Question

How would you set up the problem to find percent abundance of Magnesium if it has 3 stable isotopes, Mg-24, Mg-25, and Mg-26 and you know that Mg-26 has a percent abundance of 11%? (Mg has an atomic mass of 24.305)

Answer 1

To calculate the percent abundance of magnesium isotopes, set up a system of equations using the given atomic mass of magnesium, the mass of each isotope, and the known abundance of Mg-26. Solve for the unknown percent abundances of Mg-24 and Mg-25.

Step-by-step explanation:

When calculating the percent abundance of isotopes, such as magnesium, which has three stable isotopes (Mg-24, Mg-25, Mg-26), you must consider the given percent abundance of one isotope and the atomic mass of the element to solve for the unknown abundances.

If Mg-26 has a percent abundance of 11% and the atomic mass of magnesium is 24.305 amu, you can set up the problem as a system of equations. Given the exact masses of Mg-24: 23.98 amu, Mg-25: 24.99 amu, and Mg-26: 25.98 amu, and knowing the abundance of Mg-26, the equation can be established as follows:

• The sum of the percent abundances must equal 100%.
• The average atomic mass of magnesium (24.305 amu) is the weighted average of the masses of the isotopes multiplied by their respective abundances.

Let x be the percent abundance of Mg-24, and y be the percent abundance of Mg-25. Since Mg-26 is 11%, we have the following equations:

1. x + y + 11 = 100
2. (23.98*x + 24.99*y + 25.98*11) / 100 = 24.305

You can then solve this system of equations for x and y to find the percent abundances of Mg-24 and Mg-25.