JAMB - Chemistry (2004 - No. 12)
Explanation
Two isotopes of Chlorine are : \(^{35}\)Cl and \(^{37}\)Cl
Atomic mass of Cl : 35.5
Ratio of the isotopes of Chlorine : 3 : 1
Let the relative atomic abundance of \(^{37}\)Cl = 1 x X = X
Let the relative atomic abundance of \(^{35}\)Cl = 3 x X = 3X
N.B : The average atomic mass = sum of products of each isotope mass and its relative abundance.
A.M.M = (3x of 35) + (x of 37)
35.5 = (3x X 35) + (x X 37)
35.5 = 105x + 37x
35.5 = 142x
x = \(\frac{35.5}{142}\)
x = 0.25
Convert to percentage.
Recall that relative atomic abundance of \(^{37}\)Cl = x = 0.25 x 100 = 25%
and the relative atomic abundance of \(^{35}\)Cl = 3X = 3(0.25) = 0.75 x 100 = 75%
We were asked for the Relative abundance of isotope of mass number 37 i.e \(^{37}\)Cl is 25%
Alternatively,
Ratio of the isotopes of Chlorine : 3 : 1
Sum of ratios = 3 + 1 = 4
Relative Abundance of Cl isotopes = % ratio of \(^{35}\)Cl and % ratio of \(^{37}\)Cl
= \(\frac{3}{4}\)x 100 and \(\frac{1}{4}\) x 100
= 75% \(^{35}\)Cl and 25% \(^{37}\)Cl
Relative abundance of \(^{37}\)Cl = 25
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