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)

Question

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:

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

where:

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

Given:

• For argon-36:

  • \( f_1 = 0.90 \) (90%),
  • \( m_1 = 35.968 , \text{amu} \).

• For argon-38:

  • \( f_2 = 0.10 \) (10%),
  • \( m_2 = 37.962 , \text{amu} \).

Now, we plug in the values:

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

Calculating each term:

• For argon-36: \[ 0.90 \times 35.968 = 32.3712 \]

• For argon-38: \[ 0.10 \times 37.962 = 3.7962 \]

Now add these values together: \[ \text{Average Atomic Mass} = 32.3712 + 3.7962 = 36.1674 , \text{amu} \]

Rounding to three decimal places, we find: \[ \text{Average Atomic Mass} \approx 36.167 , \text{amu} \]

Thus, the correct response is: 36.167 amu