Err chemistry...?

Question

Chlorine has two naturally occurring isotopes, Cl-35 and Cl-37. The atomic mass of chlorine is 35.45. Which of these two isotopes of chlorine is more abundant?

how would i figgure this out?

also

Consider an element Z that has two naturally occurring isotopes with the following percent abundances: the isotope with a mass number of 19.0 is 55.0% abundant; the isotope with a mass number of 21.0 is 45.0% abundant. What is the average atomic mass for element Z?

Answer 1

Atomic masses are based of the sum of abundances (percentages) of specific isotopes multiplied by their mass, meaning the the final result a kind of average. In this case, you would naturally expect this average to be close to the mass of the most abundant isotope. Therefore, since 35.45 is much closer to 35 than to 37, it can be concluded that the more abundant isotope is Cl-35.

For the second problem, set up the formula for atomic mass as described above:

.55(19) + .45(21) = 19.9

Answer 2

Imagine Cl-35 and Cl-37 both make up 50% of the population.

Find the average weight (the 35 & 37 refer to their atomic weights)

35 + 37 = 72

72 / 2 = 36

The actual average is 35.45, so there must be more of the lighter isotope to bring the average below our 50:50 marker of 36.

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Cl-35 is more abundant.

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Have a guess at the numbers!

Average of (35 + 35 + 35 + 37) = 35.5

So a pretty good estimate is 75% Cl-35 and 25% Cl-37.

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The mystery element question can be answered using the same technique. All the data you require is in the question. Remember what percent actually means!

They are telling you that out of 100 atoms (percent's meaning), 55 of them weigh 19, and 45 of them weigh 21.

Take the average of these.

Add all the weights;

55 * 19 = 1045

45 * 21 = 945

A hundred of these atoms weighs;

1045 + 945 = 1990

The average is found by dividing this by 100 (you don't divide by 2: the 1045 is the sum of 55 atoms and the 945 is the sum of 45 atoms).

1990 / 100 = 19.9

So the average atomic weight (sorry, I should be saying atomic mass) is 19.9.