How to calculate OH- from pH?, [pH to Hydroxide ion (OH-) concentration]
The presence of hydroxide (OH–) ions in a solution denote its basicity, while pH measures the acidic strength of an aqueous solution. In this way, OH– and pH may seem like two entirely opposite parameters.
But the fascinating fact is that these two chemical parameters complement each other just like two sides of the same coin. If we know one, we can easily find the other.
Therefore, in this article, you will learn how to find hydroxide ion concentration [OH–] in an aqueous solution if its pH is known.
So without any further delay, dive into the article, and let’s start reading!
In contrast, a weak base such as NH4OH only partially ionizes to yield a limited number of OH– ions in an aqueous solution.
In either case, the number of OH– ions released in an aqueous solution determines the strength of the Arrhenius base, also known as an alkali.
The greater the number of OH– ions produced in an aqueous solution, the higher its basicity and vice versa.
The concentration of OH– ions present in an aqueous solution is represented as [OH–] in mol/L or M.
The negative logarithm to the base 10 of [OH–] is referred to as the pOH of the aqueous solution, as shown in equation (i).
pOH = -log10 [OH–]……….Equation (i)
The greater the hydroxide ion concentration [OH–] of an aqueous solution, the lower its pOH value.
Therefore, strongly basic solutions such as NaOH(aq) have low pOH values. However, these have a high pH value where pH is related to pOH as per equation (ii).
pH + pOH = 14…………Equation (ii)
Equation (ii) shows us that both pH and pOH are measured on a numerical scale ranging from 0 to 14.
The greater the pH of an aqueous solution, the lower its pOH, while the sum of its pH and pOH values is always equal to 14.
For instance; the pOH of 0.1 M NaOH solution is 1, while its pH is 13; 1+13 = 14.
What is pH?
pH stands for the power of hydrogen (H+) ions.
It usually determines the acidic strength of an aqueous solution. An acid is defined as a chemical substance that breaks down to release H+ ions in water.
Therefore, pH is calculated by taking the negative logarithm of hydrogen ion concentration [H+] in an aqueous solution, as shown in equation (iii).
pH = -log10 [H+] ……….Equation (iii)
The greaterthe strength of an acid, the more H+ ions are released in its aqueous solution; consequently, [H+] increases. However, the pH of the solution decreases as per equation (iii).
As per the Bronsted-Lowry theory of acids and bases, acids are also defined as proton donors, while bases are proton acceptors.
So a strong base with low pOH readily accepts H+ ions from an aqueous solution; thus, the pH of the solution increases and vice versa.
On the pH scale, acidic solutions have a pH ranging from 0 to 6. pH 7 represents a purely neutral solution such as water, while a pH above 7 denotes the basicity of an aqueous solution.
What is the relationship between OH– and pH?
pH is directly related to the concentration of hydroxide (OH–) ions present in an aqueous solution.
The more the OH– ions present in an aqueous solution, the more basic it is. Thus the acidity of the solution decreases, which means its pH increases and vice versa.
How to find Hydroxide (OH–) ion concentration from pH?
Rearranging equation (ii) to make pOH the subject of the formula gives us equation (iv).
pH + pOH = 14…………Equation (ii)
pOH = 14- pH ……….Equation (iv)
Thus, if the pH of an aqueous solution is known, we can easily find its pOH by using equation (iv).
Once the pOH is known, we can then determine its hydroxide (OH–) ion concentration by applying equations (i) or (v).
pOH = -log10 [OH–]……….Equation (i)
Taking the anti-log of pOH makes [OH–] the subject of the formula, as shown in equation (v).
[OH–] = 10-pOH………….Equation (v)
We have provided the following examples so that you can better understand the concept of finding OH– ion concentration from pH by applying the above equations.
So, what are you waiting for? Let the practice begin!
Solved examples for finding OH– from pH
Example # 1: What is the concentration of hydroxide ions (OH–) in an aqueous solution having pH 8.1?
