How to calculate molarity from pH?, (pH to molarity)
Molarity is a well-known term in chemistry. It is used to express the concentration of a chemical solution. It determines the amount of a substance dissolved in a specific volume of solution.
pH, on the other hand, refers to the power of hydrogen. It measures the concentration of hydrogen ions present in an aqueous solution.
You may notice that both the above concepts have one parameter in common. Yes, you guessed it right i.e., concentration. So what is the link between molarity and pH? How can we calculate the molarity of a solution if its pH is known?
You will find answers to all the intriguing answers in this article. So let’s begin reading!
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.
The number of moles (n) of solute can be determined using equation (i):
Moles (n) = mass/molar mass …………Equation (i)
For instance, 1 molar (M) solution of nitric acid (HNO3) can be prepared as per the following calculations.
The molar mass of HNO3 = 63.01 g/mol.
If we need to prepare 1 M HNO3 solution, then we require mass = moles x molar mass = 1 x 63.01 = 63.01 grams of HNO3 to be dissolved in 1 L or 1000 mL distilled water.
If the number of moles of 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 dissociates to release hydrogen ions (H+) in an aqueous solution. The amount of H+ ions released in the aqueous solution determines the strength of the acid.
The concentration of H+ ions released 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)
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.
Using equation (iv), if the pH of an aqueous solution is known, we can determine its hydrogen ion concentration [H+] in mol/L i.e., the molarity of the solution.
What is the relationship between molarity and pH?
For a strong monoprotic mineral acid that gets completely ionized to release H+ ions in an aqueous solution, molarity = [H+].
So molarity is inversely related to the pH of an acidic solution.
As molarity increases, the concentration of hydrogen ions released in the aqueous solution increases; thus, the pH of the solution decreases and vice versa.
How to find molarity from pH?
As per equation (iv), the pH of a solution can be determined by taking the negative logarithm of [H+] to the base 10.
Equation (iv) can be transformed into equation (v) by taking antilog.
[H+] = 10-pH………. Equation (v)
Hence as per the above equation, the concentration of hydrogen ions or molarity of a solution can be easily determined if its pH is known.
Let’s surf through the following solved examples and learn how we can calculate molarity from pH.
Solved examples for finding molarity from pH
Example # 1: Find the molarity of the HCl solution whose pH is 1.60.
HCl is a strong monoprotic acid i.e.; it ionizes completely to release H+ ions in an aqueous solution. 1 H+ ion is released per HCl molecule.
So we can apply equation (v) to find [H+] as shown below.
[H+] = 10-pH………. Equation (v)
[H+] = 10-1.60 = 0.025 mol/L.
Result: The molarity of the HCl solution having pH 1.60 is 0.025 M.
Example # 2: Your lab notebook says that the pH of a nitric acid solution is 2.49. How can you use this information to determine its molarity?
We can use equation (v) to calculate [H+] in the aqueous solution.
[H+] = 10-pH………. Equation (v)
[H+] = 10-2.49 = 3.24 x 10-3 = 0.00324 mol/L.
As 1 HNO3 molecule completely dissociates to give 1 H+ ion. Thus 0.00324 mol/L H+ ions = molarity of HNO3.
Result: The molarity of the nitric acid solution prepared in the lab is 0.00324 M.
Example # 3: Which out of the two solutions is more concentrated?
a) 50 mL HCl solution having pH 1.25 b) 50 mL HCl solution having pH 1.50.
Explain in terms of molarity.
The pH of both HCl solutions is given in the question statement. So we can determine their molarity using equation v.
[H+] = 10-pH………. Equation (v)
a) [H+] = 10-1.25 = 0.056 mol/L.
b) [H+] = 10-1.50 = 0.032 mol/L.
Result: As per the above calculation, solution a is more concentrated (molarity = 0.056) as compared to solution b (molarity = 0.032).
You may also note that a more concentrated HCl solution has a lower pH, reaffirming what we already discussed in the article that is higher molarity leads to greater acidic strength and, thus, lower pH.
Example # 4: Find the molarity of the H3PO4 solution having pH 2.35.
In this example, the acid given is phosphoric acid (H3PO4) i.e., a triprotic acid. 3 H+ ions are released per H3PO4 molecule on its complete dissociation in an aqueous solution.
The pH of the solution is given in the question statement; we can apply equation (v) to find [H+].
