Empirical Formula Carbon Atoms Determination using Carius Method

To find the total number of carbon atoms in the empirical formula of the bromo hydrocarbon $(X)$, we first determine the mass percentages of all the constituent elements ($\text{C}$, $\text{H}$, and $\text{Br}$).

Step 1: Calculate the percentage of Bromine ($\text{Br}$)

From Carius analysis:

• Mass of organic compound $(X) = 2.0\text{ g}$
• Mass of $\text{AgBr}$ formed = $3.36\text{ g}$
• Molar mass of $\text{AgBr} = 108 + 80 = 188\text{ g mol}^{-1}$

The mass of bromine in $3.36\text{ g}$ of $\text{AgBr}$ is: $\text{Mass of Br} = 3.36\text{ g} \times \frac{80\text{ g mol}^{-1}}{188\text{ g mol}^{-1}} \approx 1.4298\text{ g}$

The mass percentage of bromine ($\%\text{Br}$) in compound $(X)$ is: $\%\text{Br} = \frac{1.4298\text{ g}}{2.0\text{ g}} \times 100 \approx 71.49\%$

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Step 2: Calculate the percentage of Hydrogen ($\text{H}$)

The compound $(X)$ is a bromo hydrocarbon, meaning it contains only $\text{C}$, $\text{H}$, and $\text{Br}$. Given that the percentage of carbon ($\%\text{C}$) is $26.7\%$: $\%\text{H} = 100\% - (\%\text{C} + \%\text{Br})$ $\%\text{H} = 100\% - (26.7\% + 71.49\%) = 1.81\%$

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Step 3: Determine the Empirical Formula

Now, calculate the molar ratio of each element by dividing their mass percentages by their respective atomic masses:

• Carbon ($\text{C}$): $\text{Moles of C} = \frac{26.7}{12} = 2.225$

• Hydrogen ($\text{H}$): $\text{Moles of H} = \frac{1.81}{1} = 1.810$

• Bromine ($\text{Br}$): $\text{Moles of Br} = \frac{71.49}{80} = 0.8936$

Divide each value by the smallest number of moles ($0.8936$):

• Relative ratio of $\text{C}$: $\frac{2.225}{0.8936} \approx 2.49 \approx 2.5$

• Relative ratio of $\text{H}$: $\frac{1.810}{0.8936} \approx 2.02 \approx 2$

• Relative ratio of $\text{Br}$: $\frac{0.8936}{0.8936} = 1$

To get the simplest whole number ratio, multiply each value by $2$:

• $\text{C} = 2.5 \times 2 = 5$
• $\text{H} = 2 \times 2 = 4$
• $\text{Br} = 1 \times 2 = 2$

Thus, the empirical formula of the compound $(X)$ is $\text{C}_5\text{H}_4\text{Br}_2$.

The total number of carbon atoms in the empirical formula is 5.