Q41P - Chemistry: Molecular Nature Of Matter And Change

Question

A sample of 0.600 mol of a metal M reacts completely with excess fluorine to form 46.8 g of $\mathit{M}{\mathit{F}}_{\mathbf{2}}$.
 (a) How many moles of F are in the sample of that forms?
 (b) How many grams of M are in this sample of $\mathit{M}{\mathit{F}}_{\mathbf{2}}$ 
(c) What element is represented by the symbol M?

Step-by-Step Solution

Answer

1. The moles of F is 1.2 mol.
2. The grams of M is 24 g.
3. The element is represented as Calcium (Ca).

Step 1: Calculation of the moles of F

The moles of sample is 0.600 mol. Since the chemical formula of compound is $\mathit{M}{\mathit{F}}_{\mathbf{2}}$

$\mathit{M}\mathbf{+}{\mathit{F}}_{\mathbf{2}}\mathbf{\to }\mathit{M}{\mathit{F}}_{\mathbf{2}}$

This states that 2 mol of F is equal to 0.600 mol of $\mathit{M}{\mathit{F}}_{\mathbf{2}}$

From the given data,

$$\begin{gathered} \mathbf{n}\mathbf{\left(}\mathbf{F}\mathbf{\right)}\mathbf{=}\mathbf{2}\mathbf{\times }\mathbf{n}\mathbf{\left(}{\mathbf{MF}}_{\mathbf{2}}\mathbf{\right)} \\ \mathbf{n}\mathbf{\left(}\mathbf{F}\mathbf{\right)}\mathbf{=}\mathbf{2}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{6}\mathbf{mol} \\ \mathbf{n}\mathbf{\left(}\mathbf{F}\mathbf{\right)}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{mol} \end{gathered}$$

Step 2: Determine the mass of M

The mass of M is calculated as:

$$\begin{gathered} \mathbf{m}\mathbf{\left(}\mathbf{M}\mathbf{\right)}\mathbf{=}\mathbf{m}\left({\mathrm{MF}}_2\right)\mathbf{-}\mathbf{m}\left(F\right) \\ \mathbf{m}\mathbf{\left(}\mathbf{M}\mathbf{\right)}\mathbf{=}\mathbf{46}\mathbf{.}\mathbf{8}\mathbf{g}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{\times }\mathbf{19}\mathbf{g} \\ \mathbf{m}\mathbf{\left(}\mathbf{M}\mathbf{\right)}\mathbf{=}\mathbf{46}\mathbf{.}\mathbf{8}\mathbf{g}\mathbf{-}\mathbf{22}\mathbf{.}\mathbf{8}\mathbf{g} \\ \mathbf{m}\left(M\right)\mathbf{=}\mathbf{24}\mathbf{g} \end{gathered}$$

Step 3: Determine the representation of element having symbol M

The molar mass of M is calculated as:

$$\begin{gathered} \mathbf{Molar}\mathbf{ }\mathbf{mass}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{M}\mathbf{=}\frac{\mathbf{mass}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{M}}{\mathbf{moles}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{M}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\frac{\mathbf{24}\mathbf{ }\mathbf{g}}{\mathbf{0}\mathbf{.}\mathbf{600}\mathbf{ }\mathbf{mol}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{40}\mathbf{ }\mathbf{g}\mathbf{/}\mathbf{mol} \end{gathered}$$

Thus, the element is Calcium.