Question

Oxygen is composed of three isotopes: oxygen-16, oxygen-17 and oxygen-18 and has an average atomic mass of 15.9982 amu. Oxygen-17 has a mass of 16.988 amu and makes up 0.032% of oxygen. Oxygen-16 has a mass of 15.972 amu and oxygen-18 has a mass of 17.970 amu. What is the percent abundance of oxygen-18?

Answer 1

The percent abundance of oxygen-18 is 1.9066%.

Step-by-step explanation:

The average atomic mass of oxygen is given by:

`m_(O) = m_(^(16)O)*\%_(16) + m_(^(17)O)*\%_(17) + m_(^(18)O)*\%_(18)`

Where:

m: is the atomic mass

%: is the percent abundance

Since the sum of the percent abundance of oxygen isotopes must be equal to 1, we have:

`1 = \%_(16) + \%_(17) + \%_(18)`

`1 = x + 3.2 \cdot 10^(-4) + \%_(18)`

`\%_(18) = 1 - x - 3.2 \cdot 10^(-4)`

Hence, the percent abundance of O-18 is:

`m_(O) = m_(^(16)O)*\%_(16) + m_(^(17)O)*\%_(17) + m_(^(18)O)*\%_(18)`

`15.9982 = 15.972*x + 16.988*3.2 \cdot 10^(-4) + 17.970*(1 - 3.2 \cdot 10^(-4) - x)`

`x = 0.980614 * 100 = 98.0614 \%`

Hence, the percent abundance of oxygen-18 is:

`\%_(18) = (1 - 3.2 \cdot 10^(-4) - 0.980614) * 100 = 1.9066 \%`

Therefore, the percent abundance of oxygen-18 is 1.9066%.

I hope it helps you!