As the pH of the aqueous solution is given in the question statement i.e., pH = 8.1; so we can easily find its pOH by applying equation (iv).
pOH = 14- pH ……….Equation (iv)
pOH = 14 – 8.1
pOH = 5.9
Now that we know the pOH value, we can easily find the molar concentration of hydroxide ions (OH–) present in it by substituting the known value into equation (v), as shown below.
[OH–] = 10-pOH………….Equation (v)
[OH–] = 10-5.9 = 1.26 x 10-6 mol/L.
Result: 1.26 x 10-6 mol/L OH– ions are present in the given aqueous solution of pH 8.1.
Example # 2: How many OH– ions are present in an aqueous solution having pH 2.4?
As the pH of the aqueous solution is given in the question statement i.e., pH = 2.4; so we can easily find its pOH by applying equation (iv).
pOH = 14- pH ……….Equation (iv)
pOH = 14 – 2.4
pOH = 11.6
Now that we know the pOH value, we can easily find the molar concentration of hydroxide ions (OH–) present in it by substituting the known value into equation (v), as shown below.
[OH–] = 10-pOH………….Equation (v)
[OH–] = 10-11.6 = 2.51 x 10-12 mol/L.
Result: 2.51 x 10-12 mol/L OH– ions are present in the given aqueous solution of pH 2.4.
You may note that a higher [OH–] is obtained in Example 1 as compared to that in example 2.
This implies that a higher pH solution (pH = 8.1) is more basic than that of pH 2.4. This goes exactly in line with what we said earlier in the article i.e.; pH increases if OH– increases.
Example # 3: What is the hydroxide (OH–) ion concentration of pure water at room temperature (25°C)?
We are all familiar with the fact that pure water is a neutral solution i.e., it has pH = 7 at 25° C.
So using this pH value, we can easily find its pOH by applying equation (iv).
pOH = 14- pH ……….Equation (iv)
pOH = 14 – 7
pOH =7
Now that we know the pOH value of water, we can easily find the molar concentration of hydroxide ions (OH–) present in it by substituting the known value into equation (v), as shown below.
[OH–] = 10-pOH………….Equation (v)
[OH–] = 10-7 = 1 x 10-7 mol/L.
Result: The hydroxide (OH–) ion concentration of pure water at room temperature is 1 x 10-7 mol/L.
An important point to remember is that for water, pH = pOH = 7. [H+] = [OH–] = 1 x 10-7 mol/L at 25°C.
In fact, for any aqueous solution prepared at room temperature;
∴ [H+] [OH–] = (1 x 10-7)2 = 1 x 10-14……………Equation (vi)
Additionally, we can even apply equation (vi) as an alternative method to determine OH– concentration from pH, as we have done in the next example.
Example # 4: What is the hydroxide (OH–) ion concentration of an aqueous solution of hydrochloric acid (HCl) at 25°C if the pH of the solution = 1.6?
Method # 1:
HCl is a strong acid that completely ionizes in water to release 1 H+ ion per HCl molecule at 25°C, as shown below.
As the pH of the HCl solution is given, we can use equation (iii) to find its hydrogen ion concentration [H+], as shown below.
pH = -log10 [H+] ……….Equation (iii)
Taking antilog of pH gives us [H+]:
[H+] = 10-pH
Substituting the given pH value into the above formula:
[H+] = 10-1.6 = 0.025119 mol/L
Now that [H+] is known, we can apply equation (vi) to find the required [OH–] value.
[H+] [OH–] = 1 x 10-14……………Equation (vi)
(0.025119) [OH–] = 1 x 10-14
[OH–] = 1 x 10-14/0.025119
[OH–] = 3.98 x 10-13 mol/L.
Alternately, we can also apply the same method we have been using for the above three examples to find OH– from the given pH; let’s show you how.
Method # 2:
Find pOH from the given pH using equation (iv).
pOH = 14- pH ……….Equation (iv)
pOH = 14 – 1.6
pOH = 12.4
Find [OH–] from the above pOH value by substituting it into equation (v).
[OH–] = 10-pOH………….Equation (v)
[OH–] = 10-12.4 = 3.98 x 10-13 mol/L.
Identical answers via both the above methods reassure us that we can use either one to find OH– from pH.
