Final answer:
The average atomic mass of the fictitious element X is calculated to be 56.6 amu, by multiplying the percentage abundance of each isotope by its mass and summing the products.
Step-by-step explanation:
To calculate the average atomic mass of the fictitious element X, with isotopes X-55, X-56, and X-57, we need to take into account the mass of each isotope and their abundance percentage. The calculation can be done using the formula:
average atomic mass = (fraction of isotope 1 × mass of isotope 1) + (fraction of isotope 2 × mass of isotope 2) + (fraction of isotope 3 × mass of isotope 3)
By converting the percentages to fractions, we have:
- 0.100 (10.0% of isotope X-55) × 55
- 0.200 (20.0% of isotope X-56) × 56
- 0.700 (70.0% of isotope X-57) × 57
Performing the calculations:
(0.100 × 55) + (0.200 × 56) + (0.700 × 57) = 5.5 + 11.2 + 39.9 = 56.6 amu
Therefore, the average atomic mass of element X is 56.6 amu.