Mole Concept, Molar Mass and Percentage Composition

Dhristi JEE 2022-24

Introduction

Everything that surrounds us is composed of millions and millions of tiny particles, known as atoms. While these are invisible to the naked eye, they are the fundamental building blocks of this universe. Studying these substances and how their composition plays a vital role in our everyday existence is a very important part of applied sciences. 


The mole concept comes into play when we talk about atoms and their properties. 


What is a Mole? 

To introduce the concept of a mole, first, we will talk about the Avogadro's number/constant which is equal to 6.02214076 × 1023


When we talk about the number of moles of a substrate we divide the number of total particles of a molecule/compound/atom by Avogadro’s constant.


Hence, 6.02214076×1023  molecules of an oxygen molecule (O2) will constitute one mole of oxygen & similarly 6.02214076×1023 atoms of carbon will constitute one mole of carbon. In other words, when we say one mole of a substance is present in a sample that means that 6.02214076×1023 number of that specific element is present in the sample. 


Therefore, a mole is a unit just like kilograms or centimetres, which refers to the specific measure of how many atoms or molecules are contained in a substance. 1 mole of one element contains the same quantity of atoms as 1 mole of any other element. However, the mass of 1 mole is different for every element. 


What Do We Understand by Molar Mass? 

The molar mass of an element means the total mass of one mole of that element. Relative molar mass refers to the smallest mass unit of any compound in comparison to one-twelfth one of the mass of one Carbon-12 atom. This means that the number of atoms that are present on 12 grams of one Carbon-12 atom is the same as the number of moles present in one mole of it. 


Using a mass spectrometer, it has been found that the mass of a Carbon-12 atom is 1.992648×10-23 g. In any element, the total number of sub-particles present, such as atoms and molecules, is collectively referred to as one mole.


Atomic mass strictly refers to the mass of one single atom of an element and is expressed in Atomic Mass Units (u). 


One atomic mass unit =1.9944235 × 10-23 g


One molar mass of an element would be the mass of one mole of that element’s atoms.


So numerically, one molar mass = mass of (6.02214076×1023 * Atomic mass of that element).  


What Do We Understand by Molecular Mass? 

This term is used to refer to the mass of a single molecule of any given compound or element. The molecular mass of an element or a compound is calculated by first calculating the number of atoms that are bonding in the molecules and adding that with the respective atomic mass units. 


Molecular mass is denoted by Daltons (Da), where 1 Da is equal to 1 u. 


What is Mole Fraction?

Mole fraction is also a method to express the concentration of a substance in a mixture. Of a solution mixture containing different elements in different quantities, we express the concentration of a specific element(X) by dividing the number of its moles present by the total number of moles that includes the number of moles of other constituents and the moles of (X) included. 


Mole fraction of solute = Moles of Solute/ Moles of (solute + solvent) 


Mole fraction is just a ratio and is hence dimensionless.


Percentage Composition

Another indicator of concentration, percentage composition also depicts the proportion contributed to the total mass of a mixture by its mass. The formula for percentage composition is given by:


Percentage composition = (Mass of the individual component/mass of the mixture) * 100.


Taking Methane as an example, methane’s percentage composition is  74% carbon and 25% hydrogen, though there are more hydrogen atoms. 


What Does Relative Molecular Mass Indicate? 

To understand this, it is first important to know what relative atomic mass refers to. This simply means having a single and uniform atomic mass for elements that may have many different isotopes, such as Carbon. The relative atomic mass of an element can be found out by calculating the average of the weighted isotope mass, as per their frequency. 


Therefore, the relative molecular mass refers to the total relative atomic masses of all the elements that are present in one compound. 


Molarity Meaning

Molarity is a very common indicator of concentration in which we determine the number of moles of a chemical species (solute) that has been dissolved in a liter of solvent. To determine Molarity we first find out the number of moles that are present inside the solution. 


We go about it by dividing the quantity of a substance that has been dissolved in 1 L of solvent and dividing it by the molar mass of that substance which will give us the Molarity.

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FAQs (Frequently Asked Questions)

1. How are molarity and normality related?

When we calculate molarity we use the gram molecular weight of an element or a compound. That is to determine the number of moles present we divide the given mass of substance dissolved by its gram molecular weight. Similarly, in Normality, we divide the given dissolved mass by its equivalent weight which is just its gram molecular weight divided by its valence factor. 


Valence factor refers to the number of electrons it can donate or accept accordingly. In the case of sodium hydroxide (NaOH) the gram equivalent weight and the molecular weight are equal as the valence factor is equal to one.

2. What are colligative properties and give their examples?

Colligative properties are characteristic of substances that are only dependent on the number of particles present and independent of the nature of particles. In other words, the colligative properties of a solution are exhibited by the concentration of solute particles and hence are related to molarity, normality, mole fraction, molality.


Some very common examples are elevation of the boiling point of a solution compared to a pure solvent, decrease in the freezing point of a solution, and finally the increase in the osmotic pressure of a solution with the addition of a solute.

3. Are the number of atoms in a mole the same for all compounds and elements? 

Yes, this is correct. One mole of carbon weighing 12g contains 6.02214076 × 1023 atoms. Oxygen too has an equal number of atoms such as carbon, but it has a higher mass, i.e16g. What this essentially indicates is one mole of element A contains the same number of atoms as one mole of element B. While the number of atoms may be the same, the masses of these two elements may not be the same. This is because the masses of atoms are different irrespective of the number of atoms present in that element. 

4. What is avogadro’s law? 

In the theory of gas laws, Avogadro’s law comes up frequently when moles are discussed. This law describes a relationship between the volume of the gas and the amount of gas that is present. Avogadro’s law states that the same quantities of all gases have the same number of molecules present at the same temperature and same pressure conditions. This law holds somewhat true for real gases at very high temperatures and low-pressure conditions. One of the most common examples where we can see this law in action is blowing up a balloon. 

5. Are there any limitations to avogadro’s law? 

Yes, this law is not absolute and has been refuted by scientists such as Dalton for a number of reasons. Dalton believed that atoms of different kinds cannot be combined. Avogadro’s law applies to ideal gases perfectly, however, it only defines approximate relationships between the number of molecules and temperature and pressure conditions. Real gases do not behave in the same manner as ideal gases do when temperature and pressure conditions are changed. For example, at lower pressures and higher temperatures, Avogadro’s law will not always hold true.  

6. How are gas laws applicable in space?

One of the most practical applications of gas laws is seen in space by astronauts and scientists.  Avogadro’s law, in particular, is used in space. Astronauts need to be aware of how much gas they can fit in their spaceships since they need oxygen in space and their spaceships only have a limited capacity. Boyle’s law is also applicable in space. This helps astronauts determine the exact quantity of pressurised gas that they can fit into a tank or a container so that it does not burst and optimises the given space. 

7. Why is avogadro’s law important? 

Avogadro’s law describes the relationship between the volume of a gas and the amount of the same gas. It describes this relationship to be directly proportional to one another. Temperature and pressure conditions are considered to be at a constant level in this law. This law has a lot of practical implications. Other than the ones mentioned, it is also used in the industrial synthesis of methanol. This is very important for the manufacture of biodiesel, which has emerged as a major source of fuel. 

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