# 0.2 Molar concentration

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The idea of mole concept is simple. It neatly relates various reactants and products in the ratio of whole numbers. There is, however, one hitch in applying this concept. The reactants or products may not necessarily be participating in its pure form. Consider the reaction :

$Mg+2HCl\to MgC{l}_{2}+{H}_{2}$

Here, magnesium is used in its pure solid form. The hydrogen gas is evolved in pure gaseous form. On the other hand, Hydrochloric acid is used as a solution of a specific concentration in water.

Thus, magnesium and hydrogen exist in pure form. We can find moles of solid magnesium by using its molecular weight. Similarly, we can determine moles of pure hydrogen gas using Avogadro’s hypothesis. In the case of hydrochloric acid, however, the acid in the form of solute participates in reaction – not the solvent i.e. water. Clearly, we need to find a way to connect the concentration of HCl to mass or moles. In this module, we shall exactly do the same by defining different concentration terms of the solution and its relation with mass or moles of the solute as involved in the reaction.

Solution
A solution is a homogeneous mixture of two or more components. The substance present in smaller proportions is called solute and the substance in larger proportion is called the solvent.

Solution comprises of solute and solvent. In expressing concentration of solution, we make use of the fact that mass is conserved,

$\text{Mass of solution}\left({W}_{S}\right)=\text{Mass of solute}\left({W}_{B}\right)+\text{Mass of solvent}\left({W}_{A}\right)$

The concentration, however, need not be necessarily expressed in terms of mass (w). We may choose volume (v) also depending upon measuring convenience. Sometime, we may express concentration as combination of mass (w) and volume (v).

Concentration of a solution is basically measurement of solute (B) with respect to solution(S) or solvent(A). With the only exception of molality, concentration is expressed as a comparison of the quantity of solute (B) to that of solution (A+B). In the case of molality, it is comparison of solute (B) to that of solvent (A). Further, this comparative ratio is either a number or percentage (%).

There are large numbers of concentration measuring terms. They are basically classified under following three categories :

• Measurement based on mass/volume : mass percentage (w/w), volume percentage (v/v), strength of solution (w/v)
• Measurement based on molecular weight (moles) : molarity (M), molality (m)
• Measurement based on equivalent weight (gram - equivalents) : normality (N)

## Mass percentage (w/w)

The mass percentage is expressed as :

$\text{Mass percentage}\left(x\right)=\frac{\text{Mass of solute}\left(B\right)}{\text{Mass of solution}\left(A+B\right)}X100$

$⇒\text{Mass percentage}\left(x\right)=\frac{{W}_{B}}{{W}_{S}}X100=\frac{{W}_{B}}{{W}_{A}+{W}_{B}}X100$

If we measure mass in grams, we can rewrite the expression :

$⇒\text{Mass percentage}\left(x\right)=\frac{{g}_{B}}{{g}_{S}}X100=\frac{{g}_{B}}{{g}_{A}+{g}_{B}}X100$

Sometimes, we may opt to express concentration simply as fraction. In this case, we are not required to multiply ratio by 100,

$\text{Mass fraction}=\frac{{W}_{B}}{{W}_{A}+{W}_{B}}=\frac{{g}_{B}}{{g}_{A}+{g}_{B}}$

Problem : One litre of oxalic acid of density 1.08 gm/cc contains 3.24 gm of oxalic acid. Find its mass percentage.

Solution : The mass of solute (oxalic acid) is given. We need to find the mass of the solution to determine mass percentage.

${g}_{S}={V}_{S}X{\rho }_{S}=1000X1.08=1080\phantom{\rule{1em}{0ex}}gm$

$⇒\text{Mass percentage}\left(x\right)=\frac{{g}_{B}}{{g}_{A}+{g}_{B}}X100=\frac{3.28}{1008}X100=0.3$

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