The following diagram portrays a reaction of the type A(s) → B(g)...

Question

The following diagram portrays a reaction of the type A(s) → B(g) + C(g), where the different-colored spheres represent different molecular structures. Assume that the reaction has ∆H = +9.1 kcal/mol (+38.1 kJ/mol).

Is the reaction likely to be spontaneous at all temperatures, nonspontaneous at all temperatures, or spontaneous at some but nonspontaneous at others?

Accepted Answer

Welcome back everyone. The reaction Z solid forming X gas and gas is depicted in the following figure, assuming the reaction has an entropy change of 52.4 kg joules per mole also equivalent to 12.5 kilocalories per mole. Will the reaction be spontaneous at high temperatures? We're going to recall the following punnett square where we're going to compare on the left hand side of our punnett square entropy changes that are negative or less than zero versus entropy changes that are positive or greater than zero. And at the top of our punnett square, we're going to compare between entropy changes that are negative and entropy changes that are positive. So this is going to create our four quadrants where in our left top quadrant we're going to have when we have a entropy change that is negative and an entropy change that is negative. Our reaction is going to be spontaneous at low temperatures only. But when we have in the top right of our planet square, a entropy that is negative and entropy that is positive, we have a reaction that is spontaneous at all temperatures. On the left hand bottom portion of our punnett square. When we have an entropy change, that is positive and an entropy change that is negative, we have a reaction that is non spontaneous at all temperatures. And on the right hand bottom side of our punnett square, when we have an entropy that is positive and an entropy that is positive, we have a reaction that is spontaneous at all temperatures. So let's determine our entropy change based on our given image recall that entropy represented by the symbol S describes the disorder of a system. And we will have greatest entropy in the gaseous state versus our liquid state, which has less entropy. And the least amount of entropy will be associated with our solid state. Notice that are given illustration on the reaction side shows molecules that are ordered and are closely packed and tight knit. And so here we have a solid state for our reactant. We're on our product side, we have molecules of X and Y gas that are spaced out in gaseous form. So we have our gas phase. So because we go from solid to gas phase, on our product side, we therefore have a positive change in entropy. So we have an increase in entropy. And based on our given entropy value of 52.4 kg joules per mole, we can say that we have a positive entropy change and a positive entropy change. Because again, we went from solid to gas on our product side. And so therefore, based on our punnett square, our reaction is, and I'd just like to make a correction because I repeated that when we have a entropy change that is positive and an entropy change that is positive, our reaction should be spontaneous at high temperatures only. So our reaction is spontaneous at high temperatures. So our answer is going to be yes to our prompt. So now with this understanding, we can say that our final answer is yes, a reaction is spontaneous at high temperatures because we have a positive entropy change and a positive entropy change. So it's highlighted in yellow corresponds to choice a in the multiple choice to complete this example. I hope this helped and let us know if you have any questions.

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