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  39.948 amu 39.948 amu  3616.74 amu 3616.74 amu  37.763 amu

Answer 1

To calculate the average atomic mass of the mixture of argon isotopes, we can use the formula for weighted averages based on their abundances.

Let:
- \( m_1 = 35.968 \, \text{amu} \) (mass of argon-36)
- \( m_2 = 37.962 \, \text{amu} \) (mass of argon-38)
- \( p_1 = 0.90 \) (proportion of argon-36 in the mixture)
- \( p_2 = 0.10 \) (proportion of argon-38 in the mixture)

The average atomic mass \( m_{avg} \) can be calculated as follows:

\[
m_{avg} = (p_1 \cdot m_1) + (p_2 \cdot m_2)
\]

Substituting in the values:

\[
m_{avg} = (0.90 \cdot 35.968) + (0.10 \cdot 37.962)
\]

Calculating each term:

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

Now, adding these results:

\[
m_{avg} = 32.3712 + 3.7962 = 36.1674
\]

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

\[
m_{avg} \approx 36.167 \, \text{amu}
\]

Therefore, the correct answer is:

**36.167 amu**