Benzoic acid () is dissolved in benzene, where it undergoes partial intermolecular hydrogen bonding — Solutions and Colligative Properties Chemistry Question
Question
Benzoic acid ($C_6H_5COOH$) is dissolved in benzene, where it undergoes partial intermolecular hydrogen bonding to form dimers. If exactly $1.0\text{ mole}$ of benzoic acid is initially dissolved, and the total effective number of moles of particles (monomers + dimers) present at equilibrium is $0.504$, what is the percentage degree of association ($\% \alpha$) of the benzoic acid? (Round to one decimal place, e.g., 85.5)
💡 Solution & Explanation
The association equilibrium is $2 C_6H_5COOH \rightleftharpoons (C_6H_5COOH)_2$. If initial moles = 1, moles at equilibrium are: monomer = $1 - \alpha$, dimer = $\alpha/2$. Total moles = $1 - \alpha + \alpha/2 = 1 - \alpha/2$. We are given that the total moles = $0.504$. Therefore, $1 - \alpha/2 = 0.504 \implies \alpha/2 = 1 - 0.504 = 0.496 \implies \alpha = 0.992$. The percentage is exactly $99.2\%$.