Calculate ΔSsurr at the indicated temperature for each...

Calculate $\Delta S_{\text {surr }}$ at the indicated temperature for each reaction. a. $\Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{~kJ} ; 298 \mathrm{~K}$ b. $\Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{~kJ} ; 77 \mathrm{~K}$ c. $\Delta H_{\mathrm{rxn}}^{\circ}=+114 \mathrm{~kJ} ; 298 \mathrm{~K}$ d. $\Delta H_{\mathrm{rxn}}^{\circ}=+114 \mathrm{~kJ} ; 77 \mathrm{~K}$

Calculate $\Delta S_{\text {surr }}$ at the indicated temperature for each reaction.
a. $\Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{~kJ} ; 298 \mathrm{~K}$
b. $\Delta H_{\mathrm{rxn}}^{\circ}=-385 \mathrm{~kJ} ; 77 \mathrm{~K}$
c. $\Delta H_{\mathrm{rxn}}^{\circ}=+114 \mathrm{~kJ} ; 298 \mathrm{~K}$
d. $\Delta H_{\mathrm{rxn}}^{\circ}=+114 \mathrm{~kJ} ; 77 \mathrm{~K}$

Key Concepts

Sign Conventions in Thermodynamics

Understanding the sign conventions is essential for interpreting thermodynamic processes. A negative enthalpy change indicates an exothermic reaction, which releases heat to the surroundings, typically leading to an increase in their entropy, while a positive enthalpy change indicates an endothermic process, absorbing heat and generally decreasing the surroundings' entropy. These conventions help in predicting the spontaneity of a reaction when combined with entropy considerations.

Enthalpy Change of Reaction

Enthalpy or heat of reaction represents the total heat absorbed or released during a chemical reaction under constant pressure. It is a key factor in determining how much energy is exchanged with the surroundings and is directly used in calculating the entropy change of the surroundings. The sign of the enthalpy change (exothermic or endothermic) affects the direction of heat flow.

Entropy Change of the Surroundings

This concept involves calculating the change in entropy for the surroundings during a chemical process. It is determined by the amount of heat exchanged with the environment divided by the temperature at which the exchange occurs, typically expressed as ?S_surroundings = -q_rev/T. This is crucial for understanding how the environment’s disorder changes in response to the system's reaction.

Temperature Dependence in Thermodynamic Calculations

Temperature is a critical variable in thermodynamic equations, specifically in the context of calculating entropy changes. The relationship ?S = -?H/T shows how the same enthalpy change can lead to different entropy changes depending on the temperature at which the reaction occurs. This illustrates the inverse dependence of entropy change on temperature.

Transcript

00:01 In this problem, we're going to discuss how to find the entropy of the surroundings, only given information about the system.

00:09 This equation that you'll be needing is found in section 19 .5 of your book, and it basically states that the delta s of the surroundings, which is usually the opposite sign of the system, can be found by taking the negative delta h or, enthalpy of the system divided by the temperature in kelvin.

00:35 It's important that this is in kelvin.

00:40 And yeah, so the delta s of the surroundings is going to be the opposite sign of the delta s in the system, which is why you are flipping the sign of the enthalpy.

00:56 So for a, all we have to do, all we have to say is that the delta h we're given, for the system is 385 kilojoules.

01:12 And then we just divide that by temperature, which is also given to us in kelvin, so 298k.

01:20 And so we're given, and so it's going to be 1 .29 kilojoules per kelvin, and we're going to put this into joules to make it easier.

01:34 12, 1 ,290.

01:37 Joules per kelvin.

01:40 And that's the answer for the first one.

01:43 And we, i just have to repeat this pretty much the same process over the next four of them.

01:50 As the, uh, and also i forgot to put this, i made this positive because it was, this original value was actually, uh, negative 385.

02:06 So i just, i just flipped the sign.

02:08 I just didn't show it.

02:09 Um, all right.

02:11 Next one.

02:12 Delta s of the surroundings is equal to we're given the same entalpy this time i'll explicitly put it down um the sign change there just to make it easier but we're given a different temperature this time still in kelvin and uh and what we'll find is that the answer is going to be five kilojoules per kelvin or 5 000 joules per kelvin and c you're going to do a similar thing.

02:52 I think we're given some different values this time...

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