Q149CP - Chemistry: Molecular Nature Of Matter And Change

Question

The two isotopes of potassium with significant abundance in nature are ³⁹K (isotopic mass 38.9637 amu, 93.258%) and ⁴¹K (isotopic mass 40.9618 amu, 6.730%). Fluorine has only one naturally occurring isotope, ¹⁹F (isotopic mass 18.9984 amu). Calculate the formula mass of potassium fluoride.

Step-by-Step Solution

Answer

The formula mass of potassium fluoride is $\mathbf{=}\mathbf{ }\mathbf{58}\mathbf{.}\mathbf{1}\mathbf{amu}$ .

Step 1: Average atomic mass

If an element has more than one isotope then its atomic mass can be calculated by taking an average of atomic mass and the natural abundance of these isotopes. The formula is given as:

 $$\begin{gathered} \mathbf{Average}\mathbf{ }\mathbf{Mass}\mathbf{ }\mathbf{=}\mathbf{Natural}\mathbf{ }\mathbf{abundance}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{isotope}\mathbf{1}\mathbf{\times }\mathbf{Mass}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{isotope}\mathbf{ }\mathbf{1} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{+}\mathbf{Natural}\mathbf{ }\mathbf{abundance}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{isotope}\mathbf{2}\mathbf{\times }\mathbf{Mass}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{isotope}\mathbf{ }\mathbf{2} \end{gathered}$$

Step 2: Calculating the formula mass of K

The average atomic mass of K can be expressed as,

 

$$\begin{gathered} \mathbf{AtomicmassofK}\mathbf{=}\frac{\mathbf{(}\mathbf{38}\mathbf{.}\mathbf{9637}\mathbf{\times }\mathbf{93}\mathbf{.}\mathbf{258}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{40}\mathbf{.}\mathbf{9618}\mathbf{\times }\mathbf{6}\mathbf{.}\mathbf{730}\mathbf{)}}{\mathbf{100}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{39}\mathbf{.}\mathbf{1} \end{gathered}$$

Step 3: Calculating the formula mass of KF

The formula mass of KF can be denoted as,

 $$\begin{gathered} \mathbf{FormulamassofK}\mathbf{=}\mathbf{atomicmassofK}\mathbf{+}\mathbf{AtomicmassofF} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{39}\mathbf{.}\mathbf{1}\mathbf{+}\mathbf{18}\mathbf{.}\mathbf{9984} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{58}\mathbf{.}\mathbf{1}\mathbf{amu} \end{gathered}$$

The formula mass of potassium fluoride is$\mathbf{58}\mathbf{.}\mathbf{1}\mathbf{amu}$  .