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Calculating Molarity

You must be familiar with the sugar solution or solution of table salt in water. What are the difference and similarity in these two solutions? Yes, both solutions have one common component that is water. Do you know what solution is? The homogenous mixture of two components; solute and solvent are called as a solution. Here solute is present in less amount compared to solvent. Hence, in both of these solutions, water is solvent whereas sugar and table salt are solute. It is not necessary that only liquids can be solvent and solid can be solute. There are several examples of solutions in which solutes and solvents are found in different states like gas or solids.

For example; smoke is a solution of smoke particles in the air. Hence smoke particles are solute and air is solvent here. Other examples of solutions are foam, gem stone, butter, whipped cream etc. The concentration of solution can be defined as the amount of solute found in a certain volume of solution. There are several ways to express the concentration of solutions such as normality, molarity, molality, part per million, formality etc. In this article, we will discuss the molarity of the solution. Let's define molarity and learn how to determine the molarity of a solution which contains a certain amount of solute.

Let us consider some problems related to molarity.

Molarity Calculations

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Define Molarity

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In current practice, concentration is mostly expressed as Molarity. Molarity can be defined as the "number of moles of solute per 1 dm3 or 1 liter o a solution". It is denoted by "M".
If n is the number of moles of solute and V is the volume in dm3 or liter, Molarity can be expressed as
Molarity = $\frac{Moles\ of\ solute}{vol\ solution\ in\ liter\ units}$
Use the below widget to calculate molarity

Units of Molarity

Molarity is expressed, as it is defined.
M =$\frac{n\ moles}{v\ in\ dm^3}$ = $\frac{moles}{dm^3}$
So, unit is expressed as mole /dm3.

Concentration and Molarity

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A solution consists of at least two things.
  1. The substance dissolved, which is called a solute.
  2. The liquid in which it is dissolved called a solvent.
There are several methods in which concentration of a solution can be expressed. Some of them are Molarity, Molality and Normality. Molarity is a simple and effective method of expressing the concentration of a solution.

Water is a solvent itself. Since we usually calculate the amount of solute in a solvent, and refer to it as concentration term, we cannot find the molarity of solvent alone. 

Mass of Solute from Molarity

Mass of the solute can be found out from the molarity. The approach is reverse.In various chemical processes in industrial units, the mass of the solute is required to be found out from the molarity of supplied solution. It is also useful to calculate the mass of salts expected from sea water or other such procedures.

For example, Suppose the molarity of a solution of CaCl2 is o.1 M. Find the mass of CaCl2 in 100ml of the solution.

First find the no.of moles from the molarity and volume.

Moles = Molarity x volume in L

= 0.1 X 100/1000

= 0.01 moles

Now moles = Mass in g/molar mass

Mass in g = moles x molar mass

= 0.01 x 111

= 1.11 g

So the mass of CaCl2 in 100ml of the solution is 1.11 g

Uses of Molarity

The term is quite useful in all fields of chemistry. In pharmaceutical industry measuring the concentration in molarity is the backbone of all preparations.Change in molarity can cause aquatic life cease to exist.

Molality and Molarity

Another term, Molality or molal concentration can be used.
Molality of a solution is defined as the number of moles of solute per kilogram of solvent.

Molality = $\frac{Moles\ of\ the\ solute}{Mass\ of\ solvent\ in\ grams}$ = m
The difference between molarity and molality is that solvent is taken in kilograms in molality, while we take the volume of the solvent in molar calculations. Sometimes, it is difficult to calculate the mass of a solvent, say water or ethanol. So, to avoid such discrepancies, Molar concentrations are widely used.

Molar Concentration

Molarity = $\frac{Moles\ of\ the\ solute}{Volume\ in\ liter}$

M = $\frac{n}{v\ in\ dm^3}$

For one mole of solute dissolved in one liter of solution, molarity, M = 1. Such a solution is called as 1 molar solution. A solution containing two moles of solute in one liter is 2M, 2 molar solution, and so on.

Molarity with Avogadro's Number

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Molarity can also be expressed in terms of Avogadro's number.

Avogadro's number is the number of molecules present in one mole of any substance.The number has been determined to be 6.022 x 1023.

