Question

the relative atomic mass (A_r) of atoms is the average mass of all the different isotopes of an element (taking into account the amount of each isotopes) on a scale weere ^12C atoms have mass of exactly 12.
Element Chlorine isotopes 35 17 Cl 37 17 Cl Abundance 75.8% 24.2% Relative atomic mass (A_r) to (3sf)

Answer 1

To calculate the relative atomic mass (A_r) of chlorine based on its isotopes and their respective abundances, we can use the following formula:

\[
A_r = \frac{(mass_1 \times abundance_1) + (mass_2 \times abundance_2)}{100}
\]

Where:
- \( mass_1 \) and \( mass_2 \) are the masses of the isotopes,
- \( abundance_1 \) and \( abundance_2 \) are the percentages of each isotope.

For chlorine:
- \( ^{35}Cl \) has a mass of 35 and an abundance of 75.8%,
- \( ^{37}Cl \) has a mass of 37 and an abundance of 24.2%.

Now we can plug in the values:

\[
A_r = \frac{(35 \times 75.8) + (37 \times 24.2)}{100}
\]

Calculating step-by-step:

1. Calculate \( 35 \times 75.8 \):

\[
35 \times 75.8 = 2653
\]

2. Calculate \( 37 \times 24.2 \):

\[
37 \times 24.2 = 896.6
\]

3. Add the two results:

\[
2653 + 896.6 = 3549.6
\]

4. Divide by 100:

\[
A_r = \frac{3549.6}{100} = 35.496
\]

Now, rounding to three significant figures gives:

\[
A_r \approx 35.5
\]

Thus, the relative atomic mass (A_r) of chlorine is approximately **35.5** (to three significant figures).