-1
$\begingroup$

The average atomic mass of a sample of an element 'X' is 16.2u. What are the percentages of isotopes $\ce{^16_8X}$(atomic number = 8, atomic mass = 16) and $\ce{^18_8X}$(atomic number = 8, atomic mass = 18) in the sample?

$\endgroup$

marked as duplicate by Martin - マーチン Dec 8 '17 at 7:01

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

2
$\begingroup$

We have two isotopes, $A,B$ with atomic masses $m_A, m_B$. We thus have two unknowns $x_A, x_B$ representing the percentage amounts of each isotope (i.e. the mole fraction), which are trivially connected as

$$ x_A + x_B = 1 $$

We also know something about the average atomic mass $\overline{m}$, namely

$$ x_A \cdot m_A + x_B \cdot m_B = \overline{m} $$

So we now have a system of two linear equations to plug in values and solve. Steps:

$$ x_A = 1 - x_B $$

.

$$ (1 - x_B ) \cdot m_A + x_B \cdot m_B = \overline{m} $$

.

$$ x_B \cdot (m_B - m_A) = \overline{m} - m_A $$

.

$$ x_B = \frac{\overline{m} - m_A}{m_B - m_A} $$

And plug back in the first equation.

$\endgroup$
  • 1
    $\begingroup$ $x_A$ representing the percentage amounts of each isotope = mole fraction? $\endgroup$ – Martin - マーチン Dec 7 '17 at 13:03

Not the answer you're looking for? Browse other questions tagged or ask your own question.