Q20.107CP - Chemistry: Molecular Nature Of Matter And Change

Question

A chemical reaction, such as HI forming from its elements, can reach equilibrium at many temperatures. In contrast, a phase change, such as ice melting, is in equilibrium at a given pressure only at the melting point. Each of the graphs below depicts ${\mathbf{G}}_{\mathbf{sys}}$ vs. extent of change.

(a) Which graph depicts how ${\mathbf{G}}_{\mathbf{sys}}$ changes for the formation of HI? Explain. 

(b) Which graph depicts how ${\mathbf{G}}_{\mathbf{sys}}$ changes as ice melts at $\mathbf{1}\mathbf{°}\mathbf{C}$ and 1 atm? Explain.

Step-by-Step Solution

Answer

1. Graph A is the graph that depicts how ${\text{G}}_{\text{sys}}$changes in the formation of HI.
2. Graph D is the graph which depict how ${\text{G}}_{\text{sys}}$changes as ice melts at $1^{\circ }\text{C}$ and 1 atm.

Step 1: Definition of Enthalpy

The sum of the system's internal energy and the product of its pressure and volume is enthalpy, a thermodynamic property.

Step 2: Determining which graph depicts how

a) Calculate the ${\mathrm{\Delta G}}_{\mathrm{rxn}}$for both processes - HI production and ice melting - in order to comprehend and pick the appropriate graph for each reaction.

• The chemical reaction for HI production can be written first.

${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{I}}_2\left(\mathrm{g}\right)\to 2\mathrm{HI}\left(\mathrm{g}\right)$

Calculate the reaction's Gibbs change under standard conditions ($298\mathrm{K}$),

$\begin{array}{rcl}{\mathrm{\Delta G}}_{\mathrm{rxn}}^{\mathrm{o}}& =& \sum _{}^{}{\mathrm{\Delta G}}_{\mathrm{products}}^{\mathrm{o}}-\sum _{}^{}{\mathrm{\Delta G}}_{\mathrm{reactants}}^{\mathrm{o}}\\ {\mathrm{\Delta G}}_{\mathrm{rxn}}^{\mathrm{o}}& =& \left[2\mathrm{mol}\times {\mathrm{\Delta G}}_{\mathrm{HI}\left(\mathrm{g}\right)}^{\mathrm{o}}\right]-\left[1\mathrm{mol}\times {\mathrm{\Delta G}}_{{\mathrm{H}}_2\left(\mathrm{g}\right)}^{\mathrm{o}}+1\mathrm{mol}\times {\mathrm{\Delta G}}_{\left.{\mathrm{I}}_2\left(\mathrm{g}\right)\right]}^{\mathrm{o}}\right]\\ & & \end{array}$

• Since hydrogen gas is in a standard condition, use Appendix B.

$$\begin{gathered} {\mathrm{\Delta G}}_{\mathrm{rxn}}^{\mathrm{o}}= [2\mathrm{mol}\times (1.30\mathrm{kJ}/\mathrm{mol}\left)\right]-[1\mathrm{mol}\times (0.00\mathrm{kJ}/\mathrm{mol})+1\mathrm{mol}\times (19.38\mathrm{kJ}/\mathrm{mol}\left)\right] \\ {\mathrm{\Delta G}}_{\mathrm{rxn}}^{\mathrm{o}}= -16.78\mathrm{kJ} \end{gathered}$$

The ${\mathrm{\Delta G}}_{\mathrm{rxn}}$has a value of $-16.78\mathrm{kJ}$.

As a result, it is now known that the reaction favors the product (see Figure)

In an accurate representation of this process, the end point of the blue line, symbolizing the change in Gibbs energy, should be lower than the beginning points by the end of the reaction. As a result, the B and C representations do not meet this criterion and can be ruled out of further consideration.

Because there are several equilibrium points in the Task, there should be more than one vertex to represent the equilibrium state. As a result, the representation D can be ruled out.

A is the symbol for the HI formation.

Step 3: Determining which graph depict

b) Similarly, in the case of ice melting,

${\mathrm{H}}_2\mathrm{O}\left(\mathrm{s}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$

The melting of ice is an endothermic reaction, which means that the energy comes from the environment. Because the entropy of liquid water is larger than that of ice, the entropy also rises.

As a result, the system's Gibb's energy is dependent on temperature; $0^{\mathrm{o}}\mathrm{C}$ at 1 atm, the ice would melt until equilibrium was reached. The reaction is spontaneous at temperatures above $0^{\mathrm{o}}\mathrm{C}$, and thus ${\mathrm{\Delta G}}_{\mathrm{rxn}}<0$. As a result, representations B and C may be ruled out once more.

Finally, since ice melting is only in equilibrium at the melting point at a particular pressure and temperature, the representation A can be ruled out.

D represents the melting of the ice.