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# Molar Concentration

Are mixtures and compounds the same?

A mixture is formed when various elements or compounds just mix together without any chemical reaction taking place. Unlike a compound, a mixture has a variable composition with its constituents showing their individual properties. When salt is added to a beaker of water, salt readily dissolves in water without any chemical reaction taking place. Here, salt is a compound with the elements sodium and chlorine and water is another compound comprising the elements hydrogen and oxygen. Thus, we can say that all matter can be divided into elements, compounds and mixtures.

The natures of components that combine to create a mixture determine the group that a mixture can be classified into. Mixtures can be either homogeneous or heterogeneous. A mixture of uniform or evenly distributed constituents is called a homogeneous mixture. The solution can be defined as a homogeneous mixture which is composed of two parts: solute and a solvent. A solute is usually the substance of lesser quantity that dissolves in the substance of greater quantity. For example, in a salt solution salt in the solute and the water is solvent. Here solvent is a substance of greater quantity that dissolves the solute in it. The concentration of solute in the solvent can be expressed in terms of molar concentration.

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## Molar Concentration Definition

The concentration of the solution is usually expressed in terms of its molar concentration. Molar concentration of a solution is defined as "the ratio of amount in moles of the solute to the volume of the solution." Molar concentration is expressed as "c". The symbol [c] is read as "the concentration of". So molar concentration is expressed as [c]. More precisely the molar concentration is expressed as [cm].

## Molar Concentration Formula

The molar concentration (molarity) of a chemical species is symbolized by enclosing the formula of this species within brackets. For example, [H+] refers to molar concentration of hydrogen ions, [Br-] refers to the molar concentration of bromide ion, [NH3] refers to the molar concentration of ammonia. By definition, the molar concentration(c) of a solution is equal to the amount in moles of solute(n) divided by the volume of the solution(V).
Molar concentration equation is expressed as below.

$Molar\ concentration (c) = \frac{Amount\ in\ moles\ of\ solute}{Volume\ of\ the\ solution}$

$c = \frac{n}{V}$

## Molar Concentration Units

The concentration in moles per dm3 can be used to determine the number of moles present in any (other) volume of solution, V cm3.

$Number\ of\ moles\ in\ volume\ V (cm^{3}) = \frac{V\ cm^{3}}{1000\ cm^{3}} \times concentration\ in\ mol\ dm^{-1}$

Molar concentration unit is moles per cubic decimeter (mol dm-1). Concentration refers to the volume of the solution and not the volume of the solvent.

Molar Concentration of Ions

Ionic molar concentration is a measure of the actual number of ions in solution. In contrast, ionic activity is a measure of the effective concentration of electrolytes that results from the charge interaction on dissociated species. The difference between ionic concentration and ionic activity is important because the molar concentration of any electrolyte will not affect the molar concentration of any other electrolyte, but ionic activities are mutually interactive.

Molar concentration of ions is explained by the below solved example.

## Molar Concentration of Water

The molar concentration of pure water [H2O] is quite large compared to any possible concentrations of solutes and can be considered as constant. The molar concentration value is 55.5M, which is obtained by division of number of grams of water in 1L. 1000g, by the molecular weight of water, 18g/mol.
Therefore,
Ka = $\frac{[H^{+}][OH^{-}}{55.5}$

Ka $\times$ 55.5 = [H]+[OH]- = Kw

## Molar Concentration of Proteins

Nucleic acids which are present in biological material absorb UV radiation strongly with a profile overlapping that of protein, but with a maximum at 260nm. In measuring the concentration of proteins by their UV-absorbance, remember that the absorbtion coeffiecient is given by the equation
A = amcl
Where,
A = Absorbance
am = molar extinction coefficient
c = molar concentration of protein in given solution
l = length of the light path

## Molar Concentration Conversion

The conversion between units of tracer concentration requires knowledge of tracer and air or their molecular masses. Concentration of a gas is expressed in several ways.
1. Mass concentration
2. Molar concentration
3. Volume concentration
Mass concentration is expressed as Cm = $\frac{m_{x}}{\sum m_{i}}$
Molar concentration is expressed as CM = $\frac{n_{x}}{\sum n_{i}}$
Volume concentration is expressed as CV = $\frac{V_{x}}{V}$

The relations between mass concentration Cm, molar concentration CM, and volume concentration Cv are

Cm = $\frac{m_{x}}{\sum m_{i}}$ = $\frac{M_{x}}{M}$ CM = $\frac{M_{x}}{M}$ CV

## Molar Concentration Problems

Solved problems are given below to calculate molar concentration. Finding molar concentration requires the amount of solute in moles per unit volume of the solution.

### Solved Example

Question: What is the total molar concentration of ions in a 0.350M solution of the strong electrolyte Na2SO4 assuming complete dissociation?
Solution:

First it is must to know how many ions are produced by dissociation of Na2SO4. Writing the equation for dissolving Na2SO4 shows that 3 moles of ions are formed -2moles of Na2+ and 1 mole of SO42-.

Na2SO4 $\overset{H_{2}O}{\rightarrow}$ 2Na+ + SO42-

The total molar concentration of ions is three times the molarity of Na2SO4 or 1.05M

$\frac{0.350\ mol\ Na_{2}SO_{4}}{1L} \times \frac{3\ mol\ ions}{1\ mol\ Na_{2}SO_{4}}$ = 1.05M

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