Question

A process at constantandcan be described as spontaneous ifand nonspontaneous if. Over what range of temperatures is each of the following processes spontaneous? Assume that all gases are at a pressure of 1 atm. (Hint: Use Appendix D to calculateand[assumed independent of temperature and equal toand, respectively], and then use the definition of.)

(a) The rusting of iron, a complex reaction that can be approximated as

(b) The preparation offrom, a step in the manufacture of sulfuric acid:

(c) The production of the anaesthetic dinitrogen oxide through the decomposition of ammonium nitrate:

Short answer

(a)

b)

c) reaction will be spontaneous at all temperatures because is negative and is positive

Step-by-step solution

 Step 1: Given data

The reaction are given:

(a)

(b)

Concept of the spontaneous process

A spontaneous process happens when no substance or electrical energy is introduced into the system. An increase in entropy characterizes a spontaneous process in a perfectly isolated system.

 Step 3: Determination of standard enthalpy change

Standard enthalpy change is shown below:

…. (i)

where, change in enthalpy of Products and Reactants

Standard entropy change

…...(ii)

where, is change in entropy of Products and Reactants

Special temperature can be calculated as follows:

If both and are negative, the reaction will be spontaneous at temperature less than , and If is negative and is positive, then the reaction will be spontaneous at all temperature

Step 4: (a)Calculation of enthalpy change and entropy change.

Step 4: Calculate of specific temperature 

$\begin{array}{c}{\mathrm{T}}^{*}=\frac{-1648.4\mathrm{kJ}}{-549.41{\mathrm{JK}}^{-1}}\\ =\frac{-1648.4\times {10}^3\mathrm{J}}{-549.41{\mathrm{JK}}^{-1}}\\ =3000\mathrm{K}\\ \end{array}$The value of temperature can be determined as follows:

The process will be spontaneous at temperature

Step 5 (b)Calculate of change of enthalpy and entropy

Step 5 (c)Calculate of change of enthalpy and entropy