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Question: Calculate the mass of 1 oxygen atom and oxygen molecules in kg (O=16)....

Calculate the mass of 1 oxygen atom and oxygen molecules in kg (O=16).

Explanation

Solution

Hint- In order to calculate the mass of one atom and one molecule of oxygen in kg first we will use the atomic mass of oxygen given in periodic table and we will use the same to find the molecular mass of oxygen. As we know that atomic mass and molecular mass is given for one mole of atoms or molecules so by dividing the mass by Avagadro’s number we will find the mass of one atom and one molecule.

Complete answer:
Formula used- Mass of one atom=Atomic massAvagadro number,Mass of one molecule=Molecular massAvagadro number{\text{Mass of one atom}} = \dfrac{{{\text{Atomic mass}}}}{{{\text{Avagadro number}}}},{\text{Mass of one molecule}} = \dfrac{{{\text{Molecular mass}}}}{{{\text{Avagadro number}}}}
Atomic weight of one oxygen atom = 16amu
Mass of 1 mole of oxygen atoms = 1 × atomic weight of one oxygen
=16 gm
A molecule of oxygen is given as O2{O_2} , here 2 oxygen atoms are present in a single molecule of oxygen.
So, molecular mass of a oxygen is =2×16=32g = 2 \times 16 = 32g
As we know that atomic mass and molecular mass is given for one mole of atoms or molecules, so by dividing the mass by Avagadro’s number we will find the mass of one atom and one molecule.
Mass of one atom of oxygen is:
=Atomic massAvagadro number =16g6.022×1023 =166.022×10−23g =2.6561×10−23g  = \dfrac{{{\text{Atomic mass}}}}{{{\text{Avagadro number}}}} \\\ = \dfrac{{16g}}{{{\text{6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}}} \\\ = \dfrac{{16}}{{{\text{6}}{\text{.022}}}} \times {\text{1}}{{\text{0}}^{ - 23}}g \\\ = 2.6561 \times {\text{1}}{{\text{0}}^{ - 23}}g \\\
Let us convert this mass into kg
∵1g=10−3kg ⇒2.6561×10−23g=2.6561×10−23×10−3kg =2.6561×10−26kg  \because 1g = {10^{ - 3}}kg \\\ \Rightarrow 2.6561 \times {\text{1}}{{\text{0}}^{ - 23}}g = 2.6561 \times {\text{1}}{{\text{0}}^{ - 23}} \times {10^{ - 3}}kg \\\ = 2.6561 \times {\text{1}}{{\text{0}}^{ - 26}}kg \\\
Similarly let us find the mass of one oxygen molecule:
Mass of one molecule of oxygen is:
=Molecular massAvagadro number =32g6.022×1023 =326.022×10−23g =5.3139×10−23g  = \dfrac{{{\text{Molecular mass}}}}{{{\text{Avagadro number}}}} \\\ = \dfrac{{32g}}{{{\text{6}}{\text{.022}} \times {\text{1}}{{\text{0}}^{{\text{23}}}}}} \\\ = \dfrac{{32}}{{{\text{6}}{\text{.022}}}} \times {\text{1}}{{\text{0}}^{ - 23}}g \\\ = 5.3139 \times {\text{1}}{{\text{0}}^{ - 23}}g \\\
Let us convert this mass into kg
∵1g=10−3kg ⇒5.3139×10−23g=5.3139×10−23×10−3kg =5.3139×10−26kg  \because 1g = {10^{ - 3}}kg \\\ \Rightarrow 5.3139 \times {\text{1}}{{\text{0}}^{ - 23}}g = 5.3139 \times {\text{1}}{{\text{0}}^{ - 23}} \times {10^{ - 3}}kg \\\ = 5.3139 \times {\text{1}}{{\text{0}}^{ - 26}}kg \\\
Hence, the mass of 1 oxygen atom is 2.6561×10−26kg2.6561 \times {\text{1}}{{\text{0}}^{ - 26}}kg
And the mass of one molecule of oxygen is 5.3139×10−26kg5.3139 \times {\text{1}}{{\text{0}}^{ - 26}}kg

Note- The molecular mass of an element is defined as the sum of the masses of the elements present in the molecule. Molecular mass can be easily obtained by multiplying the given atomic mass of an element by the number of atoms contained in the molecule and then by applying the masses of all the elements in the molecule. In order to solve such types of problems students must remember the formula for molecular weight and must know the method to find the atomic weight of any compound.