Help please with question number 16)

Mg²⁵   =   10.00%    

Mg²⁶   =   45.04%

Mg²⁴   =   44.96%

Explanation:

Given data:

Atomic mass of Mg²⁶ = 25.983

Atomic mass of Mg²⁵ = 24.986

Atomic mass of Mg²⁴ = 23.985

Abundance of Mg²⁵ = 10.00%

Abundance of Mg²⁶ = ?

Abundance of Mg²⁴ = ?

Solution:

Average atomic weight of Mg = 25.983  + 24.986+ 23.985 / 3

Average atomic weight of Mg = 74.954/3

Average atomic weight of Mg = 24.985 amu

Abundance of          

Mg²⁵   =   10.00    

Mg²⁶   =    x      

Mg²⁴   =   100- 10 - x = 90 -x    

Formula:

Average atomic mass  = (abundance of 1st isotope × its atomic mass) +(abundance of 2nd isotope × its atomic mass) + (abundance of 3rd isotope × its atomic mass)  / 100

24.985 = (0.1×24.986)+(90-x×23.985) + ( x ×25.983 )  /100

24.985 =  249.86 + 2158.65 - 23.985x + 25.983x  / 100

24.985 = 2408.51 + 1.998 x / 100

2498.5 = 2408.51 + 1.998 x

1.998 x = 2498.5 - 2408.51

1.998 x = 89.99

x = 89.99 /1.998

x = 45.04

Now we put the value of x:

Mg²⁵   =   10.00    

Mg²⁶   =    x  (45.04)

Mg²⁴   =   90 -x   (90 - 45.04 = 44.96)