So the molarity in terms of no. of molecules is N / 6.022 x 1023 X V.

where N is number of molecules of solute,V is volume of solvent.

Solved Examples

Question 1: Find the molarity of a solution wherein 8.283 x 1023 molecules of the solute are present in 2 liters of solvent.
Molarity =$\frac{ No. of molecules }{(N \times V)}$

=$\frac{8.283 \times 10^23}{6.022 \times 10^23 \times 2}$

= 0.68 M


Question 2: Find the number of molecules in 1.7 M of solution of KOH if the volume of water is 1.43 L.
Molarity = No. of molecules /N X V

1.7 = No. of molecules / 6.022 x 1023 x 1.43

No. of molecules=1.7 X 6.022 x 1023 x 1.43

=14.63 Xx 1023

Molarity from Density

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Some of the problems based on molarity from density is given below.

Solved Example

Question: Find molarity of 11.8 g of NaCl dissolved in 100 g of water.Density of water 1g/ml.
First convert mass of water to volume.

Volume = $\frac{Mass}{density}$


Molarity = $\frac{Moles}{volume}$

Moles =${11.8}{58.4}$ = 0.2

Molarity =${ 0.2}{0.1}$

= 2

Molarity is defined for a specific temperature because increase in temperature increases the volume.


Molarity of HCl

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Some of the problems based on molarity of HCl is given below.

Solved Example

Question: What is the weight of HCl present in 155ml of a 0.540 M solution?
Molarity of HCl = 0.540 M

Calculating the volume 155ml x $\frac{1\ liter}{1000\ ml}$ = 0.155 liters.

Number of moles of HCl = Molarity x Volume in liters

= 0.540 M x 0.155 liters
= 0.0837 moles of HCl.

Since we need to calculate the weight in grams of HCl present, we can convert the moles to grams.
Molar mass of HCl = 36.5 grams/mol.

0.0837 moles of HCl x $\frac{36.5\ grams}{1\ mole\ of\ HCl}$ = 3.06 grams Of HCl.

So, weight in grams of HCl can be calculated from its Molarity value.

Problems on Molarity

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Some of the problems based on molarity is given below.

Solved Example

Question: Find the molarity of 116.8g NaCl dissolved in 1 liter of water.Molar mass of NaCl is 58.4
Step I: Find the number of moles of NaCl in 116.8g

Moles = Mass in g / Molar mass

Moles of NaCl =116.8 / 58.4


Step II:Find molarity

Molarity =$\frac{moles of solute NaCl }{ Volume of solution in L}$

= $\frac{2 }{1}$

Molarity = 2 M


Molarity Calculations

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Some of the problems based on molarity is given below.

Solved Example

Question: A solution of Silver nitrate, AgNO3, contains 1.08 grams in 250 cm3. What is its molarity?
Molar mass of Silver nitrate = 108 g/mole.

n(AgNO3) = 1.08 grams of AgNO3 x $\frac{1\ mole\ of\ AgNO_3}{108\ grams\ AgNO_3}$ = 0.01 mole.

Number of moles in 1 dm3 = 0.01 mole x $\frac{1000}{250}$ = 0.04 moles/dm3

So, Molarity of solution = 0.04M.

Molarity of NaOH

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Some of the problems based on molarity of NaOH is given below.

Solved Example

Question: What is the molarity of a solution prepared by dissolving 75.5 grams of pure NaOH in 540ml of a solution?
Molecular weight of Sodium Hydroxide, NaOH = 40 grams/mol

We know that

Molarity =

$\frac{number\ of\ moles}{decimeter\ cube\ of\ the\ solution\ or\ number\ of\ moles\ per\ liter}$

we need two things here

1. Moles of NaOH and
2. Volume in liters.

Calculating the moles

75.5 grams of NaOH x $\frac{1\ mole}{40\ grams\ of\ NaOH}$ = 1.885 moles

Calculating the volume: 540ml x $\frac{1\ liter}{1000\ ml}$ = 0.540 liters.

Molarity of NaOH = n/v = $\frac{1.885\ moles}{0.540\ liters}$ = 3.49 moles/Liters or 3. 5M

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