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?

1 Answer
Nov 6, 2014

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%#