = weak acid↓ pKa = strong acid
    depends on [H+] concentrationdepends on [HA], [H+] and A-

    pH and pKa Equation

    When we have a strong acid, such as HCl, it will completely dissociate into H+ and Cl- ions. So, we can assume that the concentration of [H+] ions will be equal to the concentration of HCl.

    $$HCl\rightarrow H^{+}+Cl^{-}$$

    However, calculating the pH of weak acids is not as simple as with strong acids. To calculate the pH of weak acids, we need to use ICE charts to determine how many H+ ions we will have at equilibrium, and also use equilibrium expressions (Ka).

    $$HA_{(aq)}\rightleftharpoons H^{+}_{(aq)}+A^{-}_{(aq)}$$

    Weak acids are those that partially ionize in solution.

    ICE Charts

    The easiest way to learn about ICE tables is by looking at an example. So, let's use an ICE chart to find the pH of a 0.1 M solution of acetic acid (The Ka value for acetic acid is 1.76 x 10-5).

    Step 1: First, write down the generic equation for weak acids:

    $$HA_{(aq)}\rightleftharpoons H^{+}_{(aq)}+A^{-}_{(aq)}$$

    Step 2: Then, create an ICE chart. "I" stands for initial, "C" stands for change, and "E" stands for equilibrium. From the problem, we know that the initial concentration of acetic acid is equal to 0.1 M. So, we need to write that number on the ICE chart. Where? On the "I" row, under HA. Before dissociation, we don't have H+ or A- ions. So, write a value of 0 under those ions.

    pH and pKa How to fill the I row on ICE charts StudySmarterFig. 3: How to fill the "I" row on the ICE chart, Isadora Santos - StudySmarter Originals

    Actually, pure water does have a little bit of H+ ions (1 x 10-7 M). But, we can ignore it for now since the amount of H+ ions that will be produced by the reaction will be way more significant.

    Step 3: Now, we need to fill out the "C" (change) row. When dissociation occurs, change goes to the right. So, the change in HA will be -x, whereas the change in the ions will be +x.

    pH and pKa How to fill the C row on ICE charts StudySmarterFig. 4: Filling out the "C" row on the ICE Chart. Isadora Santos - StudySmarter Originals.

    Step 4: The equilibrium row shows the concentration at equilibrium. "E" can be filled by using the values of "I" and "C". So, HA will have a concentration of 0.1 - x at equilibrium and the ions will have a concentration of x at equilibrium.

    pH and pKa How to fill the E row on ICE charts StudySmarterFig. 5: Filling the "E" row on the ICE chart, Isadora Santos - StudySmarter Originals.

    Step 5: Now, we have to create an equilibrium expression using the values in the equilibrium row, which will then be used to solve for x.

    • x is equal to the [H+] ion concentration. So, by finding x, we will be able to know [H+] and then calculate pH.

    $$K_{a}=\frac{[H^{+}]\cdot [A^{-}]}{HA}=\frac{x^{2}}{0.1-x}$$

    Step 6: Plugin all the known values to the Ka expression and solve for x. Since x will usually be a small number, we can ignore the x that's being subtracted from 0.1.

    $$K_{a}=\frac{x^{2}}{0.1-x}\cdot 1.76\cdot 10^{-5}=\frac{x^{2}}{0.1}x=\sqrt{(1.76\cdot 10^{-5})}\cdot 0.1=0.0013M=[H^{+}]$$

    If after doing this step it turns out that x is bigger than 0.05 then you will have to do the whole quadratic equation. After some algebra in this case you would get x^2 +Ka*x - 0.1*Ka = 0. You can just use the normal quadratic formula now to solve for x.

    Step 7: Use the [H+] value to calculate pH.

    $$=-log_{10}[H^{+}]pH=-log_{10}[0.0013]pH=2.9$$

    Normally, when finding the pH of a weak acid, you will be asked to construct an ICE table. However, for your AP exam (and also to reduce time), there is a little shortcut that you can take to find the [H+] ion concentration of a weak acid that is needed to find its pH.

    So, to calculate the [H+] all you need to know is the value for the concentration of the weak acid and the Ka value, and plug those values into the following equation:

    $$[H^{+}]=\sqrt{K_{a}\cdot initial\ concentration\ of\ HA}$$

    Then, you can use the [H+] value to calculate pH. Note that this equation will not be given to you in the AP exam, so you should try to memorize it!

    pH and pKa Formulas

    To calculate pH and pKa, you should be familiar with the following formulas:

    pH and pKa  Formulas relating pH and pKa ICE charts StudySmarterFig. 6: Formulas relating pH and pKa, Isadora Santos - StudySmarter Originals.

    Let's look at a problem!

    Find the pH of a solution containing 1.3·10-5 M [H+] ion concentration.

    All we have to do is use the first formula above to calculate pH.

    $$pH=-log_{10}[H^{+}]pH=-log_{10}[1.3\cdot 10^{-5}M]pH=4.9$$

    That was pretty straightforward, right? But, let's amp up the difficulty a bit more!

    Find the pH of 0.200 M of benzoic acid. The Ka value for C6H5COOH is 6.3 x 10-5 mol dm-3.

    $$C_{6}H_{5}COOH\rightarrow H^{+}C_{6}H_{5}COO^{-}$$

    Although we can make an ICE table to find the [H+] ion concentration of benzoic, let's use the shortcut formula:

    $$[H^{+}]=\sqrt{K_{a}\cdot initial\ concentration\ of\ HA}$$

    So, the value for the hydrogen ion concentration of H+ will be:

    $$[H^{+}]=\sqrt{(6.3\cdot 10^{-5})\cdot (0.200)}=0.00355$$

    Now, we can use the calculated [H+] value to find pH:

    $$pH=-log_{10}[H^{+}]pH=-log_{10}[0.00355]pH=2.450$$

    Now, what if you were asked to calculate pKa from Ka? All you need to do is use the pKa formula if you know the value for Ka.

