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?
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1 Answer
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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:
$$ x_A = 1 - x_B $$
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$$ (1 - x_B ) \cdot m_A + x_B \cdot m_B = \overline{m} $$
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$$ x_B \cdot (m_B - m_A) = \overline{m} - m_A $$
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$$ x_B = \frac{\overline{m} - m_A}{m_B - m_A} $$
And plug back in the first equation.
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1$\begingroup$ $x_A$ representing the percentage amounts of each isotope = mole fraction? $\endgroup$– Martin - マーチン ♦Dec 7, 2017 at 13:03
closed as OT, homework. $\endgroup$