QuestionCalculate the atomic mass of chlorine given isotopes: $91.51\%$ of ${ }^{35} \mathrm{Cl}$ ( $34.97 \mathrm{amu}$ ) and $24.57\%$ of ${ }^{37} \mathrm{Cl}$ ( $36.97 \mathrm{amu}$ ).

Studdy Solution

STEP 1

Assumptions1. The sample of Chlorine consists of two isotopes ${ }^{35} \mathrm{Cl}$ and ${ }^{37} \mathrm{Cl}$ . . The percentage of ${ }^{35} \mathrm{Cl}$ in the sample is $91.51 \%$ and its atomic mass is $34.97 \mathrm{amu}$ .
3. The percentage of ${ }^{37} \mathrm{Cl}$ in the sample is $24.57 \%$ and its atomic mass is $36.97 \mathrm{amu}$ .

STEP 2

The atomic mass of an element is the weighted average of the atomic masses of its naturally occurring isotopes. The weight of each isotope is its relative abundance. We can calculate the atomic mass of chlorine by using the following formula $Atomic\, mass = (Percentage\, of\, isotope\,1 \\times Atomic\, mass\, of\, isotope\,1) + (Percentage\, of\, isotope\,2 \\times Atomic\, mass\, of\, isotope\,2)$

STEP 3

First, we need to convert the percentages to decimal form. $91.51\% =0.9151$ $24.57\% =0.2457$

STEP 4

Now, plug in the given values for the percentages and atomic masses of the isotopes into the formula.
$Atomic\, mass = (0.9151 \\times34.97 \mathrm{amu}) + (0.2457 \\times36.97 \mathrm{amu})$

STEP 5

Calculate the atomic mass of chlorine.
$Atomic\, mass = (0.9151 \\times34.97 \mathrm{amu}) + (0.2457 \\times36.97 \mathrm{amu})$ The atomic mass of chlorine is approximately $35.48 \mathrm{amu}$ .

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