# Units of Concentration

## Units of Concentration

### Introduction

In this article you will learn different ways of expressing solute concentration that are commonly used. You will learn how to calculate concentration of solution expressed in Molality, Normality, Weight %, Parts per million (ppm), Mass per volume, Molality and mole fraction of a solution.

This article will provide you with knowledge which will help you to be able to solve any numerical questions in the units of concentration topic. Each unit of concentration has its numerical examples to help you able to understand numerical calculations of it.

Some numerical questions relating to units of concentration are given together with their densities and this makes some students to be unable to solve them successfully. However, by the end of this article, you will be able to solve every question relating to units of concentration.

Some questions which have been used as examples in this article, have been solved in different approaches to help you understand the concept. Units of concentration, is one of the topic which a lot of chemistry students find it difficult to understand and apply in solving different numerical questions and this makes them unable to get excellent grades.

This article is organized in different sections. The first part involves introducing you different ways of expressing concentration and the second part involves analysing each unit and solving several numerical questions to make you understand the concepts. An assessment is provided at the end of the course to test your understanding after completing this article.

Units of Concentration

The concentration of a solution is a measure of the amount of solute that is dissolved in a given quantity of solvent. There are a number of different ways of expressing solute concentration that are commonly used. Some of these are listed below.

## Different Ways of Expressing Solute Concentration

- Molarity, M = moles solute/liter of solution
- Normality, N = equivalents of solute/liter of solution
- Weight %, Wt % = (mass of solute/mass of solution) x 100%
- Parts per million, ppm = (mass of solute/mass of solution) x 10^6
- Mass per volume, mg/L = mass of solute/liter of solution
- Molality, m = moles of solute/mass of solvent
- Mole fraction, χ = moles of solute/total moles

Concentrations expressed as ppm and N are less familiar to most students at this stage. Be careful not to confuse molality and Molarity. Molality is represented by a small "m" whereas Molarity is represented by upper case "M". Molality (m) is also known as "molal concentration" while Molarity is also known as "molar concentration".

## Relationship Between Molality And Molarity

- Mass = Normality x volume x (RMM/ Integer)
- Normality = (mass x Integer) /(RMM x volume)
- Normality = Molarity x number of integers

Based on a simple subject of the formula above, we see that Normality is equal to Molarity multiplying it by the number of integers. Similarly, Molarity relates to Normality in that, we can divide Normality with the number of integers to get Molarity of a solution.

## Numerical Examples

### 1. Molality

Molality is defined as the number of moles of solute dissolved in one Kilogram of solvent. As it is clear Molality involve moles. Key point to take note is that one liter of water weighs 1000 grams when density of a solution is not given, we assume that (density of water = 1.0 g/mL and 1000 mL of water is equal to one liter of water). 1000g is 1.00 kg. Numerical examples;

### Numerical examples

1. Determine the molality (m) of a solution containing 42grams of glycerin, C_{3}H_{5} (OH)_{3} in 750 grams of water?**Solution**

2. How many grams of AgNO_{3} are needed to prepare a 0.125m solution in 250grams of water?

**Solution**

3. Calculate the molality of 20% w/w aqueous solution of H_{2}SO_{4} (Relative atomic mass are: H=1amu, S=32amu, O=16 amu).

**Solution**

4. what mass of glucose (C_{6}H_{12}O_{6}) is required to prepare 0.5m aqueous solution containing 200g of water (H_{2}O) (atomic masses are ; C=12amu , H = 1 , O = 16amu)

**Solution**

### 2. Molarity

This is number of moles of solute dissolved in liter of solution.

### Numerical examples

1. What mass of KCl is required to prepare a 100000cm^{3} of aqueous solution of 0.5M KCl . ( k =39.1g mol^{−1})

**Solution**

2. What is the molarity of 600. mL of potassium iodide solution that contains 5.50 moles of the solute?

**Solution**

M = mol solute / L soln.

