To calculate the relative atomic mass (R.A.M.) of chlorine using its isotopes and their percentage abundances, you can use the following formula:
\[ \text{R.A.M.} = \left( \frac{(\text{Isotope mass}_1 \times \text{Abundance}_1) + (\text{Isotope mass}_2 \times \text{Abundance}_2)}{100} \right) \]
Where:
- Isotope mass of \( ^{35}\text{Cl} = 35 , \text{u} \)
- Isotope mass of \( ^{37}\text{Cl} = 37 , \text{u} \)
- Abundance of \( ^{35}\text{Cl} = 75.78% \)
- Abundance of \( ^{37}\text{Cl} = 24.22% \)
Now substitute these values into the formula:
\[ \text{R.A.M.} = \left( \frac{(35 \times 75.78) + (37 \times 24.22)}{100} \right) \]
Calculating each term:
-
For \( ^{35}\text{Cl} \): \[ 35 \times 75.78 = 2652.3 \]
-
For \( ^{37}\text{Cl} \): \[ 37 \times 24.22 = 896.14 \]
Now add these two results:
\[ 2652.3 + 896.14 = 3548.44 \]
Now, divide by 100 to find the R.A.M.:
\[ \text{R.A.M.} = \frac{3548.44}{100} = 35.4844 \]
Thus, the relative atomic mass of chlorine, rounded to two decimal places, is approximately:
\[ \text{R.A.M.} \approx 35.48 , \text{u} \]