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

Answer:

The percent abundance of oxygen-18 is 1.9066%.

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:  

$m_{O} = m_{^{16}O}*\%_{16} + m_{^{17}O}*\%_{17} + m_{^{18}O}*\%_{18}$  

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

$x = 0.980614 \times 100 = 98.0614 \%$                                                              

Hence, the percent abundance of oxygen-18 is:

$\%_{18} = (1 - 3.2 \cdot 10^{-4} - 0.980614) \times 100 = 1.9066 \%$                      

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

I hope it helps you!