Question

(a) The relative abundance of various isotopes of silicon is as Si $(28)=92.25$, Si $(29)=4.65$ and Si $(30)=3.10$. Calculate average At. mass of silicon.
(b) Calculate the mass of $1.6$ gram atoms of oxygen.

Answer 1

Hint: To find the solution of the first question, as the required data is already given, you need to only apply the direct formula for the average or relative atomic mass and for the second question, remember mass of one-gram atom is equal to the mass of one mole of atoms of an element.

Complete step by step answer:
(a) Given that,
The relative abundance of silicon with atomic number $28$ is $92.25$.
The relative abundance of silicon with atomic number $29$ is $4.65$.
The relative abundance of silicon with atomic number $30$ is $3.10$.
We should know that, while doing any average mass calculations for an element, it should be equal to the sum of the masses of each isotope and each multiplied by its natural relative abundances.
So, here the atomic number of each isotope of silicon will be equal to its atomic mass.

Thus, the average atomic mass of an element having isotope equals the sum of mass of each isotope multiplied with abundance. So, the formula will be like,
$Average\text{ atomic mass}={\displaystyle \frac{\text{(abundance}\times \text{atomic mass) of 1st isotope +}...}{100}}$
So, Average atomic mass of silicon $={\displaystyle \frac{28\times 92.25+29\times 4.65+30\times 3.10}{100}}={\displaystyle \frac{2810.85}{100}}=28.10$
Hence, the average atomic mass of silicon is $28.10g$.

(b) As per the given question, we have to find out the mass of $1.6g$ atoms of oxygen atoms.
We know that, gram atomic mass refers to the mass of one mole of an element in grams, which is its molar mass.
So, the mass of $1g$ atom is equal to one mole of the element which is equal to the molar mass of that element.
Therefore, the mass of $1g$ atom of oxygen will be equal to $16g$.
Thus, the mass of $1.6g$ atom of oxygen will be equal to $(1.6\times 16)g=25.6g$
Hence, the mass of $1.6g$ atom of oxygen is $25.6g$.

Note: The average atomic mass for an element is calculated by summing the masses of the element’s isotopes, each multiplied by its natural abundance on earth. The mass of a one-gram atom equals the mass of one mole of elements in grams, which is its molar mass.