Question

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process?

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

Option 4

Answer 2

For the Haber process

$$\ce{N2(g) + 3H2(g) -> 2NH3(g)}$$

we know that the reaction is exothermic so that $\Delta H^\circ_R < 0$ and, because the number of moles of gas decreases, $\Delta S^\circ_R < 0$. Under standard approximations these values are nearly temperature‐independent. Consequently:

• $\Delta H^\circ_R$ (being negative) stays almost constant (with a slight warming effect due to heat capacity differences).

• $\Delta S^\circ_R$ (being negative) is nearly constant.

• $\Delta G^\circ_R = \Delta H^\circ_R - T\Delta S^\circ_R$ will thus vary predominantly as a linear function of temperature.

• Graphs that plot $-\Delta H^\circ_R/T$ and $-\Delta G^\circ_R/T$ should show decreasing trends with temperature since the denominators increase.

Among the options, Graph 4 shows:

• $\Delta H^\circ_R$ starts negative and increases slightly (i.e. becomes less negative).

• $\Delta S^\circ_R$ is maintained constant at about –180.

• $-\Delta G^\circ_R/T$ and $-\Delta H^\circ_R/T$ decrease slightly with temperature.

This behavior correctly reflects the thermodynamic variations expected for the Haber process.