how to find abundance of 3 isotopes
To calculate percentage affluence, you must recall the diminutive mass of an element is calculated by using the formula:
In the above formula you see fractional abundance.How exercise y'all get that? To get fractional abundance, you normally separate the percentage abundance of each isotope by 100. And when yous add all the fractional abundance values of all the isotopes, you will notice they all add up to 1. To summate thepercent abundance of each isotope in a sample of an chemical element, chemists unremarkably separate the number of atoms of a particular isotope by the total number of atoms of all isotopes of that element and and then multiply the result past 100. Now, let's apply our understanding to solve the following question:
Silver (Ag) has two stable isotopes: silver-107(107Ag) and silver-109 (109Ag). Silver-107 has a mass of 106.90509 amu and silverish-109 has a mass of 108.90476 amu. Calculate the percentage abundance of each isotope.
Strategy
To calculate percentage abundance, we must first know the partial affluence of each isotope. But from the question, we are not given these values, which means nosotros must think of a fashion of finding them. One way nosotros can find them is to remember that the:
partial affluence of isotope one plus the partial abundance of isotope 2 = 1
We know this considering the sum of the percentage affluence values always equal 100. And since the fractional abundance is obtained by dividing the pct abundance by 100, then, it follows that the sum of the fractional abundance must equal 1. Once we empathize this, we tin then letX represent the fractional abundance forisotope 1 and(1-X) represent the fractional abundance for isotope 2. Once we substitute these variables into the formula higher up, nosotros will generate an algebraic equation from which nosotros can solve to find X and then(1-X).Once we get the values for fractional abundance(10 and 1-X), we can and so multiply each fractional abundance by 100 to become percentage abundance.
Also, observe the question gave only the isotopic masses and not the diminutive mass of silver.How practice nosotros get the diminutive mass of silverish to plug into the above equation? We get the diminutive mass of silver by reading its value from theperiodic tabular array. And If yous exercise, you will notice the atomic mass of silver is 107.8682. Subsequently gathering all the information necessary to solve the question, here is how the setup will appear based on the higher up information and formula:
Next, we and then apply our algebra skills to solve forX. To practice this, we volition expand the correct side of the equation by multiplying10 andi-X by the numbers in front of them. If we practice, here is what we will get:
107.8682 amu = 106.90509X amu + 108.90476 amu – 108.90476Xamu
Next, we bring like terms together by moving 108.90476 amu from the correct over to the left side of the equation. Since it'due south a positive number on the right, it will become a negative number when information technology moves across the equal sign to the left. When we move it, hither is how the rearranged equation volition appear:
107.8682 amu – 108.90476 amu = 106.9050910 amu – 108.90476Xamu
Next, nosotros subtract like terms
-1.03656 amu = -1.99967X amu
Next, we divide by -one.99967 amu to isolate Ten.
-1.03656 amu/-1.99967 amu =-1.99967 amuX/-ane.99967 amu
X = 0.518
Here is a more clear representation of the partitioning step
Solving for 10, fractional abundance
10 = 0.518
Notice that the negative signs and units cancel each other when we separate past -ane.99967 amu, hence, fractional affluence has no units
Ten= 0.518 andi – X = i-.518 = 0.482
Therefore, the fractional abundance of isotope 1 (Silver-107) is0.518 and isotope two (Silver-109) is0.482.
How to discover percent abundance
To get the percent abundance, nosotros will but multiply each fractional affluence by 100. Think that fractional abundance is calculated by dividing the percentage abundance by 100. Therefore, to go dorsum percentage abundance, nosotros multiply fractional affluence by 100. If we do, the percentage abundance for argent-107 is 0.518 x 100 =51.8%. And percent abundance for silver-109 is 0.482 ten 100 =48.two%
To larn how to calculate atomic mass using percentage abundance and isotopic masses click hither.
Source: https://masterconceptsinchemistry.com/index.php/2019/08/14/how-to-calculate-percentage-abundance-using-atomic-and-isotopic-masses/
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