Result: The hydroxide (OH–) ion concentration of an aqueous HCl solution having pH 1.6 is 3.98 x 10-13 mol/L.
OH– is the chemical formula for hydroxide ions. [OH–] denotes the concentration of hydroxide ions present in an aqueous solution.
It is usually measured in mol/L or M, thus, known as the molar concentration or molarity of OH– ions in an aqueous solution.
What is pH?
pH stands for the power of hydrogen ions. It determines the acidic or basic nature of an aqueous solution. It is calculated by taking the negative logarithm of hydrogen (H+) ion concentration present in an aqueous solution.
pH = -log10 [H+].
Acidic solutions have low pH values (0-6), while basic solutions have high pH values (8-14). pH 7 denotes pure water, which is neutral.
What is pOH?
pOH is the negative logarithm of hydroxide ion concentration [OH–].
pOH = -log10 [OH–].
The greater the concentration of OH– ions present in an aqueous solution, the lower its pOH (< 7).
However, it has a high pH value (> 7) which denotes that the given solution is strongly basic in nature.
What is the relationship between pH and pOH?
The formula that relates the pH of an aqueous solution to its pOH is: pH + pOH = 14.
This implies that the pH of an aqueous solution is inversely related to its pOH. If one value increases, the other decreases and vice versa.
What is the formula that relates [H+] to [OH–]?
Pure water (H2O) dissociates to give 1 H+ and 1 OH– ion per H2O molecule at room temperature.
The equilibrium constant for the above reaction is known as the water dissociation constant (Kw) and it is represented as:
Kw = [H+][OH–]/[H2O]
As the concentration of water [H2O] stays constant in the equilibrium mixture, therefore the above equation is reduced to;
Kw = [H+] [OH–]
An equal number of H+ and OH– ions are released per mole of water. Conversely, at 25°C
pH = pOH = 7
[H+] = [OH–] = 10-7 = 1 x 10-7 mol/L.
∴ [H+] [OH–] = 1 x 10-14 mol2 L-2.
How do you calculate OH– ion concentration from pH?
If the pH of an aqueous solution is given; we can use the following two alternative methods to find the required OH– concentration:
Method # 1:
Step i) Find pOH of the solution from its pH by applying the formula: pOH = 14- pH
Step ii) Find [OH–] from the pOH determined above by substituting it into: [OH–] = 10-pOH
Method # 2:
Step i) Find hydrogen ion concentration [H+] from the given pH value by applying the formula: [H+] = 10-pH.
Step ii) Find the required [OH–] by applying the formula, [H+] [OH–] = 1 x 10-14.
Summary
OH– is the chemical formula for hydroxide ions.
[OH–] denotes the molar concentration of hydroxide ions present in an aqueous solution.
The greater the [OH–] in an aqueous solution, the higher its basicity while it has a lower acidic strength.
Strongly basic solutions have low pOH values but a high pH, and vice versa for strongly acidic solutions.
[OH–] is calculated by taking the antilog of pOH. [OH–] = 10-pOH.
pH stands for the power of hydrogen (H+) ions present in an aqueous solution. It is calculated by taking the negative logarithm of H+. pH = -log10 [H+].
pH is inversely related to the pOH of an aqueous solution but directly related to the concentration of OH– ions present in it.
The sum of pH and pOH for an aqueous solution is always equal to 14. pH + pOH = 14.
The product of the concentration of hydrogen and hydroxide ions present in an aqueous solution is always equal to 1 x 10-14e., Kw (water dissociation constant) at r.t.p. [H+] [OH–] = 1 x 10-14.
If we know the pH of an aqueous solution, we can easily find its OH– ion concentration by applying the following two formulas: (pOH = 14 – pH) and [OH–] = 10-pOH
References
vCalc LLC. (n.d.). pH from Hydroxide Concentration. vCalc LLC. https://www.vcalc.com/wiki/ph-from-hydroxide-concentration
Inspirit VR Inc. (n.d.). Hydroxide Ion Concentration Study Guide. Inspirit VR Inc. https://www.inspiritvr.com/general-chemistry/acids-and-bases/hydroxide-ion-concentration-study-guide
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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