Question

an organic acid is composed of carbon (54.52%), hydrogen (9.17%), and oxygen (36.32%). its molar mass is 88.11 g/mol. determine the molecular formula of the compound.

Explanation:

Step1: Assume 100g of the compound

If we assume 100g of the compound, then the mass of carbon \(m_{C}=54.52g\), the mass of hydrogen \(m_{H} = 9.17g\), and the mass of oxygen \(m_{O}=100-(54.52 + 9.17)=36.31g\)

Step2: Calculate the number of moles of each element

The molar mass of carbon \(M_{C}=12.01g/mol\), the molar mass of hydrogen \(M_{H}=1.008g/mol\), and the molar mass of oxygen \(M_{O}=16.00g/mol\)
The number of moles of carbon \(n_{C}=\frac{m_{C}}{M_{C}}=\frac{54.52g}{12.01g/mol}\approx4.54mol\)
The number of moles of hydrogen \(n_{H}=\frac{m_{H}}{M_{H}}=\frac{9.17g}{1.008g/mol}\approx9.10mol\)
The number of moles of oxygen \(n_{O}=\frac{m_{O}}{M_{O}}=\frac{36.31g}{16.00g/mol}\approx2.27mol\)

Step3: Find the simplest ratio of the number of moles

Divide each number of moles by the smallest number of moles (\(n_{O} = 2.27mol\))
For carbon: \(\frac{4.54}{2.27}\approx2\)
For hydrogen: \(\frac{9.10}{2.27}\approx4\)
For oxygen: \(\frac{2.27}{2.27} = 1\)
The empirical formula is \(C_{2}H_{4}O\)

Step4: Calculate the empirical formula mass

The empirical formula mass \(M_{empirical}=(2\times12.01 + 4\times1.008+1\times16.00)g/mol=(24.02+4.032 + 16.00)g/mol=44.052g/mol\)

Step5: Calculate the ratio of molar mass to empirical formula mass

Given the molar mass \(M = 88.11g/mol\)
\(n=\frac{M}{M_{empirical}}=\frac{88.11g/mol}{44.052g/mol}\approx2\)

Step6: Determine the molecular formula

Multiply the sub - scripts in the empirical formula by \(n\)
The molecular formula is \((C_{2}H_{4}O)\times2=C_{4}H_{8}O_{2}\)

Answer:

\(C_{4}H_{8}O_{2}\)