Q3.143CP - Chemistry: Molecular Nature Of Matter And Change

Question

Ferrocene, synthesized in 1951, was the first organic iron compound with bonds. An understanding of the structure of ferrocene gave rise to new ideas about chemical bonding and led to the preparation of many useful compounds. In the combustion analysis of ferrocene, which contains only and a 0.9437-g sample produced 2.233 g of and 0.457 g of What is the empirical formula of ferrocene?

Step-by-Step Solution

Answer

The empirical formula of the ferrocene is $Fe{C}_{10}{H}_{10}.$ 

Step 1: Write the combustion equation of ferrocene.

When ferrocene is heated in presence of oxygen, it gives carbon dioxide and water. The combustion equation of ferrocene is:

$C_x{H}_{y}F{e}_z\left(s\right)+O_2\left(g\right)\to C{O}_2\left(g\right)+H_{2}O\left(l\right)$

Step 2: Relation between mass and number of moles

The number of moles is calculated by the mass and Molar mass. The relationship between the number of moles, mass, and molar mass is given below.

$\text{Number} \text{of} \text{moles = }\frac{\text{mass}}{\text{Molar} \text{mass}}$

Step 3: Calculate the number of moles of carbon dioxide

The mass of ${\text{CO}}_{\text{2}}$= 2.233 g

The molar mass of ${\text{CO}}_{\text{2}}$ = 44.02 g/mol

The number of moles of CO₂ is calculated as:

$\begin{array}{rcl}moles of C{O}_2& =& \frac{mass of C{O}_2}{Molar mass of C{O}_2}\\ & =& \frac{2.233 g}{44.02 g/mol}\\ & =& 0.0507 mol\end{array}$

Step 4: Calculate the number of moles of Carbon

In$C{O}_2,$ 1 mol ofcarbonatom is present.

So, the number of moles ofcarbon is:

$\begin{array}{rcl}1 mol of C{O}_2& =& 1 mol of C\\ 0.0507 mol of C{O}_2& =& 0.0507 mol of C\\ & & \end{array}$

Step 5: Calculate the mass of carbon

The molar mass of carbon = 12.01 g/mol

Thus, the mass of carbon is:

$\begin{array}{rcl}mass of C& =& moles of C\times molar mass of C\\ & =& 0.0507 mol\times 12.01 g/mol\\ & =& 0.6089 g\\ & & \\ & & \end{array}$

Step 6: Calculate the number of moles of H2O

The mass of  H₂O= 0.457 g

The molar mass of H₂O = 18.02 g/mol

The number of moles of H₂Ois calculated as:

$\begin{array}{rcl}moles of H_{2}O& =& \frac{mass of H_{2}O}{Molar mass of H_{2}O}\\ & =& \frac{0.457 g}{18.02 g/mol}\\ & =& 0.0254 mol\\ & & \\ & & \end{array}$

Step 7: Calculate the number of moles of Hydrogen

In H2O two moles of atoms are present.

So, the number of moles of is:

$\begin{array}{rcl}1 mol of H_{2}O& =& 2 mol of H\\ 0.0254 mol of H_{2}O& =& 0.0254\times 2 mol of H\\ & & \end{array}$

Step 8: Calculate the mass of Hydrogen

The molar mass of H = 1.01 g/mol

Thus, the mass of H is:

$\begin{array}{rcl}mass of H& =& moles of H\times molar mass of H\\ & =& 0.0254\times 2 mol\times 1.01 g/mol\\ & =& 0.0513 g\end{array}$

Step 9: Calculate the mass of Fe

The given mass of the sample = 0.9437 g.

So, the mass of Fe is

$\begin{array}{rcl}mass of Fe& =& mass of sample-mass of C-mass of H\\ & =& 0.9437 g-0.6089 g-0.0513 g\\ & =& 0.2835 g\end{array}$

Step 10: Calculate the number of moles of Fe

The molar mass of  = 55.845 g/mol

The number of moles of Fe is calculated as:

$\begin{array}{rcl}moles of Fe& =& \frac{mass of Fe}{Molar mass of Fe}\\ & =& \frac{0.2835 g}{55.845 g/mol}\\ & =& 0.0051 mol\end{array}$

Step 11: Determine the ratio of moles of Fe,C and H atoms

The ratio of Fe,Cand Hatoms is

$$\begin{gathered} Fe : C : H \\ 0.0051 :0.0507:0.0508 \end{gathered}$$

Divide this ratio by 0.0051, we get

$$\begin{gathered} Fe : C : H \\ 1 :10 :10 \end{gathered}$$

Thus, the value of x,y and z are 10,10, and 1.

Step 12: Determine the empirical formula of the sample

The empirical formula is the simplest whole-number ratio of atoms present in that particular compound. Thus, the empirical formula of the ferrocene is $Fe{C}_{10}{H}_{10}.$