Calculate the average atomic mass of a simple 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.

Question

A. 37.763 amu
B. 36.167 amu
C. 39.948 amu
D. 3616.74 amu

Answer 1

To calculate the average atomic mass of the mixture, we will 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 fractions (percentages converted to decimals) of each isotope, and \( m_1 \) and \( m_2 \) are their respective atomic masses.

For this mixture:

• Argon-36 (Ar-36):

  • Fraction (\( f_1 \)) = 90% = 0.90
  • Atomic mass (\( m_1 \)) = 35.968 amu

• Argon-38 (Ar-38):

  • Fraction (\( f_2 \)) = 10% = 0.10
  • Atomic mass (\( m_2 \)) = 37.962 amu

Now plug in the values:

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

Calculating each part:

1. \( 0.90 \times 35.968 = 32.3712 \)
2. \( 0.10 \times 37.962 = 3.7962 \)

Now, add these two results together:

\[ \text{Average atomic mass} = 32.3712 + 3.7962 = 36.1674 , \text{amu} \]

Rounding to three decimal places:

\[ \text{Average atomic mass} \approx 36.167 , \text{amu} \]

Thus, the correct answer is:

B. 36.167 amu