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Stoichiometry - Engineering

Q1:

Saturated solution of benzene in water is in equilibrium with a mixture of air and vapours of benzene and water at room temperature and pressure. Mole fraction of benzene in liquid is xB and the vapour pressures of benzene and water at these conditions are pvB and pvw respectively. The partial pressure of benzene in air-vapour mixture is

A PvB

B xB.PvB

C (Patm - Pvw)xB

D xB.Patm

ANS:B - xB.PvB

In this scenario, benzene is dissolved in water to form a saturated solution. At equilibrium, the benzene molecules will exert a vapor pressure (PvB) while in the vapor phase. According to Raoult's Law, the partial pressure of a component in the vapor phase above a solution is proportional to its mole fraction in the solution. Raoult's Law states: 𝑃vap=𝑥⋅𝑃vappurePvap​=x⋅Pvappure​ Where:

  • 𝑃vapPvap​ is the vapor pressure of the component in the solution,
  • 𝑥x is the mole fraction of the component in the liquid phase,
  • 𝑃vappurePvappure​ is the vapor pressure of the pure component.
In this case, the partial pressure of benzene in the air-vapor mixture will be 𝑥𝐵×𝑃vappurexB​×Pvappure​. Since benzene is in equilibrium with the air-vapor mixture, the vapor pressure of benzene (𝑃vappurePvappure​) is equal to the partial pressure of benzene in the air-vapor mixture. So, the correct expression for the partial pressure of benzene in the air-vapor mixture is 𝑥𝐵⋅𝑃𝑣𝐵xB​⋅PvB​.