Question

what is the empirical formula for a compound containing 38.8% carbon, 16.2% hydrogen, and 45.1% nitrogen? ch₅n c₃h₁₆n₃ ch₂n c₄₀h₁₆n₄₅

Explanation:

Step1: Assume 100g of the compound

Assume we have 100g of the compound. Then, the mass of carbon (\(m_{C}\)) = \(38.8g\), the mass of hydrogen (\(m_{H}\)) = \(16.2g\), and the mass of nitrogen (\(m_{N}\)) = \(45.1g\).

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 nitrogen (\(M_{N}\)) = \(14.01g/mol\).
The number of moles of carbon (\(n_{C}\)) = \(\frac{m_{C}}{M_{C}}=\frac{38.8g}{12.01g/mol}\approx3.23mol\)
The number of moles of hydrogen (\(n_{H}\)) = \(\frac{m_{H}}{M_{H}}=\frac{16.2g}{1.008g/mol}\approx16.07mol\)
The number of moles of nitrogen (\(n_{N}\)) = \(\frac{m_{N}}{M_{N}}=\frac{45.1g}{14.01g/mol}\approx3.22mol\)

Step3: Find the mole ratio

Divide each number of moles by the smallest number of moles (\(n = 3.22mol\))
For carbon: \(\frac{3.23mol}{3.22mol}\approx1\)
For hydrogen: \(\frac{16.07mol}{3.22mol}\approx5\)
For nitrogen: \(\frac{3.22mol}{3.22mol} = 1\)

Answer:

A. \(CH_{5}N\)