An element consists of two isotopes of mass 36.4681 and 43.59612 amu. If the average atomic mass of the element is 40.741 amu, calculate the percent abundance of the first isotope.
avg*100= Percent1(weight1) + (100-Percent1)weight2
40.741*100=P*364681 + (100-P)43.59612
solve for P.
To calculate the percent abundance of the first isotope, we need to follow these steps:
Step 1: Assign variables
Let's assign variables to the given information:
- Let x represent the percent abundance of the first isotope.
- Let y represent the percent abundance of the second isotope.
- Let M1 represent the mass of the first isotope.
- Let M2 represent the mass of the second isotope.
- Let AM represent the average atomic mass of the element.
Given information:
- M1 = 36.4681 amu
- M2 = 43.59612 amu
- AM = 40.741 amu
Step 2: Set up equations
The average atomic mass (AM) is calculated using the formula:
AM = (x * M1 + y * M2) / 100
We also know that x + y = 100 (% abundance of both isotopes sums up to 100).
Step 3: Solve the equations
Substituting the given values into the equation:
40.741 = (x * 36.4681 + y * 43.59612) / 100
Rearranging the equation:
40.741 = (0.364681x + 0.4359612y)
Simplifying the equation:
407.41 = 3.64681x + 4.359612y
Since x + y = 100, we can also write:
y = 100 - x
Substitute y = 100 - x into the equation:
407.41 = 3.64681x + 4.359612(100 - x)
407.41 = 3.64681x + 435.9612 - 4.359612x
Simplifying:
407.41 - 435.9612 = -0.7128029x
-28.5512 = -0.7128029x
Divide both sides by -0.7128029:
x = 40.1053
Step 4: Calculate the percent abundance
The percent abundance of the first isotope is approximately 40.1053%.