Calculate $\Delta G_{r \times N}$ For This 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 G_{f,

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Introduction

In chemistry, the Gibbs free energy change (Ξ”G\Delta G) is a crucial thermodynamic property that helps predict the spontaneity of a reaction. The standard Gibbs free energy change of formation (Ξ”Gf∘\Delta G_{f}^{\circ}) is a specific type of Ξ”G\Delta G that is measured under standard conditions. However, when dealing with reactions that involve multiple steps or stoichiometric coefficients, we need to calculate the Ξ”GrΓ—n\Delta G_{r \times n}, which represents the Gibbs free energy change for the reaction as written. In this article, we will guide you through the process of calculating Ξ”GrΓ—n\Delta G_{r \times n} for a given chemical equation.

Understanding the Chemical Equation

Before we dive into the calculation, let's examine the given chemical equation:

4 NH3(g)+5 O2(g)β†’4 NO(g)+6 H2O(g)4 \, \text{NH}_3(g) + 5 \, \text{O}_2(g) \rightarrow 4 \, \text{NO}(g) + 6 \, \text{H}_2\text{O}(g)

This equation represents the reaction between ammonia (NH3_3) and oxygen (O2_2) to form nitric oxide (NO) and water (H2_2O).

Calculating Ξ”GrΓ—n\Delta G_{r \times n}

To calculate Ξ”GrΓ—n\Delta G_{r \times n}, we need to follow these steps:

  1. Determine the Ξ”Gf∘\Delta G_{f}^{\circ} values: We need to find the standard Gibbs free energy change of formation for each reactant and product in the equation. These values can be found in thermodynamic tables or databases.
  2. Calculate the Ξ”GrΓ—n\Delta G_{r \times n}: Once we have the Ξ”Gf∘\Delta G_{f}^{\circ} values, we can calculate the Ξ”GrΓ—n\Delta G_{r \times n} using the following equation:

Ξ”GrΓ—n=βˆ‘Ξ½iΞ”Gf,i∘\Delta G_{r \times n} = \sum \nu_{i} \Delta G_{f,i}^{\circ}

where Ξ½i\nu_{i} is the stoichiometric coefficient of the ithi^{th} species, and Ξ”Gf,i∘\Delta G_{f,i}^{\circ} is the standard Gibbs free energy change of formation for the ithi^{th} species.

Step 1: Determine the Ξ”Gf∘\Delta G_{f}^{\circ} values

Let's assume we have the following Ξ”Gf∘\Delta G_{f}^{\circ} values for the reactants and products:

Species Ξ”Gf∘\Delta G_{f}^{\circ} (kJ/mol)
NH3_3 (g) -16.4
O2_2 (g) 0
NO (g) 86.5
H2_2O (g) -228.6

Step 2: Calculate the Ξ”GrΓ—n\Delta G_{r \times n}

Now that we have the Ξ”Gf∘\Delta G_{f}^{\circ} values, we can calculate the Ξ”GrΓ—n\Delta G_{r \times n} using the equation above:

Ξ”GrΓ—n=βˆ‘Ξ½iΞ”Gf,i∘\Delta G_{r \times n} = \sum \nu_{i} \Delta G_{f,i}^{\circ}

For the given equation, we have:

Ξ”GrΓ—n=(4Γ—βˆ’16.4)+(5Γ—0)+(4Γ—86.5)+(6Γ—βˆ’228.6)\Delta G_{r \times n} = (4 \times -16.4) + (5 \times 0) + (4 \times 86.5) + (6 \times -228.6)

Simplifying the equation, we get:

Ξ”GrΓ—n=βˆ’65.6+0+346+βˆ’1367.6\Delta G_{r \times n} = -65.6 + 0 + 346 + -1367.6

Ξ”GrΓ—n=βˆ’1087.2 kJ/mol\Delta G_{r \times n} = -1087.2 \, \text{kJ/mol}

Rounding the Answer

Since we are asked to round the answer to the nearest whole number, we can round Ξ”GrΓ—n\Delta G_{r \times n} to -1087 kJ/mol.

Conclusion

In this article, we have walked you through the process of calculating Ξ”GrΓ—n\Delta G_{r \times n} for a given chemical equation. We have determined the Ξ”Gf∘\Delta G_{f}^{\circ} values for the reactants and products, and then calculated the Ξ”GrΓ—n\Delta G_{r \times n} using the equation above. The final answer is -1087 kJ/mol, which represents the Gibbs free energy change for the reaction as written.

