Question

There are three naturally occurring isotopes of the hypothetical element hilarium 45Hi, 46Hi, and 48Hi. The percentages of these isotopes are the following: Hilarium Natural Isotopes Abundance 45Hi 18.3% 46Hi 34.5% 48Hi 47.2% You can assume that the atomic masses are exactly equal to the mass number. Calculate the weight of "naturally" occurring hilarium and report it as you would for any other naturally occurring element. Answer in units of g/mol. Your answer must be within ± 0.005%

Answer 1

Answer:

46.761g/mol

Explanation:

Given parameters:

Element = Hilarium , Hi

Isotopes: Hi- 45, Hi-46 and Hi- 48

Natural abundance of Hi-45 = 18.3%

                                     Hi-46 = 34.5%

                                     Hi-48 = 47.2%

Unknown:

Atomic weight of naturally occurring Hilarium = ?

Solution:

Isotopes have been studied extensively by mass spectrometry. The method is used to determine the proportion/percentage/fraction by which each of the isotopes of an element occurs in nature. The proportion is called geonormal abundance. From this we can calculate the atomic weight of an element.

 We can use the expression below to find this value:

       Atomic weight = m₄₅α₄₅ + m₄₆α₄₆ + m₄₈α₄₈

    m is the atomic mass of each isotope and α is the abundance

Atomic weight = (45 x $\frac{18.3}{100}$ ) + (46 x  $\frac{34.5}{100}$ ) + (48 x  $\frac{47.2}{100}$)

Atomic weight of Hi = 8.235 + 15.870 +  22.656 = 46.761g/mol