   # What determines ∆ S surr for a process? To calculate ∆ S surr at constant pressure and temperature, we use the following equation: ∆ S surr = −∆ H / T . Why does a minus sign appear in the equation, and why is ∆ S surr inversely proportional to temperature? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 16, Problem 3RQ
Textbook Problem
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## What determines ∆Ssurr for a process? To calculate ∆Ssurr at constant pressure and temperature, we use the following equation: ∆Ssurr = −∆H/T. Why does a minus sign appear in the equation, and why is ∆Ssurr inversely proportional to temperature?

Interpretation Introduction

Interpretation: The characteristics that determine ΔSsurr are to be stated. The significance of minus sign in the equation used for calculating ΔSsurr and the reason for its inverse relation with temperature is to be stated.

Concept introduction:

Thermodynamics is associated with heat, temperature and its relation with energy and work. It helps us to predict whether a process will take place or not. The spontaneity of the process is determined by the entropy change it produces in the universe.

To determine: The characteristics that determine ΔSsurr ; the significance of minus sign in the equation used for calculating ΔSsurr and the reason for the inverse relation of ΔSsurr with temperature.

### Explanation of Solution

The sign of ΔSsurr depends upon the direction of heat flow. In exothermic reactions, heat is flowed into the surroundings which increase the entropy of the surrounding. Therefore, ΔSsurr is positive.

For exothermic reactions, ΔSsurr is negative.

The ΔSsurr depends upon the quantity of heat transferred and inversely on temperature.

The formula to calculate ΔSsurr is,

ΔSsurr=ΔHT

Where,

• ΔH is the change in enthalpy.
• T is the temperature.

The minus sign is necessary because the sign of ΔH is determined with respect to the reaction system and the equation expresses a property of the surroundings

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