Question

Cl-35 has an atomic weight of `"34.9689` and Cl-37 has an atomic weight of `"36.9695`. What is the percent abundance of Cl-35?

Answer 1

The percent abundance of Cl-35 = 76.0%.

Explanation:

The percent abundance of chlorine-35 and chlorine-37 must equal 100, or, in decimal form 1.

Given/Known:

atomic weight of Cl-35`=` `"34.9689`

atomic weight of Cl-37`=` `"36.9695`

atomic weight of chlorine`=` `"35.45`

Unknown:

`x="abundance of Cl-35"`

`1-x="abundance of Cl-37"`

SOLUTION:

1. Set up the equation as follows:

`(34.9689)x + (36.9695)(1-x) = 35.45`

2. Carry out multiplication.

`34.9689x + 36.9695 - 36.9695x = 35.45`

3. Combine the x values.

`-2.0006x + 36.9695 = 35.45`

4. Subtract 36.9695 from both sides.

`-2.0006x = - 1.52`

(rounded to two decimal places due to significant figure rounding rules for addition and subtraction)

5. Divide both sides by -2.0006 to calculate abundance.

`x = 0.760`

(rounded to three significant figures due to rounding rules for multiplication and division)

`1 - 0.760 = 0.240`

(In this case 1 is an exact number, which has an infinite number of significant figures, so significant figures are dependent upon `0.760`, which has three decimal places.)

6. Multiply abundance times `100%` to get percent abundance.

`"% abundance of Cl-35"` is `0.760xx100% = 76.0%`

`"% abundance of Cl-37"` is `0.24xx100% = 24.0%`