There are three naturally occurring isotopes
of the hypothetical element hilarium 41Hi, 42Hi, and 44Hi. The percentages of these
isotopes are the following:
Hilarium Natural
Isotopes Abundance
41Hi 18.7%
42Hi 43.6%
44Hi 37.7%
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%
1.00*avgweight=.187*41+.436*42+.377*44
Put this into your google search windown:
.187*41+.436*42+.377*44=
42.57
To calculate the weight of naturally occurring hilarium, we need to consider the atomic masses and abundances of each isotope.
Given:
- Isotope 41Hi has an abundance of 18.7%.
- Isotope 42Hi has an abundance of 43.6%.
- Isotope 44Hi has an abundance of 37.7%.
We can calculate the weighted average atomic mass using the formula:
Average Atomic Mass = (Mass1 * Abundance1 + Mass2 * Abundance2 + Mass3 * Abundance3) / 100
Calculating the average atomic mass for hilarium:
Average Atomic Mass = (41 * 18.7 + 42 * 43.6 + 44 * 37.7) / 100
= (767.7 + 1831.2 + 1656.8) / 100
= 4255.7 / 100
= 42.557 g/mol
Therefore, the weight of naturally occurring hilarium is approximately 42.557 g/mol.
To calculate the weight of naturally occurring hilarium, we need to consider the atomic masses of each isotope and their respective abundances.
First, we need to convert the percentages of each isotope into decimal form.
41Hi abundance = 18.7% = 0.187
42Hi abundance = 43.6% = 0.436
44Hi abundance = 37.7% = 0.377
Next, we need to calculate the weighted average atomic mass, which is the sum of the individual atomic masses multiplied by their abundances.
Weighted average atomic mass = (41Hi atomic mass * 41Hi abundance) + (42Hi atomic mass * 42Hi abundance) + (44Hi atomic mass * 44Hi abundance)
As the atomic mass is equal to the mass number for this hypothetical element, the atomic masses are:
41Hi atomic mass = 41
42Hi atomic mass = 42
44Hi atomic mass = 44
Plugging in the values:
Weighted average atomic mass = (41 * 0.187) + (42 * 0.436) + (44 * 0.377)
Calculation: (7.667) + (18.312) + (16.488) = 42.467
Therefore, the weight of naturally occurring hilarium is approximately 42.467 g/mol.