How to calculate pH from molarity?, (molarity to pH)
pH refers to the power of hydrogen. It measures the concentration of hydrogen (H+) or hydronium (H3O+) ions present in an aqueous solution.
There are different ways for defining the concentration of an aqueous solution. One of the most popular ways is by using the term ‘molarity’’.
This signifies that there is a close relationship between pH and molarity. If one is known, we can amicably find the other. But how? Let’s discover this through this article.
There are two primary components of a solution, i.e., a solute and a solvent. The solute is usually a solid substance. It is the minor component of the solution that gets completely dissolved in its major component, such as a liquid known as a solvent, to form a homogeneous solution.
The concentration of the solution can be expressed using a term called ‘molarity’’.
As discussed at the beginning of the article, molarity is defined as the amount of solute that dissolves in a specific volume of solution. For molarity, the amount is in moles, while volume is taken in liters (L).
So molarity refers to the moles of solute dissolved per liter of the solution.
Units used for molarity: mol/L or M.
For instance, to prepare 1 M (molar) HCl solution, we can use equation (i).
Moles (n) = mass/molar mass …………Equation (i)
The molar mass of HCl is 36.458 g/mol. Putting this value into equation (i).
⇒ Mass = moles x molar mass = 1 x 36.458 = 36.458 grams.
The above calculation shows that 1 M HCl solution is prepared by dissolving 36.458 grams of hydrochloric acid in 1 L of distilled water, which is a very concentrated solution that you need to handle with great care.
If the number of moles of solute in a solution is given, we can find its molarity using equation (ii).
n = C x V …………… Equation (ii)
n= no of moles of solute, C = concentration (molarity), V= volume of the solution in litres.
If the volume of the solution is given in milliliters (mL) which is commonly the case, then the volume given in equation (ii) can be divided by 1000 as;
1 L = 1000 mL or 1 mL = 1/1000 L.
Equation (ii) then transforms into equation (iii).
n = (C × V)/1000……………Equation (iii)
This shows that consistency in units is very important. As the molarity of a solution is always determined in moles/liters so the volume must be in liters (L).
What is pH?
An acid is defined as a chemical substance that dissociates to produce H+ ions in an aqueous solution. The H+ ions combine with water (H2O) molecules to form hydronium (H3O+) ions.
The greater the strength of an acid, the more readily it gets dissociated to release a large number of H+ ions in the solution.
The concentration of H+ ions released or H3O+ ions formed in an aqueous solution can be measured against a parameter called pH (power of hydrogen).
The pH of a solution is related to [H+] by the formula given in equation (iv).
pH = -log10 [H+] ….Equation (iv)
Equation (iv) can also be written as equation (v) considering H3O+ ions formed in the aqueous solution. The greater the H+ ions released, the more H3O+ ions will be formed.
pH = -log10 [H3O+] ….Equation (v)
The hydrogen ion concentration of a solution usually varies from 1 to 10-14 g eq./L. When converted into pH, it is represented in numbers from 0 to 14.
The greater the acidity of a solution, the higher [H+], so as per equation (iv), it has a lower pH.
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 pH and molarity?
There are two possibilities to discuss the relationship between the pH of an aqueous solution and its molarity.
(1). Comparing different acids of the same molarity
The pH of 1 M HCl is 0, while the pH of 1 M CH3COOH is 2.4. This implies that 1 M HCl is stronger than 1 M CH3COOH even though both have the same molarity.
This is because 1 M hydrochloric acid dissociates completely to release a large number of H+ ions in an aqueous solution.
Contrarily, 1 M acetic acid only partially ionizes to release a small number of H+ ions; thus, as per equation (i), the latter has a higher pH than the former.
In this case, acidic strength predominantly influences pH, and there is little to no role of molarity.
(2). Comparing different molarities of the same acid
The pH of 1 M HCl is lower than that of 0.1 M HCl. This is because there are a greater number of H+ ions in a 1 M HCl solution than in its 0.1 M solution. Thus, in this case, molarity is inversely related to pH.
