Element L has an average atomic mass of 54.2488 amu and is composed of two isotopes. The first has a mass of 55.2036 amu and makes up 41.030% of a standard sample. What is the mass of the second isotope?

I under how to get average atomic mass but not sure how to get the second isotope. The first mass is 22.65003708 but not sure about the second isotope. Do I subtract the first from the total?

isotope 1 = 41.030% so

isotope 2 = 100.000% - 41.030%
mass isotope 1 = 55.2036
let x = mass isotope 2.
[x(1-0.41030)] + (55.3036*0.41030) = 54.2488
Solve for x.

To determine the mass of the second isotope, you can use the concept of weighted average atomic mass. The average atomic mass is calculated by taking into account the masses and abundances of all isotopes present in a sample.

Let's break down the problem step by step:

1. We know that the average atomic mass of element L is 54.2488 amu.
2. We also know that the first isotope has a mass of 55.2036 amu and makes up 41.030% of the sample.
3. Now, let's assume that the second isotope has a mass of "x" amu. We want to find the value of "x."

To get the mass of the second isotope, we need to consider the abundance of the second isotope in relation to the first isotope.

Since the first isotope accounts for 41.030% of the sample, the abundance of the second isotope would be 100% minus 41.030%, which is 58.970%.

Since we now have the abundance of the second isotope (58.970%), we can set up the equation:

(55.2036 amu * 0.41030) + (x amu * 0.58970) = 54.2488 amu

Simplifying the equation:

22.65003708 + 0.5897x = 54.2488

To solve for x, subtract 22.65003708 from both sides:

0.5897x = 31.59876292

And then divide both sides by 0.5897:

x = 53.639943669088 amu

So, the mass of the second isotope is approximately 53.6399 amu.

Therefore, to answer your question, you do not subtract the mass of the first isotope from the total; instead, you consider the abundance of both isotopes to find the mass of the second isotope.