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