References

  • Thermodynamic tables: These tables provide the Ξ”Gf∘\Delta G_{f}^{\circ} values for various species.
  • Thermodynamic databases: These databases contain the Ξ”Gf∘\Delta G_{f}^{\circ} values for various species, as well as other thermodynamic properties.

Future Work

Introduction

In our previous article, we discussed the process of calculating the Gibbs free energy change for a reaction (Ξ”GrΓ—n\Delta G_{r \times n}). However, we understand that there may be many questions and concerns regarding this topic. In this article, we will address some of the most frequently asked questions about calculating Ξ”GrΓ—n\Delta G_{r \times n}.

Q: What is the difference between Ξ”Gf∘\Delta G_{f}^{\circ} and Ξ”GrΓ—n\Delta G_{r \times n}?

A: Ξ”Gf∘\Delta G_{f}^{\circ} is the standard Gibbs free energy change of formation, which is a specific type of Ξ”G\Delta G that is measured under standard conditions. On the other hand, Ξ”GrΓ—n\Delta G_{r \times n} is the Gibbs free energy change for the reaction as written, which takes into account the stoichiometric coefficients of the reactants and products.

Q: How do I determine the Ξ”Gf∘\Delta G_{f}^{\circ} values for the reactants and products?

A: You can find the Ξ”Gf∘\Delta G_{f}^{\circ} values in thermodynamic tables or databases. These tables provide the Ξ”Gf∘\Delta G_{f}^{\circ} values for various species under standard conditions.

Q: What if I don't have access to thermodynamic tables or databases?

A: In that case, you can use online resources or software that provide thermodynamic data. Some popular options include the National Institute of Standards and Technology (NIST) Webbook and the Thermodynamic Data Bank.

Q: Can I calculate Ξ”GrΓ—n\Delta G_{r \times n} for a reaction that involves multiple steps?

A: Yes, you can calculate Ξ”GrΓ—n\Delta G_{r \times n} for a reaction that involves multiple steps. However, you need to calculate the Ξ”GrΓ—n\Delta G_{r \times n} for each step separately and then sum them up to get the overall Ξ”GrΓ—n\Delta G_{r \times n} for the reaction.

Q: How does temperature affect the Ξ”GrΓ—n\Delta G_{r \times n} value?

A: Temperature can affect the Ξ”GrΓ—n\Delta G_{r \times n} value. As temperature increases, the Ξ”GrΓ—n\Delta G_{r \times n} value typically decreases. This is because the entropy change (Ξ”S\Delta S) increases with temperature, which can make the reaction more spontaneous.

Q: Can I calculate Ξ”GrΓ—n\Delta G_{r \times n} for a reaction that involves non-standard conditions?

A: Yes, you can calculate Ξ”GrΓ—n\Delta G_{r \times n} for a reaction that involves non-standard conditions. However, you need to use the appropriate thermodynamic equations and data that take into account the non-standard conditions.

Q: What is the significance of the Ξ”GrΓ—n\Delta G_{r \times n} value?

A: The Ξ”GrΓ—n\Delta G_{r \times n} value is a measure of the spontaneity of a reaction. A negative Ξ”GrΓ—n\Delta G_{r \times n} value indicates that the reaction is spontaneous, while a positive Ξ”GrΓ—n\Delta G_{r \times n} value indicates that the reaction is non-spontaneous.

Conclusion

In this article, we have addressed some of the most frequently asked questions about calculating Ξ”GrΓ—n\Delta G_{r \times n}. We hope that this article has provided you with a better understanding of the process of calculating Ξ”GrΓ—n\Delta G_{r \times n} and its significance in chemistry.

References

  • Thermodynamic tables: These tables provide the Ξ”Gf∘\Delta G_{f}^{\circ} values for various species.
  • Thermodynamic databases: These databases contain the Ξ”Gf∘\Delta G_{f}^{\circ} values for various species, as well as other thermodynamic properties.
  • National Institute of Standards and Technology (NIST) Webbook: This online resource provides thermodynamic data for various species.
  • Thermodynamic Data Bank: This online resource provides thermodynamic data for various species.

Future Work

In the future, we can explore other thermodynamic properties, such as the enthalpy change (Ξ”H\Delta H) and the entropy change (Ξ”S\Delta S), and how they relate to the spontaneity of a reaction. We can also investigate the effects of temperature and pressure on the Ξ”GrΓ—n\Delta G_{r \times n} value.