Question

Calculate the average atomic mass of naturally occurring magnesium using the following data

Answer 1

We are asked to find the average atomic mass. We are going to use the concept of mathematics known as Weighted Mean.


Basically, if there are $n$ variables $x_1, \, x_2 , \, ... , \, x_n$ and their weights are $m_1, \, m_2 , \, ... , \, m_n$ then the weighted mean is given by:

$\overline{x} = \frac{m_1x_1+m_2x_2+...+m_nx_n}{m_1+m_2+...+m_n}$

Here, we have three isotopes of Magnesium. The relative abundance of each isotope is different. 

Here, the atomic mass of each isotope form the variables of $x$ in the Weighted Mean formula.


We cannot take a simple mean for finding the average mass since in any random sample of Magnesium, the contribution of each isotope is different. 

Think of it like this: There is a company, and three people A, B and C work there. A does 70 % of the work. B does 15 % of the work, and C does only 5 % work.
We cannot divide total money simply. A has done more work. So he should receive more money. He should receive 70 % money because he did 70 % of the work. Similarly, C should receive only 5 % money.

Here, the relative abundance of each isotope is different. So we have to consider the relative abundance to calculate the Average Atomic Mass. 
The Relative Abundance Values form the Weights $m$ in the Weighted Mean Formula above. 


Here, we can take the following values:

$x_1 = 23.99 \, \, \, and \, \, \, m_1 = 78.99 \\ \\ x_2 = 24.99 \, \, \, and \, \, \, m_2 = 10.00 \\ \\ x_3 = 25.98 \, \, \, and \, \, \, m_3 = 11.01$


Now, we can find average atomic mass, say $M$, as follows:


$M = \overline{x} = \frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3} \\ \\ \\ \implies M = \frac{(78.99\times 23.99)+(10.00 \times 24.99)+(11.01\times 25.98)}{78.99+10.00+11.01} \\ \\ \\ \implies M = \frac{1894.9701+249.90+286.0398}{100} \\ \\ \\ \implies M = \frac{2430.9099}{100} \\ \\ \\ \implies M = 24.309099 \\ \\ \\ \implies \boxed{M \approx 24.31}$


Thus, Average Atomic Mass of Magnesium is 24.31


Hope it helps
Purva
Brainly Community
 

Answer 2

Answer:

Average atomic mass of magnesium is 24.31