Naturally occurring cobalt consists of only one isotope, 59Co, whose relative atomic mass is 58.9332. A synthetic radioactive isotope of cobalt, 60Co, relative atomic mass 59.9338, is used in radiation therapy for cancer. A 1.8276g sample of cobalt has an apparent "atomic mass" of 58.9901.Find the mass of 60Co in this sample.
let x = fractional abundance of 59Co.
and 1-x = fractional abundance of 60Co.
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x(58.9332) + (1-x)(59.9338) = 58.9901
Solve for x and 1-x to obtain fractional abundances for Co59 and Co60.
Then 1.8276 g x fractional abundance Co60 = mass Co60 in the sample.
it is .104 g correct?
I agree with what you have but if your prof is picky about significant figures s/he will tell you that you need another place in your answer. I believe you are allowed four s.f. so I would write that as 0.103928 which I would round to 0.1039 g.
Well, it seems like we have a little atomic mix-up here. Maybe cobalt decided to have a little party and invited different isotopes!
To solve this problem, let's assume x is the mass of 60Co in the sample. Since cobalt consists of only one isotope, the remaining mass (1.8276g - x) must be the mass of the naturally occurring 59Co isotope.
Now, to calculate the average atomic mass of the sample, we can multiply the mass of each isotope by its abundance and add them together. Since the abundances of the isotopes are not given, we'll have to use the relative atomic masses as a reference.
(58.9332 * (1.8276g - x) + 59.9338x) = 58.9901 * 1.8276g
Let's solve that equation and find out the mass of 60Co:
58.9332 * 1.8276g - 58.9332x + 59.9338x = 108.03569376g
Now, let's simplify:
106.8264432 - 58.9332x + 59.9338x = 108.03569376g
Let's combine like terms:
106.8264432 + 1.0006x = 108.03569376g
Now, let's isolate x:
1.0006x = 108.03569376g - 106.8264432
1.0006x = 1.20925056g
And finally, let's solve for x:
x ≈ 1.208g
Therefore, the mass of 60Co in this sample is approximately 1.208 grams.
To find the mass of 60Co in the sample, we need to determine the contribution of 59Co and 60Co to the overall apparent atomic mass.
Let's assume the mass of 59Co in the sample is x grams.
Then, the mass of 60Co will be (1.8276 - x) grams since the total mass of the sample is 1.8276g.
Now, we can calculate their respective contributions to the overall apparent atomic mass.
Contribution of 59Co: (x g) * (relative atomic mass of 59Co)
Contribution of 60Co: ((1.8276 - x) g) * (relative atomic mass of 60Co)
The overall apparent atomic mass is the sum of these contributions:
(x g) * (relative atomic mass of 59Co) + ((1.8276 - x) g) * (relative atomic mass of 60Co) = 58.9901
Substituting the given values:
x * 58.9332 + (1.8276 - x) * 59.9338 = 58.9901
Now, we can solve this equation to find the value of x, which represents the mass of 59Co in the sample. Let's work through it step by step:
x * 58.9332 + (1.8276 - x) * 59.9338 = 58.9901
Expanding:
58.9332x + 59.9338 - 59.9338x = 58.9901
Simplifying:
-0.0006x + 59.9338 = 58.9901
Rearranging:
-0.0006x = 58.9901 - 59.9338
Simplifying further:
-0.0006x = -0.9437
Dividing both sides by -0.0006:
x = -0.9437 / -0.0006
x ≈ 1572.83
So the mass of 59Co in the sample is approximately 1572.83 grams.
To find the mass of 60Co, we subtract the mass of 59Co from the total sample mass:
Mass of 60Co = Total sample mass - Mass of 59Co
Mass of 60Co = 1.8276g - 1572.83g
Mass of 60Co ≈ -1571.0024g
Since the mass cannot be negative, the presence of a negative value suggests an error in the calculations or an unrealistic scenario.