Calculate $\Delta G_{\text{rxn}}$ For This Equation, Rounding Your Answer To The Nearest Whole Number.$\[ \begin{array}{l} 2 N_2(g) + O_2(g) \rightarrow 2 N_2 O(g) \\ \Delta H_{\text{Dn}} = 163.2 \, \text{kJ} \\ \Delta S_{\text{Dn}} = -148

**Calculating $\Delta G_{\text{rxn}}$: A Step-by-Step Guide**

What is $\Delta G_{\text{rxn}}$?

$\Delta G_{\text{rxn}}$ is the change in Gibbs free energy, which is a measure of the energy change that occurs during a chemical reaction. It is an important concept in thermodynamics and is used to predict the spontaneity of a reaction.

How is $\Delta G_{\text{rxn}}$ calculated?

$\Delta G_{\text{rxn}}$ can be calculated using the following equation:

$\Delta G_{\text{rxn}} = \Delta H_{\text{rxn}} - T\Delta S_{\text{rxn}}$

where:

• $\Delta H_{\text{rxn}}$ is the change in enthalpy
• $\Delta S_{\text{rxn}}$ is the change in entropy
• $T$ is the temperature in Kelvin

What is the relationship between $\Delta G_{\text{rxn}}$ and spontaneity?

If $\Delta G_{\text{rxn}}$ is negative, the reaction is spontaneous and will occur on its own. If $\Delta G_{\text{rxn}}$ is positive, the reaction is non-spontaneous and will not occur on its own.

How do we calculate $\Delta H_{\text{rxn}}$ and $\Delta S_{\text{rxn}}$?

$\Delta H_{\text{rxn}}$ can be calculated using the following equation:

$\Delta H_{\text{rxn}} = \sum \Delta H_{\text{f}}(\text{products}) - \sum \Delta H_{\text{f}}(\text{reactants})$

where:

• $\Delta H_{\text{f}}$ is the standard enthalpy of formation

$\Delta S_{\text{rxn}}$ can be calculated using the following equation:

$\Delta S_{\text{rxn}} = \sum S(\text{products}) - \sum S(\text{reactants})$

where:

• $S$ is the standard entropy

Example Problem

Calculate $\Delta G_{\text{rxn}}$ for the following equation:

$2 N_2(g) + O_2(g) \rightarrow 2 N_2 O(g)$

Given:

• $\Delta H_{\text{rxn}} = 163.2 \, \text{kJ}$
• $\Delta S_{\text{rxn}} = -148 \, \text{J/K}$

Solution

First, we need to convert $\Delta S_{\text{rxn}}$ from J/K to kJ/K:

$\Delta S_{\text{rxn}} = -148 \, \text{J/K} = -0.148 \, \text{kJ/K}$

Next, we can plug in the values into the equation:

$\Delta G_{\text{rxn}} = \Delta H_{\text{rxn}} - T\Delta S_{\text{rxn}}$

Assuming a temperature of 298 K, we get:

$\Delta G_{\text{rxn}} = 163.2 \, \text{kJ} - (298 \, \text{K})(-0.148 \, \text{kJ/K})$

$\Delta G_{\text{rxn}} = 163.2 \, \text{kJ} + 44.0 \, \text{kJ}$

$\Delta G_{\text{rxn}} = 207.2 \, \text{kJ}$

Rounding to the nearest whole number, we get:

$\Delta G_{\text{rxn}} = 207 \, \text{kJ}$

Conclusion

Calculating $\Delta G_{\text{rxn}}$ is an important step in understanding the spontaneity of a chemical reaction. By using the equation $\Delta G_{\text{rxn}} = \Delta H_{\text{rxn}} - T\Delta S_{\text{rxn}}$, we can determine whether a reaction is spontaneous or non-spontaneous. In this example, we calculated $\Delta G_{\text{rxn}}$ for the reaction $2 N_2(g) + O_2(g) \rightarrow 2 N_2 O(g)$ and found that it is non-spontaneous.

Frequently Asked Questions

• Q: What is the relationship between $\Delta G_{\text{rxn}}$ and spontaneity? A: If $\Delta G_{\text{rxn}}$ is negative, the reaction is spontaneous and will occur on its own. If $\Delta G_{\text{rxn}}$ is positive, the reaction is non-spontaneous and will not occur on its own.
• Q: How do we calculate $\Delta H_{\text{rxn}}$ and $\Delta S_{\text{rxn}}$? A: $\Delta H_{\text{rxn}}$ can be calculated using the equation $\Delta H_{\text{rxn}} = \sum \Delta H_{\text{f}}(\text{products}) - \sum \Delta H_{\text{f}}(\text{reactants})$. $\Delta S_{\text{rxn}}$ can be calculated using the equation $\Delta S_{\text{rxn}} = \sum S(\text{products}) - \sum S(\text{reactants})$.
• Q: What is the significance of $\Delta G_{\text{rxn}}$ in chemistry? A: $\Delta G_{\text{rxn}}$ is an important concept in chemistry as it helps us understand the spontaneity of a chemical reaction. It is used to predict whether a reaction will occur on its own or not.