pH refers to the power of hydrogen. It measures the concentration of hydrogen ions [H+] present in an aqueous solution. The [H+] usually ranges from 1 to 10-14 g eq./L. When converted into pH, it is represented in numbers from 0 to 14.
Acidic solutions have a pH below 7, while basic or alkaline solutions have a pH above 7 on the pH scale. In this way, pH determines the acidity or basicity present in an aqueous solution.
Greater the H+ concentration, the lower the pH, thus the more acidic the aqueous solution.
In this article, you will learn how to calculate pH if the acid dissociation constant (Ka) for a solution is given. So, what are we waiting for? Let’s start reading!
As discussed already, pH stands for the power of hydrogen. It measures the concentration of H+ ions present in an aqueous solution according to equation (i).
pH = -log [H+] …. Equation (i)
What is Ka?
Ka stands for acid dissociation constant.
A strong acid such as HCl ionizes completely in water to release H+ and Cl– ions. It is an irreversible reaction; therefore, an equilibrium constant is not an ideal parameter for determining the strength of strong acids.
However, the strength of weak acids such as acetic acid (CH3COOH) and propanoic acid (CH3CH2COOH) can be compared in between by determining their Ka values.
A weak acid (HA) dissociates to give H+ and A– ions in an aqueous solution. A– refers to the conjugate base of an acid. Thus, HA and A– together are called a conjugate acid-base pair.
The ionization equilibrium for the dissociation of a weak acid (HA) in an aqueous solution is represented as follows:
The acid dissociation constant (Ka) for the above reaction can be represented as equation (ii).
Ka = \frac{[H_{3}O^{+}][A^{-}]}{[HA][H_{2}O]}………. Equation (ii)
Where;
[H3O+] = concentration of hydronium ions formed in the aqueous solution
[A–] = concentration of conjugate base of the acid
[HA] = acid concentration at equilibrium
[H2O] = concentration of water
As water concentration stays constant throughout the reaction, while [H3O+] = [H+], i.e., the concentration of H+ ions released in the aqueous solution. So, equation (ii) can be rearranged as equation (iii).
Ka = \frac{[H^{+}][A^{-}]}{[HA][H_{2}O]}………. Equation (iii)
The greater the strength of an acid, the higher the Ka value for its aqueous solution and vice versa.
What is the relationship between pH and Ka?
The pH of an acidic solution is inversely proportional to the acid dissociation constant (Ka).
As per equation (i), the pH value decreases as [H+] increases. In contrast, a higher [H+] denotes that the acid ionizes to a large extent; thus, it possesses a higher Ka value.
How to calculate pH from Ka? (Ka to pH)
You may have noticed that [H+] is the main connection between pH and Ka. It is the common term present in both equations (i) and (iii).
Hence, if Ka is known, the concentration of hydrogen ions [H+] can be determined using equation (iii). By plugging in [H+] in equation (i), we can easily find the pH of the given solution.
Conversely, we can also combine the two equations. For that, make [H+] the subject of the formula in equation (iii).
Have a look at the solved examples given below so that you may have a better idea about how to use all the above equations in order to determine pH.
Solved examples for finding pH from Ka?
Example # 1:An aqueous solution of propanoic acid (CH3CH2COOH) dissociates to produce propanoate (CH3CH2COO–) ions and hydrogen (H+) ions. The Ka value is 8.69 x 10-10. The amount of acid undissociated at the equilibrium point is 1.96 x 10-2 M.
Use this information to find the pH of the solution at equilibrium.
The ionization equilibrium for CH3CH2COOH is shown below. 1 mole propanoic acid dissociates to produce 1 mole propanoate ion (conjugate base) and 1 mole H+.
So [CH3CH2COO–] = [H+] at equilibrium.
Let’s suppose, [CH3CH2COO–] equilibrium = [H+] equilibrium = x M.
Now that we know [H+], we can easily apply equation (i) to find the pH of the solution as follows.
pH = -log [H+] …. Equation (i)
pH = -log (4.13 x 10-6) = 5.38
Result: The pH of the given propanoic acid solution is 5.38.
Example # 2:The Ka of an unknown acid (HA) is 1.77 x 10-5. Can you help us determine the pH of the acidic solution at the point where the acid is 1/10th dissociated?
