A flowchart of a methanol synthesis process is shown below.
The following specifications apply to the labeled streams and process units:
A. Fresh feed $-$ a mixture of $\mathrm{CO}, \mathrm{H}_{2}, \mathrm{N}_{2},$ and $\mathrm{CO}_{2}$
B. Feed to the reactor -30.0 mole $\%$ CO $, 63.0 \% \mathrm{H}_{2}, 2.0 \% \mathrm{N}_{2},$ and $5.0 \% \mathrm{CO}_{2}$
Two reactions occur and proceed to equilibrium at $200^{\circ} \mathrm{C}$ and $4925 \mathrm{kPa}$ absolute:
C. Reactor effluent - contains all feed and product species at the reactor temperature and pressure. Species partial pressures satisfy the two given equations.
Sep1. Condenses all methanol and water in reactor effluent.
D. Liquid methanol and water. (These species will be separated by distillation in a unit not shown.)
E. Gas containing $\mathrm{N}_{2}$ and unreacted $\mathrm{CO}, \mathrm{H}_{2},$ and $\mathrm{CO}_{2}$
Sep2. Multiple-unit separation process.
F. All of the nitrogen and some of the hydrogen in Stream E.
G. Recycle stream $-\mathrm{CO}, \mathrm{CO}_{2},$ and $10 \%$ of the hydrogen fed to Sep2.
(a) Taking 100 kmol/h of Stream B as a basis of calculation, calculate the molar flow rates (kmol/h) and molar compositions of the remaining six labeled streams.
(b) The process is to be used to provide $237 \mathrm{kmol} / \mathrm{h}$ of methanol. Scale up the flowchart of Part (a) to calculate the required fresh feed rate (SCMH), the flow rate of the reactor effluent (SCMH), and the actual volumetric flow rate of the reactor effluent $\left(\mathrm{m}^{3} / \mathrm{h}\right),$ assuming ideal-gas behavior.
(c) Use the rule of thumb for a diatomic gas given in Equation $5.2-3$ to test the ideal-gas assumption at the reactor outlet. If the assumption is invalid, which of the values calculated in Part ( $b$ ) are in error?