Question

Question
Calculate the average atomic mass of a sample of a mixture of argon (Ar). The mixture is 90% argon-36 and 10% argon-38. Argon-36 has an atomic mass of 35.968 amu. Argon-38 has an atomic mass of 37.962 amu. (1 point)
Responses

36.167 amu
36.167 amu

3616.74 amu
3616.74 amu

37.763 amu
37.763 amu

39.948 amu

Answer 1

To calculate the average atomic mass of the mixture of argon isotopes, we can use the weighted average formula. The formula is:

\[
\text{Average Atomic Mass} = (f_1 \times m_1) + (f_2 \times m_2)
\]

where \( f_1 \) and \( f_2 \) are the fractional abundances of the isotopes, and \( m_1 \) and \( m_2 \) are the atomic masses of the isotopes.

Given:

- Argon-36:
- Abundance \( f_1 = 0.90 \)
- Atomic mass \( m_1 = 35.968 \, \text{amu} \)

- Argon-38:
- Abundance \( f_2 = 0.10 \)
- Atomic mass \( m_2 = 37.962 \, \text{amu} \)

Now, substitute the values into the formula:

\[
\text{Average Atomic Mass} = (0.90 \times 35.968) + (0.10 \times 37.962)
\]

Calculating each term:

\[
0.90 \times 35.968 = 32.3712
\]
\[
0.10 \times 37.962 = 3.7962
\]

Adding these results together:

\[
\text{Average Atomic Mass} = 32.3712 + 3.7962 = 36.1674 \, \text{amu}
\]

Rounding to three decimal places, the average atomic mass is approximately:

\[
36.167 \, \text{amu}
\]

Thus, the correct response is:

**36.167 amu**