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There are three stable isotopes of magnesium. Their masses are 23.9850, 24.9858, and 25.9826 u. If the average atomic mass of magnesium is 24.3050 u and the natural abundance of the lightest isotope is 78.99%, what are the natural abundances of the other two isotopes?

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Answer:

²⁵ Mg = 10.00%

²⁶ Mg = 11.0%

Explanation:

Given that:

Magnesium ²⁴Mg has an abundance of 78.99%

Hence, (100 - 78.99)% = 21.01%

21.01% is the abundance of ²⁵ Mg and ²⁶ Mg

Suppose,

²⁵ Mg = x

²⁶ Mg = (21.01 - x)%

Then;

avg. atomic mass = [tex]\dfrac{78.99}{100 }(23.9850)+\dfrac{x}{100}(24.9858) +\dfrac{21.01-x}{100}(25.9826)[/tex]

where the avg. atomic mass = 24.3050

∴

[tex]24.3050 \times 100 = {78.99}(23.9850)+\dfrac{x}{100}(24.9858) +\dfrac{21.01-x}{100}(25.9826)[/tex]

2430.5 = 2440.46915 -0.9968 x

0.9968x = 2440.46915 - 2430.5

0.9968x = 9.96915

x  =  9.96915/0.9968

x  =  10.00%

∴ Recall that:

²⁵ Mg = x

²⁶ Mg = (21.01 - x)%

²⁵ Mg = 10.00%

²⁶ Mg = (21.01 - 10.00)%

²⁶ Mg = 11.0%

The natural abundances of the other two isotopes, that is, Mg-25 and Mg-26 are 10% and 11.01%.

What is Natural abundance?

It is the abundance of isotopes of a chemical element as naturally found on a planet.

Based on the given information:

  • The three stable isotopes of Mg are Mg-24, Mg-25 and Mg-26.
  • The natural abundance of the lightest isotope, that is, Mg-24 is 78.99%.
  • The masses of the isotopes are 23.9850 u, 24.9858 u and 25.9826 u.
  • The average atomic mass of Mg is 24.3050 u.

Now the natural abundance of all the isotopes of Mg is 100%.

Mg-24 + Mg-25 + Mg-26 = 100

Mg-25 + Mg-26 = 100-78.99

Mg-25 + Mg-26 = 21.01

Now let us assume that Mg-25 is x% then Mg-26 will be (21.01% -x).

Now,

Average atomic mass of Mg = [(Natural abundance of Mg-24) × (isotopic mass of Mg-24) + (Natural abundance of Mg-25) × (Isotopic mass of Mg-25) + (Natural abundance of Mg-26) × (Isotopic mass of Mg-26)]

Putting the values we get,

24.3050 amu = (78.99% × 23.9580 amu) + (x% × 24.9858 amu) + (21.01% - x%) × 25.9826 amu

24.3050 amu = 18.9458 + 24.9858 × x + 5.4589 - (25.9826x)

24.3050 = 24.4047 - (0.9968x)

0.9968x = 24.4047 - 24.3050

x = 0.1000

x = 10%

The natural abundance of Mg-25 is 10%.

The natural abundance of Mg-26 = 21.01% - x% = 21.01% - 10% = 11.01%.

Thus, the natural abundances of the other two isotopes are 10% and 11.01%.

Find out more information about natural abundances here:

https://brainly.com/question/4880347

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