International Chemistry Olympiad · 2002

Problems

Problem 4Production of methanol. Methanol ( $\ce{CH3OH}$ ) is used for gasoline additives and many plastics. A factory is based on $\ce{CO + 2H2 -> CH3OH}$ ; the $\ce{H2}$ and CO are obtained by reforming $\ce{CH4 + H2O -> CO + 3H2}$ . The plant has three units: the reformer, the methanol reactor, and a separator that removes methanol from CO and $\ce{H2}$ . Positions α, β, γ, δ are: α = feed to reformer ( $\ce{CH4}$ , $\ce{H2O}$ ), β = gas entering the methanol reactor (CO, $\ce{H2}$ ), γ = stream leaving the reactor before separation (CO, $\ce{H2}$ , $\ce{CH3OH}$ ), δ = recycled/burnt excess CO and $\ce{H2}$ after the separator. The methanol flow at γ is $n(\ce{CH3OH}, \gamma) = 1000$ mol s $^{-1}$ , and the design converts 2/3 of the CO to methanol; the reformer reaction goes to completion. (4.1) Calculate the flows of CO and $\ce{H2}$ at β. (4.2) Calculate the flows of CO and $\ce{H2}$ at γ. (4.3) Calculate the flows of $\ce{CH4}$ and $\ce{H2O}$ needed at α. (4.4) All species are gaseous at γ; with total pressure $p = 10$ MPa, calculate the partial pressures of CO, $\ce{H2}$ and $\ce{CH3OH}$ at γ using $p_i = p\, n_i/n_{\mathrm{tot}}$ . (4.5) When the reactor is large enough the reaction reaches equilibrium and the partial pressures obey $K_p = \dfrac{p(\ce{CH3OH})\,p^0}{p(\ce{CO})\,p(\ce{H2})^2}$ with $p^0 = 0.1$ MPa. Calculate $K_p$ (the corresponding temperature from the graph of $\log K_p$ vs $T$ is about 630 K).Solutions: 1