Chapter 9, Problem 9.143SP

Methanol $\left(C{H}_{3}OH\right)$ is made industrially in two steps from COand H₂. It is so cheap to make that it is being considered for use as a precursor to hydrocarbon fuels, such as methane (CH₄):

step 1. $CO\left(g\right)+2H_2\left(g\right)\to C{H}_{3}OH\left(l\right)\Delta S°=+332\text{ J/K}$

step 2. $C{H}_{3}OH\left(l\right)\to C{H}_4\left(g\right){\text{=1/2O}}_2\left(g\right)\Delta S°=162\text{ J/K}$

1. Calculate 1 $\Delta H°$ in kilojoules for Step 1.
2. Calculate $\Delta G°$in kilojoules for Step 1.
3. Is step 1 spontaneous at 298 K?

Which term is more important, $\Delta H°$ or $\Delta S°$?

In what temperature range is Step 1 spontaneous?

Calculate $\Delta H°$for Step 2.

Calculate $\Delta G°$ for Step 2.

Is Step 2 spontaneous at 298 K?

Which term is more important, $\Delta H°$ or $\Delta S°$?

In what temperature range is Step 2 spontaneous?

Calculate an overall $\Delta G°$ , $\Delta H°$ , and $\Delta S°$ for the formation of CH₄ from CO and H₂.

Is the overall reaction spssontaneous at 298 K?

If you were designing a production facility, would you plan on carrying out the reactions in separate Steps or together? Explain.