What is an example of an endothermic process practice problem?

1 Answer

LONG ANSWER. Here are some of the questions you could get in an endothermic process problem:

You are given the following chemical rection

#N_(2(g)) + O_(2(g)) -> 2NO_((g))#

Provide an explanaition for why this reaction is endothermic (both conceptual, and mathematical);
Is this reaction spontaneous at 298 K?
If not, at what temperature does it become spontaneous?

Data given: #DeltaH_f^@ = +90.4 "kJ/mol"# for #NO# and #DeltaS_("reaction") = 24.7 "J/K"#

Let's start with the math to get it out of the way. A reaction is said to be endothermic if its change in enthalpy, #DeltaH_("reaction")#, is positive. We can calculate this change in enthalpy from what the data provides us.

#DeltaH_("reaction") = "2 moles NO" * 90.4 (kJ)/(mol) - ("1 mole" N_2) * 0 (kJ)/(mol) - ("1 mole" O_2) * 0 (kJ)/(mol)#

#DeltaH_("reaction") = "2 moles NO" * 90.4 (kJ)/(mol) = 180.8# #"kJ#

The trick here was to be aware of the fact that the enthalpy of formation (#DeltaH_f^@#) for elements is zero.

Since #DeltaH_("reaction") >0#, the reaction is indeed endothermic.

Conceptually, this reaction is endothermic despite the fact that a bond (between #N# and #O#) is formed; this happens because the #N_2# molecule has its two atoms bonded together by a very strong triple bond, which means that more energy must be put into breaking this bond than is released when the #NO# molecule is formed.

Now, in order for a reaction to be spontaneous, the sign of #DeltaG# - the Gibbs free energy - must be negative at the given temperature.

We can therefore determine this reaction's spontaneity by using

#DeltaG_("reaction") = DeltaH_("reaction") - T * DeltaS_("reaction")#

#DeltaG_("reaction") = 180.8 * 10^3 J - 298 K * 24.71 * J/K = 173.4 kJ#

The reaction is not spontaneous at this temperature. We can determine at what temperature the reaction starts to be spontaneous by setting #DeltaG_("reaction") = 0#.

#0 = DeltaH_("reaction") - T * DeltaS_("reaction")#

#T = (DeltaH_("reaction"))/(DeltaS_("reaction")) = (180.8 * 10^3 J)/(24.71J/K) = 7317K#

This reaction becomes spontaneous at #7317# #"K"#.

As a conclusion, questions about endothermic or exothermic processes revolve around #DeltaH#, #DeltaS#, and #DeltaG# - if a reaction's spontaneity is in question.