So, in general, for strong acids that completely ionize in water to liberate H+ ions, increasing the molarity of the solution decreases its pH and vice versa.
How to find pH from molarity?
We can easily use molarity or [H+] in moles/L to find the pH of the solution.
If the concentration of H+ ions is known, we can determine the pH of the aqueous solution by taking the negative logarithm of that numerical value, as shown in equation (iv).
pH = -log10 [H+] ….Equation (iv)
log10 is sometimes simply written as log only. However, in either case, it refers to a logarithm to the base 10.
You will understand this concept more clearly through the solved examples given in the next section, so continue reading.
Solved examples for finding pH from molarity?
Example # 1: Find the pH of a 0.005 M HCl solution.
We know that HCl is a strong acid that completely ionizes to release H+ and Cl– ions in water.
So the concentration of HCl solution = concentration of H+ ions released in the solution.
As the concentration or molarity of the HCl solution is given in the question statement i.e., 0.005 M.
So we know [H+] = 0.005 mol/L.
We can use equation (iv) and put the value of [H+] given above to determine the pH of the solution as follows:
pH = -log10 [H+] ….Equation (iv)
pH = -log10 (0.005) = 2.30
Result: The pH of 0.005 M HCl solution is 2.30.
Example # 2: What is the pH of a 0.1 M HCl solution?
The concentration or molarity of HCl solution (given in the question statement) = concentration of H+ ions released in the solution
So we know [H+] = 0.1 mol/L.
We can use equation (iv) and put the value of [H+] given above to determine the pH of the solution as follows:
pH = -log10 [H+] ….Equation (iv)
pH = -log10 (0.1) = 1
Result: The pH of a 0.1 M HCl solution is 1.
Example # 3: Compare using the pH values calculated in examples 1 and 2 to comment on the strength of different molarity acidic solutions.
As per example 1, the pH of a 0.005 M HCl solution is 2.30. In contrast, example 2 illustrates that the pH of a 0.1 M HCl solution is 1.
2.30 > 1. Acidic strength is inversely related to pH; thus, 0.1 M HCl solution is more acidic than its 0.005 M solution.
In conclusion, the greater the molarity, the lower the pH, thus higher acidic strength.
Example # 4: Calculate the pOH of a 0.0025 M HCl solution.
To solve this example, we must know the relationship between pH and pOH as given in equation (vi).
pH + pOH = 14………Equation (vi)
So, if the pH of an aqueous solution is known, we can easily determine its pOH by rearranging equation (vi).
pOH = 14 – pH………Equation (vii)
In the question statement, the molarity of the HCl solution is known.
Molarity of HCl = [H+] in mol/L= 0.0025
Now putting this value into equation (iv).
pH = -log10 [H+] ….Equation (iv)
pH of 0.0025 M HCl solution = -log10 (0.0025) = 2.6
Now substitute the value of pH in equation (vii).
pOH = 14 -2.6 = 11.4
Result: The pOH of 0.0025 M HCl solution is 11.4.
Interesting fact:Acidic solutions have a lower pH and higher pOH values. Contrarily, basic solutions have high pH and low pOH values.
Example # 5: Find the pH of a 0.005 M sulfuric acid (H2SO4) solution.
In this example, the acid given is sulfuric acid (H2SO4) which is a diprotic acid.
A diprotic acid is defined as an acid that yields 2 H+ ions per acid molecule.
1 M monoprotic acid (HCl) = 1 M H+ ions released in the aqueous solution.
1 M diprotic acid (H2SO4) = 2 M H+ ions liberated in the aqueous solution.
As per the question statement, it is 0.005 M H2SO4 which denotes its complete ionization results in [H+] = 2(0.005) = 0.01 mol/L.
Now we need to plug in the above value into equation (iv) and find pH.
pH = -log10 (0.01) = 2
Result: The pH of a 0.005 M H2SO4 solution is 2.
Example # 6: A chemist prepared in his lab an acidic solution by dissolving 1.56 grams of hydrobromic acid (HBr) in 100 mL of distilled water. Can you help him find the pH of the solution?
