Calculate Δ G Rxn \Delta G_{\text{rxn}} Δ G Rxn ​ For This Equation, Rounding Your Answer To The Nearest Whole Number.$[ \begin{array}{l} 2 , \text{N}_2(g) + \text{O}_2(g) \rightarrow 2 , \text{N} 2\text{O}(g) \ \Delta H {\text{rxn}} = 163.2 ,

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Introduction

In chemistry, the calculation of $\Delta G_{\text{rxn}}$ (Gibbs free energy change) is a crucial step in understanding the spontaneity of a reaction. The Gibbs free energy change is a measure of the energy change that occurs during a reaction, taking into account the enthalpy change ($\Delta H_{\text{rxn}}$), entropy change ($\Delta S_{\text{rxn}}$), and temperature ($T$). In this article, we will calculate $\Delta G_{\text{rxn}}$ for the nitrogen dioxide reaction, which is given by the equation:

$$2 \, \text{N}_2(g) + \text{O}_2(g) \rightarrow 2 \, \text{N}_2\text{O}(g)$$

Given Information

The given information for this reaction is:

• $\Delta H_{\text{rxn}} = 163.2 \, \text{kJ/mol}$
• $T = 298 \, \text{K}$ (standard temperature)
• $\Delta S_{\text{rxn}}$ is not given, but we will calculate it using the standard entropy values of the reactants and products.

Calculating $\Delta S_{\text{rxn}}$

To calculate $\Delta S_{\text{rxn}}$, we need to know the standard entropy values of the reactants and products. The standard entropy values are given in units of J/mol·K. We will use the following values:

• $\Delta S^{\circ}(\text{N}_2(g)) = 191.5 \, \text{J/mol·K}$
• $\Delta S^{\circ}(\text{O}_2(g)) = 205.0 \, \text{J/mol·K}$
• $\Delta S^{\circ}(\text{N}_2\text{O}(g)) = 215.1 \, \text{J/mol·K}$

Using the formula for $\Delta S_{\text{rxn}}$, we get:

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

$$\Delta S_{\text{rxn}} = 2 \times 215.1 \, \text{J/mol·K} - (2 \times 191.5 \, \text{J/mol·K} + 205.0 \, \text{J/mol·K})$$

$$\Delta S_{\text{rxn}} = 430.2 \, \text{J/mol·K} - 487.0 \, \text{J/mol·K}$$

$$\Delta S_{\text{rxn}} = -56.8 \, \text{J/mol·K}$$

Calculating $\Delta G_{\text{rxn}}$

Now that we have the values of $\Delta H_{\text{rxn}}$ and $\Delta S_{\text{rxn}}$, we can calculate $\Delta G_{\text{rxn}}$ using the formula:

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

$$\Delta G_{\text{rxn}} = 163.2 \, \text{kJ/mol} - (298 \, \text{K}) (-56.8 \, \text{J/mol·K})$$

$$\Delta G_{\text{rxn}} = 163.2 \, \text{kJ/mol} + 16.96 \, \text{kJ/mol}$$

$$\Delta G_{\text{rxn}} = 180.16 \, \text{kJ/mol}$$

Rounding the Answer

The problem asks us to round our answer to the nearest whole number. Therefore, we round $\Delta G_{\text{rxn}}$ to the nearest whole number:

$$\Delta G_{\text{rxn}} = 180 \, \text{kJ/mol}$$

Conclusion

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Q: What is the significance of calculating $\Delta G_{\text{rxn}}$ for a reaction?

A: Calculating $\Delta G_{\text{rxn}}$ is crucial in understanding the spontaneity of a reaction. A negative $\Delta G_{\text{rxn}}$ value indicates a spontaneous reaction, while a positive value indicates a non-spontaneous reaction.

Q: What is the formula for calculating $\Delta G_{\text{rxn}}$?

A: The formula for calculating $\Delta G_{\text{rxn}}$ is:

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

Q: What is the difference between $\Delta H_{\text{rxn}}$ and $\Delta G_{\text{rxn}}$?

A: $\Delta H_{\text{rxn}}$ is the enthalpy change of a reaction, which is a measure of the energy change that occurs during a reaction. $\Delta G_{\text{rxn}}$ is the Gibbs free energy change of a reaction, which takes into account the enthalpy change, entropy change, and temperature.

Q: How do you calculate $\Delta S_{\text{rxn}}$?

A: To calculate $\Delta S_{\text{rxn}}$, you need to know the standard entropy values of the reactants and products. You can use the formula:

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

Q: What is the standard entropy value of a gas?

A: The standard entropy value of a gas is typically given in units of J/mol·K. For example, the standard entropy value of nitrogen gas (N2) is 191.5 J/mol·K.

Q: Can you give an example of how to calculate $\Delta G_{\text{rxn}}$ using the formula?

A: Yes, let's use the example of the nitrogen dioxide reaction:

$$2 \, \text{N}_2(g) + \text{O}_2(g) \rightarrow 2 \, \text{N}_2\text{O}(g)$$

Given:

• $\Delta H_{\text{rxn}} = 163.2 \, \text{kJ/mol}$
• $T = 298 \, \text{K}$
• $\Delta S_{\text{rxn}} = -56.8 \, \text{J/mol·K}$

Using the formula:

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

$$\Delta G_{\text{rxn}} = 163.2 \, \text{kJ/mol} - (298 \, \text{K}) (-56.8 \, \text{J/mol·K})$$

$$\Delta G_{\text{rxn}} = 163.2 \, \text{kJ/mol} + 16.96 \, \text{kJ/mol}$$

$$\Delta G_{\text{rxn}} = 180.16 \, \text{kJ/mol}$$

Q: What is the final answer for $\Delta G_{\text{rxn}}$?

A: The final answer for $\Delta G_{\text{rxn}}$ is 180 kJ/mol.

Q: Can you summarize the key points of calculating $\Delta G_{\text{rxn}}$?

A: Yes, the key points of calculating $\Delta G_{\text{rxn}}$ are:

• Calculate $\Delta H_{\text{rxn}}$ and $\Delta S_{\text{rxn}}$
• Use the formula: $\Delta G_{\text{rxn}} = \Delta H_{\text{rxn}} - T \Delta S_{\text{rxn}}$
• Take into account the standard entropy values of the reactants and products
• Round the answer to the nearest whole number