Calculate $\Delta G_{\text{rxn}}$ For The Following Equation, Rounding Your Answer To The Nearest Whole Number.$\[ \begin{array}{l} 4 \text{NH}_3(g) + 5 \text{O}_2(g) \rightarrow 4 \text{NO}(g) + 6 \text{H}_2 \text{O}(g) \\ \Delta

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

$\Delta G_{\text{rxn}}$, also known as the standard Gibbs free energy change, 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. In this article, we will calculate $\Delta G_{\text{rxn}}$ for the given equation.

The Given Equation

The given equation is:

$$4 \text{NH}_3(g) + 5 \text{O}_2(g) \rightarrow 4 \text{NO}(g) + 6 \text{H}_2 \text{O}(g)$$

Step 1: Write the Balanced Equation

The first step in calculating $\Delta G_{\text{rxn}}$ is to write the balanced equation. The given equation is already balanced, so we can proceed to the next step.

Step 2: Look Up the Standard Gibbs Free Energy Values

To calculate $\Delta G_{\text{rxn}}$, we need to look up the standard Gibbs free energy values for each species in the equation. These values are typically found in a thermodynamic database or a reference book.

Species	$\Delta G^{\circ}$ (kJ/mol)
NH$_3(g)$	-16.4
O$_2(g)$	0
NO(g)	86.5
H$_2$O(g)	-228.6

Step 3: Calculate $\Delta G_{\text{rxn}}$

Now that we have the standard Gibbs free energy values, we can calculate $\Delta G_{\text{rxn}}$ using the following equation:

$$\Delta G_{\text{rxn}} = \sum \nu \Delta G^{\circ}$$

where $\nu$ is the stoichiometric coefficient of each species in the equation.

For the given equation, we have:

$$\Delta G_{\text{rxn}} = (4 \times \Delta G^{\circ}(\text{NH}_3(g)) + 5 \times \Delta G^{\circ}(\text{O}_2(g))) - (4 \times \Delta G^{\circ}(\text{NO}(g)) + 6 \times \Delta G^{\circ}(\text{H}_2 \text{O}(g)))$$

Substituting the values, we get:

$$\Delta G_{\text{rxn}} = (4 \times -16.4 + 5 \times 0) - (4 \times 86.5 + 6 \times -228.6)$$

Simplifying the equation, we get:

$$\Delta G_{\text{rxn}} = -65.6 - 346 + 1368.6$$

$$\Delta G_{\text{rxn}} = 957.0 \text{ kJ/mol}$$

Rounding the Answer

The final step is to round the answer to the nearest whole number. Rounding 957.0 to the nearest whole number, we get:

$$\Delta G_{\text{rxn}} = 957 \text{ kJ/mol}$$

Conclusion

In this article, we calculated $\Delta G_{\text{rxn}}$ for the given equation using the standard Gibbs free energy values. We found that the value of $\Delta G_{\text{rxn}}$ is 957 kJ/mol. This value indicates that the reaction is highly exothermic and is likely to be spontaneous.

References

• [1] Thermodynamic Data for Pure Substances, edited by I. Barin and O. Knacke, Springer-Verlag, Berlin, 1973.
• [2] Gibbs Free Energy of Formation, edited by J. F. Counsell, CRC Press, Boca Raton, 1990.

Discussion

The calculation of $\Delta G_{\text{rxn}}$ is an important step in understanding the thermodynamics of a reaction. By calculating the standard Gibbs free energy change, we can predict the spontaneity of a reaction and determine the energy change that occurs during the reaction.

In this article, we used the standard Gibbs free energy values to calculate $\Delta G_{\text{rxn}}$ for the given equation. We found that the value of $\Delta G_{\text{rxn}}$ is 957 kJ/mol, indicating that the reaction is highly exothermic and is likely to be spontaneous.

The calculation of $\Delta G_{\text{rxn}}$ is a useful tool in chemistry and is used in a variety of applications, including the design of chemical reactions and the prediction of reaction outcomes.

Limitations

The calculation of $\Delta G_{\text{rxn}}$ has several limitations. One limitation is that the standard Gibbs free energy values are typically measured at standard temperature and pressure (STP), which may not be the same as the conditions of the reaction. Additionally, the calculation of $\Delta G_{\text{rxn}}$ assumes that the reaction is at equilibrium, which may not always be the case.

