Question

Question #2f1c1

Answer 1

a) `ΔG^° = "-685.5 kJ"`; spontaneous.
b) `ΔG^° =color(white)(m)"-4.8 kJ"`; spontaneous.

Explanation:

Your essential formula is:

`color(blue)(bar(ul(|color(white)(a/a)ΔG^° = ΔH^° – TΔS^°color(white)(a/a)|)))" "`

a)

`"CH"_3"OH(l)" + "1.5O"_2("g") ⇌ "CO"_2"(g)" + "2H"_2"O(g)"`

`ΔH^° = "-638.4 kJ"`

`ΔS^° = "156.9 J·K"^"-1"`

`ΔG^° = "-638.4 kJ" - 298 color(red)(cancel(color(black)("K"))) × "0.1569 kJ"·color(red)(cancel(color(black)("K"^"-1"))) = "(-638.4 - 46.8) kJ" = "-685.2 kJ"`

`ΔG < 0`, so the reaction is spontaneous.

b)

`"2NO"_2"(g)" ⇌ "N"_2"O"_4"(g)"`

`ΔH^° = "-57.2 kJ"`

`ΔS^° = "-175.9 J·K"^"-1"`

`ΔG^° = "-57.2 kJ" + 298 color(red)(cancel(color(black)("K"))) × "0.1759 kJ"·color(red)(cancel(color(black)("K"^"-1"))) = "(-57.2 + 52.4) kJ" = "-4.8 kJ"`

`ΔG < 0`, so the reaction is spontaneous.