Question

\[{C_2}{H_6}(g) + 3.5{O_2}(g) \to 2C{O_2}(g) + 3{H_2}O(l)\]
Given that moles of ethane are \[0.1\]and complete the combustion of \[3g\] Ethane gives \[x \times {10^{22}}\]molecules of water. The value of \[x\] is: (Round off to the nearest integer).
[Use: \[{N_A} = 6.023 \times {10^{23}}\], Atomic masses in u: \[C:12,O = 16,H = 1\]]

Answer 1

Hint: A mole is an amount of matter, not weight, which is the force of mass, but only the amount of entities within a substance. There is always the same number of entities in a mole of any substance.

Complete Step by Step Solution:
1. Mole: It is a unit of measurement for the amount of substance. The amount of a chemical substance that contains as many elementary entities as atoms, molecules, ions, electrons, or photons. One mole contains exactly \[6.02214076 \times {10^{23}}\]elementary entities which are also known as Avogadro’s number.
2. The SI unit of a mole is mol which is the amount of substance.
3. The mass of one mole of a substance in grams is called the molar mass.
4. It is used to identify the particle size of the atoms or molecules.
5. Given: 0.1 mol of Ethane and combustion of 3g Ethane
6. According to stoichiometry, 1 molecule of Ethane produces 3 moles of water.
7. The total number of moles of water molecules is:\[0.1 \times 3 = 0.3\].
8. The total number of water molecules is:
\[Number\,of\,molecules = moles \times Avogadro's\,number\]
\[Number\,of\,water\,molecules = 0.3 \times 6.022 \times {10^{23}}\]
\[Number\,of\,water\,molecules = 18.066 \times {10^{22}}\]
The value of x is 18.
Additional information:
1. The mole is also defined in terms of volume, mass, and particles.
2. There are various formulas to calculate the number of moles:
\[Number\,of\,moles\,of\,molecules = \dfrac{{weight\,in\,gms}}{{molecular\,mass}}\]
\[Number\,of\,moles\,of\,atoms = \dfrac{{weight\,in\,gms}}{{atomic\,mass}}\]
\[Number\,of\,moles\,of\,gases = \dfrac{{Volume\,at\,STP}}{{Molar\,volume\,}}(Molar\,volume\,at\,STP = 22.4lit)\]
\[Number\,of\,moles\,of\,particles = \dfrac{{Number\,of\,particles}}{{Avogadro\,number}}\]

Note: An atom's mole of an element is equal to the Avogadro's number, and a molecule of an element is equal to the number of atoms times the Avogadro's number.