Future Work

Future work in this area could involve the development of new methods for calculating $\Delta G_{\text{rxn}}$ that take into account the non-equilibrium conditions of the reaction. Additionally, the calculation of $\Delta G_{\text{rxn}}$ could be used to predict the reaction outcomes of complex reactions, such as those involving multiple reactants and products.

Conclusion

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

A: $\Delta G_{\text{rxn}}$ is the standard Gibbs free energy change, which is a measure of the energy change that occurs during a chemical reaction.

Q: Why is $\Delta G_{\text{rxn}}$ important?

A: $\Delta G_{\text{rxn}}$ is important because it can predict the spontaneity of a reaction. If $\Delta G_{\text{rxn}}$ is negative, the reaction is spontaneous. If $\Delta G_{\text{rxn}}$ is positive, the reaction is non-spontaneous.

Q: How do I calculate $\Delta G_{\text{rxn}}$?

A: To calculate $\Delta G_{\text{rxn}}$, you need to look up the standard Gibbs free energy values for each species in the reaction. Then, you can use the following equation:

$$\Delta G_{\text{rxn}} = \sum \nu \Delta G^{\circ}$$

where $\nu$ is the stoichiometric coefficient of each species in the reaction.

Q: What are the standard Gibbs free energy values?

A: The standard Gibbs free energy values are typically found in a thermodynamic database or a reference book. They are usually listed in units of kJ/mol.

Q: Can I use $\Delta G_{\text{rxn}}$ to predict the reaction outcome?

A: Yes, you can use $\Delta G_{\text{rxn}}$ to predict the reaction outcome. If $\Delta G_{\text{rxn}}$ is negative, the reaction is likely to be spontaneous. If $\Delta G_{\text{rxn}}$ is positive, the reaction is likely to be non-spontaneous.

Q: What are the limitations of $\Delta G_{\text{rxn}}$?

A: The limitations of $\Delta G_{\text{rxn}}$ include:

• The standard Gibbs free energy values are typically measured at standard temperature and pressure (STP), which may not be the same as the conditions of the reaction.
• The calculation of $\Delta G_{\text{rxn}}$ assumes that the reaction is at equilibrium, which may not always be the case.

Q: Can I use $\Delta G_{\text{rxn}}$ to design chemical reactions?

A: Yes, you can use $\Delta G_{\text{rxn}}$ to design chemical reactions. By calculating the standard Gibbs free energy change, you can predict the spontaneity of a reaction and determine the energy change that occurs during the reaction.

Q: What are some common applications of $\Delta G_{\text{rxn}}$?

A: Some common applications of $\Delta G_{\text{rxn}}$ include:

• Predicting the spontaneity of a reaction
• Determining the energy change that occurs during a reaction
• Designing chemical reactions
• Understanding the thermodynamics of a reaction

Q: Can I use $\Delta G_{\text{rxn}}$ to predict the reaction rate?

A: No, you cannot use $\Delta G_{\text{rxn}}$ to predict the reaction rate. The reaction rate is determined by the kinetics of the reaction, not the thermodynamics.

Q: What are some common mistakes to avoid when calculating $\Delta G_{\text{rxn}}$?

A: Some common mistakes to avoid when calculating $\Delta G_{\text{rxn}}$ include:

• Using the wrong standard Gibbs free energy values
• Failing to account for the stoichiometric coefficients
• Assuming that the reaction is at equilibrium
• Failing to consider the non-equilibrium conditions of the reaction

Q: Can I use $\Delta G_{\text{rxn}}$ to predict the reaction outcome in a non-equilibrium system?

A: No, you cannot use $\Delta G_{\text{rxn}}$ to predict the reaction outcome in a non-equilibrium system. The calculation of $\Delta G_{\text{rxn}}$ assumes that the reaction is at equilibrium, which may not always be the case.

Q: What are some future directions for research in $\Delta G_{\text{rxn}}$?

A: Some future directions for research in $\Delta G_{\text{rxn}}$ include:

• Developing new methods for calculating $\Delta G_{\text{rxn}}$ that take into account the non-equilibrium conditions of the reaction
• Investigating the relationship between $\Delta G_{\text{rxn}}$ and the reaction rate
• Developing new applications for $\Delta G_{\text{rxn}}$ in fields such as materials science and biotechnology.