Mass spectrometry analysis reveals that a sample has magnesium-23 and magnesium-25.5. Given that the relative…

Question

Mass spectrometry analysis reveals that a sample has magnesium-23 and magnesium-25.5. Given that the relative atomic mass of magnesium is 24, calculate the percentage abundance of the isotopes.

ScanSolve AI Tutor · Accepted Answer

This problem requires us to work backward from the relative atomic mass to find the percentage abundances of the isotopes.

Define variables for the fractional abundances.
Let $x$ be the fractional abundance of Magnesium-23.
Since there are only two isotopes, the fractional abundance of Magnesium-25.5 will be $(1-x)$ .
Set up the equation for relative atomic mass.
The formula for relative atomic mass is:
$\text{Relative Atomic Mass} = (\text{mass of isotope 1} \times \text{fractional abundance 1}) + (\text{mass of isotope 2} \times \text{fractional abundance 2})$
Given the relative atomic mass of magnesium is 24, we can write:
$24 = (23 \times x) + (25.5 \times (1-x))$
Solve the equation for $x$ .
$24 = 23x + 25.5 - 25.5x$
Combine the terms with $x$ :
$24 = 25.5 - 2.5x$
Subtract 25.5 from both sides:
$24 - 25.5 = -2.5x$ $-1.5 = -2.5x$
Divide by -2.5:
$x = \frac{-1.5}{-2.5}$ $x = \frac{1.5}{2.5}$ $x = 0.6$
Calculate the fractional abundance of the second isotope.
The fractional abundance of Magnesium-25.5 is $1-x$ :
$1 - 0.6 = 0.4$
Convert fractional abundances to percentage abundances.
- Percentage abundance of Magnesium-23: $0.6 \times 100\% = 60\%$
- Percentage abundance of Magnesium-25.5: $0.4 \times 100\% = 40\%$
The percentage abundance of Magnesium-23 is 60% and Magnesium-25.5 is 40%.
\text{Magnesium-23: 60%}, \text{ Magnesium-25.5: 40%}

Mass spectrometry analysis reveals that a sample has magnesium-23 and magnesium-25.5. Given that the relative atomic mass of magnesium is 24, calculate the percentage abundance of the isotopes.

Answer

Step-by-step solution

Define variables for the fractional abundances.

Set up the equation for relative atomic mass.

Solve the equation for $x$ .

Calculate the fractional abundance of the second isotope.

Convert fractional abundances to percentage abundances.

Try one yourself

Still stuck on this one?

More Chemistry Questions

Mass spectrometry analysis reveals that a sample has magnesium-23 and magnesium-25.5. Given that the relative atomic mass of magnesium is 24, calculate the percentage abundance of the isotopes.

Answer

Step-by-step solution

Define variables for the fractional abundances.

Set up the equation for relative atomic mass.

Solve the equation for xxx.

Calculate the fractional abundance of the second isotope.

Convert fractional abundances to percentage abundances.

Try one yourself

Still stuck on this one?

More Chemistry Questions

Solve the equation for $x$ .