Do you remember the equation (vi) we learnt in this article? Well, we need to use that here.
………..Equation (vi)
The question statement says that the unknown acid is 1/10th dissociated. This implies [A–]/[HA] = 1/10.
Ka is also given so we can find pKa as follows:
pKa = -log Ka = -log (1.77 x 10-5) = 4.75
Now plug in all the required values into equation (vi) in order to determine the required pH.
pH = 4.75 + log(1/10)
pH = 4.75 + (-1) = 3.75
Result: The pH of the unknown acidic solution is 3.75.
Example # 3:The Ka value for 0.9 M acetic acid solution is 1.8 x 10-5. What is its pH?
As per the question statement, the initial concentration of CH3COOH is given, i.e., [HA]initial = 0.9 M. The value of Ka is also given, i.e., Ka = 1.8 x 10-5.
Step I:
1 mole CH3COOH breaks down to give 1 mole H+ and CH3COO– ions each. Let’s suppose x moles of each of H+ and CH3COO– are produced at equilibrium.
Thus the concentration of acid unreacted at equilibrium is:
The ± sign indicates that there are two possible solutions for the above equation. However, we will only consider the positive solution because x is a concentration that cannot be a negative value.
∴ x = 4.02 x 10-3 M
Thus, [H+] = 4.02 x 10-3 M.
Step II:
Now that the concentration of hydrogen ions produced at equilibrium is known, we can easily find the pH of the solution by applying equation (i).
pH = -log [H+] …. Equation (i)
pH = -log (4.02 x 10-3) = 2.4
Result: The pH of the acetic acid solution given in this example is 2.4.
pH stands for the power of hydrogen. It is a numerical representation of the acidity or basicity of an aqueous solution.
Acidic solutions have a pH between 0-6, while basic solutions have a pH ranging from 8-14. The pH of a purely neutral liquid such as water is 7 at 25°C.
What is Ka?
Ka stands for acid dissociation constant. It is an equilibrium constant that determines the extent of ionization of a weak acid in an aqueous solution.
What is the difference between pH and Ka?
Ka determines the extent of ionization of an acid in an aqueous solution. Contrarily, pH specifically measures the concentration of H+ ions present in the aqueous solution.
pH determines whether a solution is acidic or basic, while Ka determines the strength of an acid.
The stronger the acid, the higher its Ka value, while the lower its pH.
What is the relationship between pH and Ka?
The acid dissociation constant (Ka) is inversely related to the pH of an acidic solution.
The numerical relation between Ka and pH can be represented as follows:
where pKa = -log Ka
[HA] = concentration of acid left undissociated at equilibrium
[A–] = concentration of conjugate base of the acid at equilibrium
How can we calculate the pH of a solution from Ka?
We can apply the formula given below to determine [H+] from Ka.
Ka = \frac{[H^{+}][A^{-}]}{[HA][H_{2}O]}
Once the value of [H+] is determined, we can then find pH by applying log10.
pH = -log [H+]
Summary
pH denotes the power of hydrogen. It measures the concentration of H+ ions present in an aqueous solution.
pH = -log [H+].
Ka stands for acid dissociation constant. It represents the extent of ionization of an acid in an aqueous solution.
If the Ka value for acid is known, we can determine the concentration of [H+] ions in its aqueous solution by applying the formula given below.
Ka = [H+][A–]/[HA]
Once the [H+] is known, the pH of the solution can be easily determined using pH = -log [H+].
pH is also related to Ka via the equation pH = pKa + log[A-]/[HA] where pKa = -log Ka
Ammara Waheed is a highly qualified and experienced chemist, whose passion for Chemistry is evident in her writing. With a Bachelor of Science (Hons.) and Master of Philosophy (M. Phil) in Physical and Analytical Chemistry from Government College University (GCU) Lahore, Pakistan, with a hands-on laboratory experience in the Pakistan Council of Scientific and Industrial Research (PCSIR), Ammara has a solid educational foundation in her field. She comes from a distinguished research background and she documents her research endeavors for reputable journals such as Wiley and Elsevier. Her deep knowledge and expertise in the field of Chemistry make her a trusted and reliable authority in her profession. Let's connect - https://www.researchgate.net/profile/Ammara-Waheed
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