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

39.948 amu
39.948 amu

36.167 amu
36.167 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:

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

where:

• \(f_1\) and \(f_2\) are the fractions (percentages expressed as decimals) of each isotope,
• \(m_1\) and \(m_2\) are the atomic masses of the isotopes.

From the problem, we have:

• For argon-36:

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

• For argon-38:

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

Now, we can substitute these values into the formula:

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

Calculating each term:

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

Now, we add these two results together:

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

Rounding to three decimal places, we get:

\[ \text{Average Atomic Mass} \approx 36.167 , \text{amu} \]

Therefore, the answer is:

36.167 amu