Yes, we can first determine the molarity of the HBr solution prepared above by using equations (i) and (iii) and then use equation (iv) to find the pH of the acidic solution.
Moles (n) = mass/molar mass …………Equation (i)
The molar mass of HBr is 80.91 g/mol. The mass of HBr dissolved is given in the question statement i.e., mass = 1.56 grams.
So the moles of HBr dissolved = 1.56/80.91 = 0.0193.
Now we plug in these moles into equation (iii) to determine C in mol/L i.e., molarity. V= volume of the solution = 100 mL (also given in the question statement).
n = (C × V)/1000……………Equation (iii)
C = (0.0193 × 1000)/100 = 0.193 moles/L
Molarity of HBr = [H+] released in the aqueous solution as HBr is a strong acid, so we can substitute the value of C determined above in equation (iv) to find the pH of the respective solution as follows:
pH = -log10 [H+] ….Equation (iv)
pH = -log10 (0.193) = 0.71
Result: The pH of hydrobromic acid prepared in this example is 0.71, which indicates an extremely high acidic strength.
Molarity is one way of representing the concentration of an aqueous solution. It is defined as the moles of solute dissolved per liter of the solution. The units of molarity are mol/L, mol/dm3 or simply M.
What is the relationship between the pH and molarity of a strongly acidic solution?
For a strongly acidic solution such as HCl that completely ionizes in water, the pH of the solution is inversely proportional to its molarity.
The higher the molarity, the more H+ ions are in the aqueous solution, thus lowering its pH, and indicating a higher acidic strength.
What is the formula to calculate pH from molarity and concentration?
pH = – log10 [H+]
As per the above formula, if the concentration of hydrogen ions present in an aqueous solution is known in mol/L (i.e., molarity), then its pH can be calculated by taking the negative logarithm to the base 10 of the molarity value.
How is the molarity of a monoprotic acidic solution related to its [H+]?
A monoprotic acid releases 1 H+ ion per acid molecule.
Some well-known examples of monoprotic acids are HCl and HNO3.
A strong acid completely breaks down to release all H+ ions present in it.
Molarity of a monoprotic acid = concentration of hydrogen ions released in its aqueous solution.
1 M HCl = 1 mol/L H+ ions. So we can directly plug in this value in the pH formula to determine the pH of the solution.
How is the molarity of a diprotic acid related to [H+] present in its acidic solution?
A diprotic acid releases 2 H+ ions per acid molecule.
H2SO4 and H2CO3 are examples of diprotic acids.
The concentration of hydrogen ions released in its aqueous solution = 2 x molarity of diprotic acid.
1 M H2SO4 = 2 mol/L H+ ions.
How is the molarity of a triprotic acid related to [H+] present in its acidic solution?
A triprotic acid releases 3 H+ ions per acid molecule. For e.g., H3PO4 is a triprotic acid.
The concentration of hydrogen ions released in the acidic solution = 3 x molarity of triprotic acid.
1 M H3PO4 = 3 mol/L H+ ions.
Summary
pH denotes the power of hydrogen. It measures the concentration of H+ ions present in an aqueous solution.
If the concentration of H+ ions present in an aqueous solution is known in mol/L (i.e., molarity), we can easily determine its pH using the formula pH = -log10 [H+].
Molarity is one way of measuring the concentration of an aqueous solution.
Molarity is defined as moles of solute dissolved per liter of solution (unit: mol/L or M).
For a monoprotic strong acid, molarity = [H+] as it completely breaks down to release hydrogen ions in an aqueous solution.
Molarity is inversely related to pH for completely ionizable strong acids.
The higher the molarity, the greater [H+], thus lowering the pH of the acidic solution.
References
study.com. (n.d.). How to Calculate the pH or pOH of a Solution: Quiz & Worksheet. Retrieved from https://study.com/academy/practice/quiz-worksheet-how-to-calculate-the-ph-or-poh-of-a-solution.html
Purdue University Department of Chemistry. (n.d.). Calculating pH and pOH. Retrieved from https://www.chem.purdue.edu/gchelp/howtosolveit/Equilibrium/Calculating_pHandpOH.htm
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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