**Expressing Concentration Terms with Formula**

**Concentration Can be Expressed in the Following Ways:**

**(1) Mass percent (w/w or m/m): **It is defined as the number of parts solute present in 100 parts by mass of solution. i.e.

Mass % of a component = __Mass of solute__ × __100__

^{ }Mass of solution

**(2) Molarity (M):** It is defined as the number of moles of solute dissolved per liter of solution. i.e.

Molarity (M) = Number of moles of solute (n)/The volume of solution in litre (V)

**1 M NaOH solution means 1 mole of NaOH is present in 1 L of solution.**

**Molarity equation: **M_{1}V_{1} = M_{2}V_{2 }

(Before dilution) = (After Dilution)

The molarity of a solution decreases in increasing temperature. The molarity of pure water is 55.56 mol L^{-1}.

**(3) Molality (m) = **It is number of moles of solute dissolved per 1000g (1kg) of solvent.

** Molality = **Number of moles of solute/Mass of solvent in kg

Among the above concentration terms, __Molarity depends on temperature because it is related to volume__, which changes with temperature. Whereas __Molality is Independent of Temperature__.

Expressing Concentration Terms with Formula

**(4) Mole Fraction (x):** It is defined as the ratio of the number of moles of a particular component to the total number of moles of solution. i.e.

Mole fraction of a component = Number of moles of the component/Total number of moles of all the components

Let us consider we have two components 1 and 2. Therefore mole fraction of component 1 is x_{1}, and component 2 is x_{2}.

x_{1} + x_{2} = 1 __i.e the sum of the mole fractions of all the components in a solution is always equal to 1__.

Expressing Concentration Terms with Formula

**Numerical Problems **

**Que 1. According to nutritional guidelines from the US Department of Agriculture, the estimated average requirement for dietary potassium is 4.7 g. What is the estimated average requirement of potassium in moles?**

**Ans 1.** We Know

Number of Moles = Given Mass/ Molecular Mass

Number of moles of K = 4.7/39 = 0.12 mol

**Que 2. A litre of air contains 9.2 × 10 ^{-4} mol argon. What is the mass of Ar in a litre of air?**

**Ans 2.**We Know

Number of Moles = Given Mass/ Molecular Mass

9.2 × 10

^{-4}= Mass of Argon (Given Mass) / 40

Mass of Argon (Given Mass) = 9.2 × 10

^{-4}× 40 = 0.037 g

**Que 3. Copper is commonly used to fabricate electrical wire. How many copper atoms are in 5.00 g of copper wire?**

**Ans 3.**We Know

Number of Atoms/Molecules = Number of Moles × Avogadro’s No.

No. of moles of Cu = 5/63.5 = 0.079 mol

Number of Atoms = 0.079 × 6.022 × 10

^{23}

= 4.74 × 10

^{22}atoms of Cu

**Que 4. A packet of an artificial sweetener contains 40.0 mg of saccharin (C**

_{7}H_{5}NO_{3}S). Given that saccharin has a molar mass of 183.18 g/mol, how many saccharin molecules are in a 40.0 mg (0.0400g) sample of saccharin? How many carbon atoms are in the same sample?**Ans 4.**We Know

Number of Atoms/Molecules = Number of Moles × Avogadro’s No.

No of Moles of Saccharin = 0.040/183.18 = 0.000218 mol

Number of Molecules = 0.000218 × 6.022 × 10

^{23}= 0.00131 × 10

^{23}

= 1.3 × 10

^{20}Molecules

The compound’s formula (C

_{7}H

_{5}NO

_{3}S) shows that each molecule contains 7 carbon atoms, so the number of C atoms in the given sample is 7 × 1.3 × 10

^{20}= 9.1 × 10

^{20}atoms.

Expressing Concentration Terms with Formula