average atomic mass of magnesium is 24.31 amu. this magnesium is composed of 79 mole % of ^24 Mg and remaining 21mole % of ^25 Mg. calculate mole % of ^26Mg.
79(24)+x(26)+(21-x)25 whole divided by 100 = 24.31 you get answer by solving X as 10
To calculate the mole percentage of ^26Mg in magnesium, we first need to determine the mole percentage of ^24Mg and ^25Mg in magnesium.
Given:
Mole percentage of ^24Mg = 79%
Mole percentage of ^25Mg = 21%
Step 1: Calculate the mole fraction of ^24Mg and ^25Mg.
Mole fraction of ^24Mg = (mole percentage of ^24Mg / 100) = 79 / 100 = 0.79
Mole fraction of ^25Mg = (mole percentage of ^25Mg / 100) = 21 / 100 = 0.21
Step 2: Calculate the atomic masses of ^24Mg and ^25Mg.
The given information states that the average atomic mass of magnesium is 24.31 amu.
Let x = atomic mass of ^24Mg
Let y = atomic mass of ^25Mg
0.79x + 0.21y = 24.31 (1)
Step 3: Substitute values for the atomic masses.
We know that the atomic masses of ^24Mg and ^25Mg add up to the average atomic mass of magnesium, which is 24.31 amu.
Substituting values, we get:
0.79x + 0.21y = 24.31 (1)
Step 4: Calculate the mole fraction of ^26Mg.
We can assume that all three isotopes (^24Mg, ^25Mg, and ^26Mg) account for 100% of the sample. Therefore,
Mole fraction of ^26Mg = 1 - (mole fraction of ^24Mg + mole fraction of ^25Mg)
Mole fraction of ^26Mg = 1 - (0.79 + 0.21) = 1 - 1 = 0
The mole fraction of ^26Mg is 0.
Since the mole fraction of ^26Mg is 0, the mole percentage of ^26Mg in magnesium is also 0%.