Calculate the free energy change for this reaction at 25 °C. Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.) 2 Ca(s) + O2( g) → 2 CaO(s) ΔH° rxn = -1269.8 kJ; ΔS° rxn = -364.6 J/K

Video transcript

Hey, everyone and welcome back to another video. Calculate the free energy change for this reaction at 48 °C is the reaction spontaneous. Assume that all reactants and products are in their standard states. The reaction is two moles of calcium react with one mole of oxygen to produce two moles of calcium oxide. The entropy change of the reaction is negative 1269.8 kilojoules. And the entropy change of this reaction is negative 364.6 joules per gallon. The four answer choices are a zero kilojoules equilibrium B 2583.1 kilojoules, non spontaneous c negative 1152.8 kilojoules spontaneous and the 1928.2 kilojoules spontaneous. So first of all, let's recall that the Gibbs free energy change formula states that the free energy change is equal to the entropy change of the reaction minus the absolute temperature multiplied by the entropy change of the reaction. And in this case, we want to get our absolute temperature converting 48 °C into Kelvin. So we are going to add 273.15 Kelvin, which gives us 321 Kelvin as the temperature for this reaction. So now, all that we have to do now is just substitute the given variables. We're going to start with the entropy change negative 1269.8 kilojoules and subtract 321. Kelvin multiplied by the entropy change. But we want to make sure that our units are kilojoules per Kelvin. So we're going to move our decimal three positions to the left to account for this conversion. And we will get negative zero point 3646 kilojoules per Calvin. If we perform the calculations, we end up with negative 1152.8 kilojoules. Now, the very last question, is it spontaneous? Well, the answer is yes. And now finally, how do we know? Well, that's based on the negative sign of the gibbs free energy. If it's negative, the reaction is spontaneous. If it's positive, it's not spontaneous. If it's zero, the reaction is at equilibrium. And based on our answer, we can conclude that C is the correct option. That would be it for today. And thank you for watching.