    For example, if you know that the Ka value for benzoic acid is 6.5x10-5 mol dm-3, you can use it to calculate pKa:

    $$pK_{a}=-log_{10}(K_{a})pK_{a}=-log_{10}(6.3\cdot 10^{-5})pKa=4.2$$

    Calculating pKa from pH and Concentration

    We can use the pH and concentration of a weak acid to calculate the pKa of the solution. Let's look at an example!

    Calculate the pKa of a 0.010 M solution of a weak acid containing a pH value of 5.3.

    Step 1: Use the pH value to find [H+] ion concentration by rearranging the pH formula. By knowing the concentration of [H+], we can also apply it to the concentration of A- since the reaction of weak acids is at equilibrium.

    $$H^{+}=10^{-pH}[H^{+}]=10^{-5.3}=5.0\cdot 10^{-6}$$

    Step 2: Make an ICE chart. Remember that "X" is the same as the [H+] ion concentration.

    pH and pKa ICE Chart Calculating pKa from pH and Concentration StudySmarterFig. 8: ICE chart for a 0.010 M solution of a weak acid, Isadora Santos - StudySmarter Originals.

    Step 3: Write the equilibrium expression using the values in the equilibrium row (E), and then solve for Ka.

    Ka = [products][reactants]= [H+][A-]HA = X20.010 - XKa = (5.0×10-6)(5.0×10-6)0.010 - 5.0×10-6 = 2.5×10-9 mol dm-3

    Step 4: Use the calculated Ka to find pKa.

    $$K_{a}=\frac{[products]}{[reactants]}=\frac{[H^{+}]\cdot[A^{-}]}{HA}=\frac{x^{2}}{0.010-x}K_{a}=\frac{(5.0\cdot 10^{-6})(5.0\cdot 10^{-6})}{0.010-5.0\cdot 10^{-6}}=2.5\cdot 10^{-9}mol\cdot dm^{-3}$$

    Finding Percent Ionization given pH and pKa

    Another way of measuring the strength of acids is through percent ionization. The formula to calculate percent ionization is given as:

    $$%\ ionization=\frac{concentration\ of\ H^{+}\ ions\ in\ equilibrium}{initial\ concentration\ of\ the\ weak\ acid}=\frac{x}{[HA]}\cdot 100$$

    Remember: the stronger the acid, the greater the % ionization. Let's go ahead and apply this formula to an example!

    Find the Ka value and the percent ionization of a 0.1 M solution of a weak acid containing a pH of 3.

    1. Use the pH to find [H+].

    $$[H^{+}]=10^{-pH}\cdot [H^{+}]=10^{-3}$$

    2. Make an ICE table to find the concentrations of HA, H+, and A- in equilibrium.

    pH and pKa ICE Chart Calculating percent ionization pH and pKa StudySmarterFig. 9: ICE table of a 0.1 M solution of a weak acid, Isadora Santos - StudySmarter Originals.

    3. Calculate percent ionization using the value for x ([H+]) and for HA from the ICE table.

    $$%\ ionization= \frac{[H^{+}]}{[HA]}\cdot 100%\ ionization=\frac{[10^{-3}M]}{0.1M-10^{-3}M}\cdot 100=1%$$

    Now, you should have what it takes to find the pH and pKa of weak acids!

    pH and pKa - Key takeaways

    • pH is a measurement of the [H+] ion concentration in a solution.
    • pKa is referred to as the negative log of Ka.
    • To calculate the pH and pKa of weak acids, we need to use ICE charts to determine how many H+ ions we will have at equilibrium, and also Ka.
    • If we know the concentration of H+ ions in equilibrium, and the initial concentration of the weak acid, we can calculate percent ionization.

    References:

    Brown, T. L., Nelson, J. H., Stoltzfus, M., Kemp, K. C., Lufaso, M., & Brown, T. L. (2016). Chemistry: The central science. Harlow, Essex: Pearson Education Limited.

    Malone, L. J., & Dolter, T. (2013). Basic concepts of of Chemistry. Hoboken, NJ: John Wiley.

    Ryan, L., & Norris, R. (2015). Cambridge International as and A level chemistry. Cambridge: Cambridge University Press.

    Salazar, E., Sulzer, C., Yap, S., Hana, N., Batul, K., Chen, A., . . . Pasho, M. (n.d.). Chad's general chemistry Master course. Retrieved May 4, 2022, from https://courses.chadsprep.com/courses/general-chemistry-1-and-2

    Frequently Asked Questions about pH and pKa

    How to calculate pH from pKa and concentration

    To calculate the pH and pKa of weak acids, we need to use an equilibrium expression and an ICE chart. 

    Are pH and pKa the same?

    No, they are not the same. pH is a measurement of the [H+] ion concentration in a solution. On ther other hand, pKa is used to show whether an acid is strong or weak. 

    How are pH and pKa related?

    In buffers, pH and pKa are related through the Henderson-Hasselbalch equation.


    What is pKa and pH?

    pH is the negative log (base 10) of [H+]. pKa is the negative log (base) of Ka.

    Test your knowledge with multiple choice flashcards

    Bronsted-Lowry acids are proton (H+) _____.

    Bronsted-Lowry bases are proton (H+) _____ .

    _____ is a measurement of the [H+] ion concentration in a solution.

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