Chapter 13, Problem 101FP

The graph shows how shows how ${\Delta }_{t}G°$ varies with temperature for three different oxidation reactions: the oxidations of C(graphite), Zn, and Mg to CO, ZnO and MgO. respectively Such graphs as these can be used to show the temperatures st which carbon is an effective reducing agent to reduce metal oxides to the free metals. As a result, such graphs are important to metallurgists Use these graphs to answer the following questions.

a. Why can Mg be used to reduce ZnO to Zn at all temperatures, but Zn cannot be used to reduce MgO to Mg at any temperature?
b. Why can C be used to reduce ZnO to Zn at some temperatures but not at others? At what temperatures can carbon be used to reduce zine oxide?
c. Is it possible to produce Zn from ZnO by its direct decomposition without requiring a coupled reaction? If so, at what approximate temperatures might this occur?
d. Is it possible to decompose CO to C end ${\text{CO}}_{\text{2}}$ in a spontaneous reaction? Explain<

${\Delta }_{t}G°$ or Brae reactions as a function of temperature. The reactions are indicated by the equations written above the graphs. The points noted by arrows are the melting points (mp) and boiling points, (bp) of zinc and magnesium.

e. To the set of graphs, add straight lines representing the reactions

$\begin{array}{l}\text{C}\left(\text{graphite}\right){\text{+O}}_{\text{2}}\to {\text{CO}}_{\text{2}}\left(\text{g}\right)\\ 2\text{CO}\left(g\right)+{\text{O}}_2\to {\text{2CO}}_{\text{2}}\left(\text{g}\right)\end{array}$

given that the three lines representing the formation of oxides of carbon intersect at about 800 ^eC. [Hint: At what other temperature can you relate and temperature?] The slopes of the three lines described above differ sharply Explain why this is so—that is, explain the slope of each line in terms of principles governing Gibbs energy change.
f. The graphs for the formation of oxides of other metals are similar to the ones shown for Zn and Mg: that is. they all have positive slopes Explain why carbon is such a good reducing agent for the reduction of metal oxides.