M = 5.50 mol / .600 L

**M = 9.16 molar**

3. Household laundry bleach is a dilute aqueous solution of sodium hypochlorite (NaClO). How many moles of solute are present in 1.5L of 0.70M NaClO?

**Solution**

M= mol/L

0.7 = x/1.5

**x= 1.05 mol_NaClO**

4. What mass of _{K3}PO_{4} is required to prepare 400mL solution that contains 6 x 10^{21} K_{3}PO_{4} particles per liter of solution? ( atomic masses are K=39amu, P=31amu O=16amu)

**Solution**

5. When 25.0 mL of NaOH solution was titrated, 23.4 mL of 0.286 M H_{2}SO_{4} were required to reach the end point.

a) Find the molarity of the NaOH.

b) find concentration in parts per million of sodium (Na^{+} )

**Solution**

### 3. Normality

This is the number of mole equivalents per liter of solution.

### Numerical examples

1. Suppose you dissolved 104 g Al(OH)_{3} in 2000ml of solution, what would be the normality of the solution? (Relative atomic masses Al=27amu , H=1amu , O=16amu).

**Solution**

The problem can be solved using two methods

**First approach**

**Second Approach**

Normality = (mass x Integer) /(RMM x volume)

Normality = (104 x 3) /(78 x 2)

**Normality = 2N**

### 3. Mole Fraction

### Numerical examples

1. A solution is prepared by mixing 25g of water, H_{2}O and 25g of ethanol C_{2}H_{5}OH. Determine the mole fraction of each substance?

**Solution**

**OR**

We know sum of mole fraction equal to 1. So mole fraction of C_{2}H_{5}OH can be found by subtraction mole fraction of water from 1.

That is **Mole fraction of C _{2}H_{5}OH= 1 – mole fraction of H_{2}O**

Mole fraction of C_{2}H_{5}OH= 1 − 0.71875

**Mole fraction of C _{2}H_{5}OH=0.28125**

2. 0.100mole of sodium chloride [ NaCl] is dissolved into 100 grams of pure water H_{2}O. What is the mole fraction of sodium chloride [ NaCl]?

**Solution**

3. How many grams of water must be used to dissolve 100grams of sucrose (C_{12}H_{22}O_{11}) to prepare a 0.020 mole fraction of sucrose in the solution?

**Solution**

4. The molality of an aqueous solution of sugar (C_{12}H_{22}O_{11}) is 1.62m. calculate the mole fraction of sugar and water.

**Solution**

**OR**

Mole fraction of H_{2}O + Mole fraction of C_{12}H_{22}O_{11}= 1

0.971666213 + Mole fraction of C_{12}H_{22}O_{11} = 1

Mole fraction of _{C12}H_{22}O_{11} = 1 − 0.971666213

**Mole fraction of C _{12}H_{22}O_{11} = 0.028333787**

### 5. Parts Per Million (ppm)

Parts per million (ppm) is the number of units of mass of a contaminant per million units of total mass. The number of milligrams of solute per kg of solution = one ppm.

### Numerical examples

1. What weight of silver nitrate (AgNO_{3}) is required to prepare:

(i) 400 mL of 0.2M solution

(ii) 600 mL 0.2 parts per million Ag^{+}?

**Solution**

2. What is the concentration in parts per million of sulfur atoms if 120g of H_{2}O is mixed with 5g of sulfur?

**Solution**

3. A sample of NaCl was analyzed and found to contain concentration of 0.05%. What is the concentration of Nacl in parts per million?

**Solution**

4. 8g of Al_{2}(SO_{4})_{3} is dissolved in 180 ml of water. Calculate the concentration of Al^{+3} in ppm.

**Solution**

### Mass percentage

### Numerical examples

1. How many grams of water is needed to make a 10% of salt solution of NaCl if 20g of NaCl is to be completely dissolved?

**Solution**

2. What mass of H_{2}SO_{4} is contained in 25g of 15% w/w solution? (Relative atomic mass are H=1amu , S=32amu, O=16amu)

**Solution**