Problems Based on Mole Concepts

Indian philosopher Maharishi kanad postulated that if a matter is divided into further smaller pieces, it will have smaller parts. However, there shall come a point when the matter no longer can be divided further and that smallest part is called Parmanu. By the end of the 18th century, scientists realized that there are elements and molecules and the combination of elements form a molecule. Let’s learn in detail about atoms and molecules,

What are Atoms?

The most basic or the building blocks of matter are atoms. Atoms are extremely small, when millions of atoms are combined together, a very small piece of matter is obtained. The radius of the atom is measured in a nanometer. The name of the atoms and elements are now given by IUPAC (International union of pure and applied chemistry). Mostly, the symbol of the name of atoms is the first letter in the capital, if there are 2 letters used, the other letter is a small letter. For instance, the Oxygen atom is denoted as O, aluminum is denoted as Al, and so on.

What is Atomic Mass?

Dalton gave the concept of atomic mass. According to dalton, each element has a certain mass known as atomic mass. Since the law of constant proportions could be explained because of the introduction of atomic mass, scientists decided to determine the mass. The absolute mass of an atom is hard to find and therefore, the relative mass of an atom is introduced. The unit for atomic mass is “u”, earlier it was “amu”. Therefore, atomic mass can be defined as the average mass of atoms of any element which is measured in the atomic mass unit (amu). Since atomic mass tells the size of an atom, it is the mass of the nucleus (protons and neutrons).

Molecular Mass and Concept of Mole

The concept of atomic mass has been discussed in the previous section. This concept can also be extended to molecules. The molecular mass of a substance is the sum of the atomic masses of all the individual atoms present inside the molecule. To understand the concept behind the term “Mole”. Let’s consider a chemical reaction through the equation mentioned below.  

2H₂ + O₂ ⇒ H₂O

The above reaction indicates: 

1. Two molecules of hydrogen combine with one molecule of oxygen.
2. 4u of Hydrogen combines with 32u of oxygen to produce 36u of water.

It can be inferred that the quantity of the substance can be characterized by the mass or the number of molecules. It can be seen in the chemical reaction, it is more convenient to represent them in the form of the number of atoms and molecules. “Mole” was the unit that was introduced for this job. 

The number of particles present in 1 mole of any substance is fixed with a value of 6.022 × 10²³. This number is called avogadro number. The mass of 1 mole of a substance is equal to it’s molecular mass in grams. 

Sample Problems 

Question 1: Find the molecular mass of the H₂O. 

Answer: 

It is known that, the molecular mass of a substance is the sum of the atomic masses of all the individual atoms present inside the molecule.

Molecular Mass of H = 1u 

Molecular Mass of O = 16u 

Molecular Mass of H₂O = 2(Molecular Mass of H) + Molecular Mass of O 

⇒ Molecular Mass of H₂O = 2(1) + (16) 

⇒ Molecular Mass of H₂O = 18u

Question 2: Find the molecular mass of the H₂SO₄. 

Answer: 

It is known that, the molecular mass of a substance is the sum of the atomic masses of all the individual atoms present inside the molecule.

Molecular Mass of H = 1u 

Molecular Mass of O = 16u 

Molecular Mass of S = 32u

Molecular Mass of H₂SO₄ = 2(Molecular Mass of H) + Molecular Mass of S + 4(Molecular Mass of O)

⇒ Molecular Mass of H₂SO₄ = 2(1) + (32) + 4(16) 

⇒ Molecular Mass of H₂SO₄ = 2 + 32 + 64

⇒ Molecular Mass of H₂SO₄ = 98u

Question 3: Calculate the mass of 0.5 moles of the H₂O₂. 

Answer: 

It is known that, the molecular mass of a substance is the sum of the atomic masses of all the individual atoms present inside the molecule.

Molecular Mass of H = 1u 

Molecular Mass of O = 16u 

Molecular Mass of H₂O₂ = 2(Molecular Mass of H) + 2(Molecular Mass of O)

⇒ Molecular Mass of H₂O₂ = 2(1) + 2(16) 

⇒ Molecular Mass of H₂O₂ = 34u 

So, the mass of 1 mole of H₂O₂ is 34g. 

Thus, 0.5 mole of H₂O₂ will be 17g. 

Question 4: Calculate the mass of 2 moles of N₂. 

Answer: 

It is known that, 

Molecular Mass of N = 14u 

Thus, molar mass of N₂ will be 28g. 

Mass of 2 moles N₂ = 2 × 28 

Mass of 2 moles N₂ is 56g. 

Question 5: Calculate the mass of 0.5 moles of the HSO₄. 

Answer: 

It is known that, the molecular mass of a substance is the sum of the atomic masses of all the individual atoms present inside the molecule.

Molecular Mass of H = 1u 

Molecular Mass of O = 16u 

Molecular Mass of S = 32u

Molecular Mass of HSO₄ = Molecular Mass of H + Molecular Mass of S  + 4(Molecular Mass of O)

⇒ Molecular Mass of HSO₄ = 1 + (32) + 4(16) 

⇒ Molecular Mass of HSO₄ = 1 + 32 + 64

⇒ Molecular Mass of HSO₄ = 97u

So, the mass of 1 mole of HSO₄ is 97g. 

Thus, 0.5 mole of HSO₄ will be 48.5g. 

Question 6: Find the number of atoms in 8g of O₂. 

Answer: 

It is known that, 

Molecular Mass of O = 16u 

Thus, molar mass of O will be 16g. 

Number of moles = Given Mass/Molar Mass 

= (8)(32) 

= 1/4 

= 0.25 moles 

Number of Atoms in 0.25 moles = 0.25 × 6.022 × 10²³

⇒ Number of Atoms in 0.25 moles = 1.5 × 10²³

Question 7: Find the number of atoms in 46g of Na. 

Answer: 

It is known that, 

Molecular Mass of Na = 23u 

Thus, molar mass of O will be 23g. 

Number of moles = Given Mass / Molar Mass 

= (46)(23)

= 2 moles 

Number of Atoms in 2 moles = 2 × 6.022 × 10²³

⇒ Number of Atoms in 0.25 moles = 12.044 × 10²³ atoms. 

Question 8: What is the molecular mass of C₂H₅OH. Explain while breaking down the molecule into atoms.

Solution:

As it is clear that there are three different types of atoms involved in the molecule C₂H₅OH. They are carbon, hydrogen, and oxygen.

Molecular mass of C = 12u

The molecular mass of O = 16u

The molecular mass of H = 1u

2 atoms of C = 12 × 2 = 24u

6 atoms of H = 1 × 6 = 6u

1 atom of O = 16 × 1 = 16u

Molecular mass of C₂H₅OH = 24 + 6 + 16 = 46u

Question 9: What is the difference between O₂ and 2O?

Answer:

The difference between O₂ and 2O is that the former is a molecule consisting of 2 atoms of oxygen while the latter is not a molecule, they are two separate oxygen atoms. O₂ is a stable molecule and is present in the air, on the other hand, 2O is unstable and is ready to combine with other atoms like hydrogen.

Question 10: In water, the ratio of hydrogen to oxygen by mass is given as 1:8. Find out the mass of oxygen required for 5g of hydrogen?

Solution:

The ratio of H:O by mass = 1:8

Now, equating the actual masses with the ratios,

1/8 = 5/y

Here, y is the unknown mass of oxygen.

1 × y = 8 × 5

y = 40g

Therefore, 40g of oxygen is required for 5g of hydrogen.