A hypothetical pure element consists entirely of two isotopes. The natural percent abundance of the isotope with mass 25.5 u is 78.8 percent. The other isotope has mass 29.5 u. Calculate the atomic weight of the naturally occurring element.

(0.788&25.5)+(1-0.788)*X = 29.5

Solve for X.

To calculate the atomic weight of the naturally occurring element, we need to use the average atomic mass formula.

The formula to calculate the average atomic mass is:
Average Atomic Mass = (mass1 * abundance1 + mass2 * abundance2 + ...) / 100

In this case, we have two isotopes with their respective masses and abundances:

Isotope 1:
Mass = 25.5 u
Abundance = 78.8% (which we need to convert into a decimal, so 78.8 / 100 = 0.788)

Isotope 2:
Mass = 29.5 u
Abundance = 100% - 78.8% = 21.2% (again, we convert to a decimal, so 21.2 / 100 = 0.212)

Now, let's calculate the atomic weight using the formula:

Atomic Weight = (mass1 * abundance1 + mass2 * abundance2) / 100

Atomic Weight = (25.5 u * 0.788) + (29.5 u * 0.212) / 100

Atomic Weight = (20.094 u) + (6.254 u) / 100

Atomic Weight = 26.348 u / 100

Atomic Weight = 26.348 u

Therefore, the atomic weight of the naturally occurring element is approximately 26.348 u.