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How would you calculate the percent relative abundance of Cu-63 with the mass 62.9296 g and Cu-65 with the mass 64.9278 g, when the average mass of Cu is 63.546?

Md Ariful Islam

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Md Ariful Islam

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As you know, the average of an element is determined by taking the weighted average of the atomic masses of its naturally occurring .

Simply put, an element's naturally occurring will contribute to the average atomic mass of the element proportionally to their abundance.

$color(blue)("avg. atomic mass" = sum_i ("isotope"_i xx "abundance"_x))$

When it comes to the actual calculation, it's easier to use decimal abundances, which are simply percent abundances divided by $100$.

So, you know that copper has two naturally occurring isotopes, copper-63 and copper-65. This means that their respective decimal abundance must add up to give $1$.

If you take $x$ to be the decimal abundance of copper-63, you can say that the decimal abundance of copper-65 will be equal to $1-x$.

Therefore, you can say that

$overbrace(x * 62.9296 color(red)(cancel(color(black)("u"))))^(color(blue)("copper-63")) + overbrace((1-x) * 64.9278 color(red)(cancel(color(black)("u"))))^(color(red)("copper-65")) = 63.546 color(red)(cancel(color(black)("u")))$

Solve this equation for $x$ to get

$62.9296 * x - 64.9278 * x = 63.546 - 64.9278$

$1.9982 * x = 1.3818 implies x = 1.3818/1.9982 = 0.69152$

This means that the percent abundances of the two isotopes will be

  • $69.152% -> ""^63"Cu"$
  • $30.848% -> ""^65"Cu"$
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2. The element copper has naturally occurring isotopes with mass numbers of 63 and 65. The relative abundance and atomic masses are 69.2% for a mass of 62.93 amu and 30.8% for a mass of 64.93 amu. How do you calculate the average atomic mass of copper?

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1 Answers 1 views
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The average mass is simply the weighted average: $(34.968852xx75.77%+36.965903xx24.23%)*"amu"$ $=$ $35.4527*"amu"$

1 Answers 1 views

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