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

3616.74 amu
3616.74 amu

37.763 amu
37.763 amu

36.167 amu
36.167 amu

39.948 amu

Answer 1

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

Let's denote:

• The mass of argon-36 (Ar-36) as \( m_1 = 35.968 \) amu
• The mass of argon-38 (Ar-38) as \( m_2 = 37.962 \) amu
• The fraction of Ar-36 as \( f_1 = 0.90 \)
• The fraction of Ar-38 as \( f_2 = 0.10 \)

The average atomic mass \( M \) can be calculated using the formula:

\[ M = f_1 \cdot m_1 + f_2 \cdot m_2 \]

Plugging in the values:

\[ M = (0.90 \cdot 35.968 , \text{amu}) + (0.10 \cdot 37.962 , \text{amu}) \]

Calculating each term:

\[ 0.90 \cdot 35.968 = 32.3712 , \text{amu} \] \[ 0.10 \cdot 37.962 = 3.7962 , \text{amu} \]

Now, add these two results:

\[ M = 32.3712 , \text{amu} + 3.7962 , \text{amu} = 36.1674 , \text{amu} \]

Rounding to three decimal places, we find:

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

Thus, the average atomic mass of the mixture of argon is approximately:

36.167 amu