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.

Question

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).