# Methods for expressing concentration

Learning Objectives

At the end of this lecture, the student will be able to

• List the methods for expressing concentrations in volumetric analysis

• Different methods for expressing concentrations in volumetric analysis

• Define Normality and molarity

• Discuss about the preparation of different concentrations of solution in terms of normality and molarity

## Methods for expressing concentration

Introduction:

A solution is a mixture of a solute and a solvent

A solvent: is a substance that dissolves other materials

A solute:  is the substance that dissolves in the solvent

A concentrated solution contains a large amount of solute per litre of solution e.g. strong coffee

A dilute solution contains a small amount of solute per litre of solution e.g. weak coffee

The concentration of a solution is the amount of solute that is dissolved in a given volume of solution

There are several ways of expressing the concentration of a solution:

1) Percentage of solute – 3 forms

2) Parts per million (ppm)

3) Moles of solute per litre of solution (MOLARITY)

4) Gram equivalent of solute per litre of solution (NORMALITY)

5) Moles of solute per kg of solution (MOLALITY)

### 1. Percentage of Solute

This method of expressing concentration is usually used in many household solutions and in medicine

There are 3 ways in which the percentage of solute in a solution is expressed:

a) Percentage weight per weight (w/w)

b) Percentage weight per volume (w/v)

c) Percentage volume per volume (v/v)

#### a)  Percentage weight per weight (w/w):

This is the number of grams of solute per 100g of solution e.g.

10% w/w NaCl → 10g of sodium chloride per 100g of solution

2% w/w salicylic acid ointment → 2g of salicylic acid per 100g of ointment

#### b)  Percentage weight per volume (w/v):

This is the number of grams of solute per 100cm3 of solution e.g.

10% w/v NaCl → 10g of sodium chloride per 100cm3 of solution

5% w/v NaCl → 5g of NaCl in 100cm3 of solution

*Note: usually the units are grams per litre (g/L) therefore you would have to bring it to a litre*

#### c)   Percentage volume per volume (v/v):

This is the number of cm3 of solute per 100cm3 of solution e.g.

5% v/v ethanoic acid solution → 5cm3 of ethanoic acid per 100cm3 of ethanoic acid

13% v/v ethanol    solution → 13cm3 of ethanol (alcohol) per 100cm3 of ethanol

### 2. Parts Per Million (ppm)

This method of expressing the concentration of a solution is only used for very dilute solutions i.e. when dealing with very low concentrations of substances.

• This is the number of milligrams per litre (mgL-1)

*Note:  1 Litre of water has a mass of 1 million milligrams*

• So, can say 1mg/L   = 1 mg per million mg

= 1 ppm

• Example: the concentration of chlorine in water is 2 ppm this means there are 2 mg of chlorine per litre of water

### 3) Moles of Solute per Litre of Solution (MOLARITY)

Remember:

One mole of a substance is the amount of that substance which contains 6 x 1023 particles (atoms, ions, molecules) of that substance

Mass of 1 mole of an element = Relative Atomic Mass in grams

e.g.

1 mole of Na = 23 g

1 mole of Mg = 24g

1 mole of hydrogen=1g

The most important way of expressing the concentration of a solution is in terms of moles per litre of solution (molarity)

Definitions:

• The Molarity of a solution is the number of moles of solute per litre of solution

• A 1 molar solution is a solution which contains one mole of solute per litre of solution (1 M)

also,

– A solution which contains 5 moles of solute in a litre of solution is said to be 5 molar (5M)

– A solution which contains 0.5 moles of solute in a litre of solution is said to be 0.5 molar (0.5M)

• Symbols Used:

– M

– mol/L or mol L-1

Remember:

Mass of Substance per litre

No. of Moles of Substance (Molarity)    =  ——————————————                                                                                                                      Molar Mass/Molecular weight

Concentration
Examples:

-1 mol/L NaOH = 40g NaOH (Mr NaOH = 40) per litre of solution

– 2mol/L NaOH = 80g NaOH per litre of solution

– 0.5mol/L NaOH = 20g NaOH per litre of solution

– 0.1 M (decimolar) NaOH = 4g NaOH per litre of solution

Complete the following:

1M Sulphuric acid = ________________________

0.5M Potassium hydroxide = ________________________

3M Nitric acid = ________________________

5M Sodium thiosulphate = ________________________

### 4) Gram Equivalent of Solute per Litre of Solution (NORMALITY)

The most important way of expressing the concentration of a solution is in terms of gram equivalent per litre of solution (Normality)

Definitions:

• The Normality of a solution is the number of gram equivalent weight of solute per litre of solution

•A 1 Normal solution is a solution which contains one gram equivalent weight of solute per litre of solution (1 N)

also,

– A solution that contains 5 gram equivalent weight of solute in a litre of solution is said to be 5 Normal (5N)

A solution which contains 0.5 gram equivalent weight of solute in a litre of solution is said to be 0.5 normal (0.5N)

• Symbols Used:

– N

Gram equivalent/L

Remember:

Gram equivalent weight of Substance per litre

No. of gram equivalent weight of a Substance (Normality) = ————————————————

Equivalent weight

Concentration
Examples:

-1 N/L NaOH = 40g NaOH (Mr NaOH = 40) per litre of solution

– 2 N/L NaOH = 80g NaOH per litre of solution

– 0.5 N/L NaOH = 20g NaOH per litre of solution

– 0.1N (decimolar) NaOH = 4g NaOH per litre of solution

Complete the following:

1N Sulphuric acid =

0.5N Potassium hydroxide =

3N Nitric acid =

5 N Sodium thiosulphate=

### 5) Moles of solute per kg of solution (MOLALITY)

Molality is defined as the “total moles of a solute contained in a kilogram of a solvent.”

Molality is also known as molal concentration.

It is a measure of solute concentration in a solution.

The standard unit of molality is moles per kilogram (mol kg−1). It also an SI unit. mol kg−1 is also called molal. In other words, 1 molal = 1 mol kg−1.

• Symbols Used:

m            =             molality

mol        =             moles of solute

kg           =             kilogram of solvent

Moles of solute

m = ————————–

Kilogram of solvent

## Difference between Molarity and Molality

 Molarity Molality The molarity of a given solution is defined as the total number of moles of solute per litre of solution. Molality is defined as the total moles of a solute contained in a kilogram of a solvent. Mathematical expression is M = number of moles of the solute /Volume of solution given in terms of litres. The mathematical expression is m = Numbers of moles of solute/Mass of solvent in kgs m = (g ✕ 1000)/(W ✕ m). Depends on the volume of the whole solution. Depends on the mass of the solvent. Unit sign expressed as (M). Unit sign expressed as (m). Molarity has a unit of moles/litre. Molality has units of moles/kg.

Summary:

• Concentrations are expressed in terms of different methods: Percentage of solute – 3 forms, Parts per million (ppm), Normality, Molarity

• Molarity: No of gram moles of solute per litre of solvent

• Normality: No of gram equivalent of solute per litre of solvent

• Molality : Moles of solute per kg of solution

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