Question

Naturally occurring magnesium has an atomic mass of 24.312 and consists of three isotopes. The major isotope is 24Mg, natural abundance 78.99%, relative atomic mass 23.98504. The next most abundant isotope is 26Mg, relative atomic mass 25.98259. The third most abundant isotope is 25Mg whose natural abun- dance is in the ratio of 0.9083 to that of 26Mg. Find the relative atomic mass of 25Mg.

Answer 1

Step-by-step explanation:

It is known that the sum of natural abundances of all the isotopes is equal to 100.

When x is the % represented by
`^(26)Mg`, then 0.9083x represents % for
`^(25)Mg`.

Therefore, x + y + 78.99 = 100

x + y = 100 - 78.99

x + y = 21.01%

Therefore, x + 0.9083x + 0.7899 = 1.00 (as y = 0.9083x)

x = 0.1101

Hence, relative atomic mass of
`^(25)Mg` is calculated as follows.

(0.7899)(23.98504) + (0.1101)(25.98259) + (0.1000)(a) = 24.312

18.9458 + 2.8607 + 0.1000a = 24.312

0.1000a = 2.5055

a = 25.055

Thus, we can conclude that the atomic mass of
`^(25)Mg` is 25.055.

Answer 2

the relative atomic mass of 25-Mg is 25.05539

Solution and Explanation:

• Isotopes are atoms that belong to the same element having the same number of protons, however they have a different number of neutrons making them differ in their mass number.
• Relative atomic number is calculated by getting the sum of product of the mass of atoms and their relative abundances then dividing by 100.

In this case, magnesium has three isotopes with different masses and relative abundances. We need to calculate the atomic mass of 25-Mg

Step 1: Calculating relative abundances of 26-Mg and 25-Mg

24 Mg - atomic mass of 23.98504 and relative abundance of 78.99%

26 Mg - atomic mass of 25.98259 and relative abundance of y %

25 Mg - atomic mass of x and relative abundance of 0.9083y%

But, the sum of relative abundances add up to 100%

Therefore;

y + 0.9083y + 78.99 = 1000

1.9083y = 21.01

y = 11.00980

Thus, the relative abundances of 26-Mg and 25-Mg are 11.00980 and 10.0002 respectively.

Step 2: Calculating the atomic mass of 25-Mg

R.A.M of Mg is 24.312

Assuming the atomic mass of 25-Mg is x

Then;

`24.312 = ((23.98504)(78.99)+(25.98259)(11.00980)+(10.0002x))/(100) \\24.312 =((1894.578)+(286.0631)+(10.0002x))/(100)`

`2431.2 = (1894.578)+(286.0631)+(10.0002x)`

Solving for x

`x=25.05539`

Therefore the relative atomic mass of 25-Mg is 25.05539