[H+] = 10-pH………. Equation (v)
[H+] = 10-2.35= 0.00447 mol/L.
Now as 1 M H3PO4 = 3 M H+ ions
1 M H+ ions are released from 1/3 M H3PO4
0.00447 M H+ ions are released from (1/3 × 0.00447) = 0.00149 M H3PO4.
Result: The molarity of the H3PO4 solution having pH 2.35 is 0.00149 M.
Example # 5: Acetic acid is a weak acid that only partially dissociates to give H+ ions in an aqueous solution. At the equilibrium point, the pH of the acetic acid solution is determined to be 2.55. If the concentration of CH3COOH is left undissociated at equilibrium = 0.135 M., find its initial molarity.
CH3COOH partially dissociates to give H+ and CH3COO– ions in water.
As per the balanced chemical equation, [H+] equilibrium = [CH3COOH] dissociated
We can use equation (v) to find [H+] at equilibrium as the pH of the solution is given. pH = 2.55.
[H+] = 10-pH………. Equation (v)
[H+] = 10-2.55 = 0.0028 mol/L.
Now [H+]equilibrium = [CH3COOH]dissociated = 0.0028 M
So initial molarity of the acid = [CH3COOH] dissociated + [CH3COOH] undissociated
= 0.0028 + 0.135 = 0.1378 M.
Result: 0.1378 M acetic acid was used initially.
Example # 6: The pH of a strongly acidic HCl solution is 0.35. How many grams of HCl were dissolved in water to prepare 100 mL of the given acidic solution?
The grams of acid dissolved (mass) can be determined using equations (i) and (iii) if we have its molarity.
So the first step is to calculate [H+] i.e., molarity, using equation (v) and the pH given in the question statement.
[H+] = 10-pH………. Equation (v)
[H+] = 10-0.35 = 0.447 mol/L.
Now plug in the above value into equation (iii) to determine the moles of acid used. You may note that the volume (V) of the acidic solution is given i.e., V = 100 mL.
n = (C × V)/1000……………Equation (iii)
∴ (0.447 × 100)/1000 = 0.0447 moles
Finally, we need to substitute the value of n in equation (i) given in the article to determine the required mass. The molar mass of HCl = 36.458 g/mol.
Moles (n) = mass/molar mass…………Equation (i)
Mass = moles (n) x molar mass = 0.0447 x 36.458 = 1.63 grams.
Result: 1.63 grams of HCl were dissolved in 100 mL water to prepare an acidic solution of pH 0.35.
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 pH?
pH stands for the power of hydrogen. It determines the concentration of hydrogen ions present in an aqueous solution.
What is the formula to calculate molarity from pH?
pH is related to the hydrogen ion concentration (in mol/L) or molarity of an acidic solution by the equation given below.
∴ pH = – log10 [H+]
The above equation can be rearranged as [H+] = 10-pH.
Using this formula, if the pH of an acidic solution is known, we can easily find its molarity by taking the antilog of the pH value.
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 released in the aqueous solution, thus the lower its pH, indicating a higher acidic strength.
Does a more concentrated HCl solution possess a higher acidity as well?
Yes.
The molarity of an HCl solution having pH 0.5 is 10-0.5 = 0.32 M.
Contrarily, an HCl solution having pH 0.25 is 10-0.25 molar = 0.56 M.
Thus, a more concentrated solution has a lower pH and consequently a greater acidity and vice versa.
Why is the pH of a 0.1 M CH3COOH solution higher than that of a 0.1 M HCl solution? Although both have the same molarity.
CH3COOH is a weak acid that only partially ionizes in water to yield a limited number of H+ ions.
In contrast, HCl completely ionizes to yield a large number of H+ ions in the aqueous solution.
Therefore, a 0.1 M acetic acid solution is weaker than the hydrochloric acid of the same molarity.
Summary
Molarity is one way of measuring the concentration of an aqueous solution.
Molarity is defined as moles of solute dissolved per litre of solution (unit: mol/L or M).
pH denotes the power of hydrogen. It measures the concentration of H+ ions present in an aqueous solution.
For a monoprotic strong acid, molarity = [H+] as it completely breaks down to release hydrogen ions in an aqueous solution.
If the pH of a solution is known, we can easily determine its molarity using the formula [H+] = 10-pH.
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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