Question

leaded gasoline, which has been phased out in the us, contains an additive to prevent engine knocking. the analysis of a particular additive compound shows that it contains carbon, hydrogen, and lead (pb)(hence the name leaded gasoline). when 53.96 g of this compound is burned in a combustion analysis apparatus, 58.87 g of co₂ and 30.08 g of h₂o are produced. determine the empirical formula of the gasoline additive.

Explanation:

Step1: Calculate moles of \(C\)

From \(CO_2\), moles of \(C=\frac{58.87\ g}{44.01\ g/mol}=1.338\ mol\) (since \(1\ mol\ CO_2\) has \(1\ mol\ C\))

Step2: Calculate moles of \(H\)

From \(H_2O\), moles of \(H = 2\times\frac{30.08\ g}{18.02\ g/mol}=3.34\ mol\) (since \(1\ mol\ H_2O\) has \(2\ mol\ H\))

Step3: Calculate mass of \(Pb\)

Mass of \(C = 1.338\ mol\times12.01\ g/mol = 16.07\ g\)
Mass of \(H=3.34\ mol\times1.008\ g/mol = 3.367\ g\)
Mass of \(Pb=53.96\ g-(16.07\ g + 3.367\ g)=34.52\ g\)
Moles of \(Pb=\frac{34.52\ g}{207.2\ g/mol}=0.1666\ mol\)

Step4: Find mole ratios

Divide each mole value by the smallest (\(0.1666\)):
\(C:\frac{1.338}{0.1666}\approx8\)
\(H:\frac{3.34}{0.1666}\approx20\)
\(Pb:\frac{0.1666}{0.1666} = 1\)

Answer:

\(PbC_8H_{20}\)