The Standard Free Energy Change of Acetylene

Oct 13, 2025 by magicalceylontours.com 58 views

Understanding the Standard Free Energy Change

The standard free energy change, denoted by $\Delta G_{\text{reaction}}$ , is a measure of the spontaneity of a chemical reaction. It is a crucial concept in thermodynamics, as it helps predict whether a reaction will occur under standard conditions. In this article, we will guide you through the process of calculating the standard free energy change of a given chemical reaction.

The Given Reaction

The reaction we will be working with is:

2 \text{C}_2\text{H}_2(g) + 5 \text{O}_2(g) \rightarrow 4 \text{CO}_2(g) + 2 \text{H}_2\text{O}(g)

The Standard Free Energy Change of Acetylene

The standard free energy change of acetylene ( $\Delta G_{\text{C}_2\text{H}_2}$ ) is given as 209.2 kJ/mol.

Calculating the Standard Free Energy Change of the Reaction

To calculate the standard free energy change of the reaction, we need to use the following equation:

\Delta G_{\text{reaction}} = \sum \Delta G_{\text{products}} - \sum \Delta G_{\text{reactants}}

where $\Delta G_{\text{products}}$ and $\Delta G_{\text{reactants}}$ are the standard free energy changes of the products and reactants, respectively.

Step 1: Identify the Products and Reactants

From the given reaction, we can identify the products and reactants as follows:

Products: 4 CO2(g) and 2 H2O(g)
Reactants: 2 C2H2(g) and 5 O2(g)

Step 2: Look Up the Standard Free Energy Changes of the Products and Reactants

We need to look up the standard free energy changes of the products and reactants in a thermodynamic database or table. The standard free energy changes of the products and reactants are as follows:

$\Delta G_{\text{CO}_2}$ = -394.4 kJ/mol
$\Delta G_{\text{H}_2\text{O}}$ = -237.1 kJ/mol
$\Delta G_{\text{C}_2\text{H}_2}$ = 209.2 kJ/mol
$\Delta G_{\text{O}_2}$ = 0 kJ/mol (since O2 is an element in its standard state)

Step 3: Calculate the Standard Free Energy Change of the Reaction

Now that we have the standard free energy changes of the products and reactants, we can calculate the standard free energy change of the reaction using the equation:

\Delta G_{\text{reaction}} = \sum \Delta G_{\text{products}} - \sum \Delta G_{\text{reactants}}

Substituting the values, we get:

\Delta G_{\text{reaction}} = (4 \times -394.4 \, \text{kJ/mol}) + (2 \times -237.1 \, \text{kJ/mol}) - (2 \times 209.2 \, \text{kJ/mol}) - (5 \times 0 \, \text{kJ/mol})

Simplifying the equation, we get:

\Delta G_{\text{reaction}} = -1577.6 \, \text{kJ/mol} - 474.2 \, \text{kJ/mol} - 418.4 \, \text{kJ/mol}

\Delta G_{\text{reaction}} = -2470.2 \, \text{kJ/mol}

Conclusion

In this article, we calculated the standard free energy change of a given chemical reaction using the standard free energy changes of the products and reactants. We used the equation $\Delta G_{\text{reaction}} = \sum \Delta G_{\text{products}} - \sum \Delta G_{\text{reactants}}$ to calculate the standard free energy change of the reaction. The result is $\Delta G_{\text{reaction}} = -2470.2 \, \text{kJ/mol}$ , indicating that the reaction is non-spontaneous under standard conditions.

References

[1] Thermodynamic Data for Pure Substances, edited by I. Barin and O. Knacke, Springer-Verlag, Berlin, 1973.
[2] Thermodynamic Properties of Organic Compounds, edited by R. C. Weast, CRC Press, Boca Raton, 1982.

Note

Q: What is the standard free energy change?

A: The standard free energy change, denoted by $\Delta G_{\text{reaction}}$ , is a measure of the spontaneity of a chemical reaction. It is a crucial concept in thermodynamics, as it helps predict whether a reaction will occur under standard conditions.

Q: How do I calculate the standard free energy change of a reaction?

A: To calculate the standard free energy change of a reaction, you need to use the following equation:

\Delta G_{\text{reaction}} = \sum \Delta G_{\text{products}} - \sum \Delta G_{\text{reactants}}

where $\Delta G_{\text{products}}$ and $\Delta G_{\text{reactants}}$ are the standard free energy changes of the products and reactants, respectively.

Q: What are the standard free energy changes of the products and reactants?

A: The standard free energy changes of the products and reactants can be found in a thermodynamic database or table. For example, the standard free energy change of CO2 is -394.4 kJ/mol, and the standard free energy change of H2O is -237.1 kJ/mol.

Q: How do I look up the standard free energy changes of the products and reactants?

A: You can look up the standard free energy changes of the products and reactants in a thermodynamic database or table, such as the one provided by the National Institute of Standards and Technology (NIST).

Q: What is the unit of the standard free energy change?

A: The unit of the standard free energy change is typically kJ/mol (kilojoules per mole).

Q: What does a negative standard free energy change indicate?

A: A negative standard free energy change indicates that the reaction is spontaneous, meaning that it will occur under standard conditions.

Q: What does a positive standard free energy change indicate?

A: A positive standard free energy change indicates that the reaction is non-spontaneous, meaning that it will not occur under standard conditions.

Q: Can I calculate the standard free energy change of a reaction using a calculator?

A: Yes, you can calculate the standard free energy change of a reaction using a calculator. Simply plug in the values of the standard free energy changes of the products and reactants, and use the equation $\Delta G_{\text{reaction}} = \sum \Delta G_{\text{products}} - \sum \Delta G_{\text{reactants}}$ .

Q: Are there any limitations to calculating the standard free energy change of a reaction?

A: Yes, there are several limitations to calculating the standard free energy change of a reaction. For example, the standard free energy change of a reaction is only valid under standard conditions, and it does not take into account the effects of temperature, pressure, and other factors on the reaction.

Q: Can I use the standard free energy change of a reaction to predict the rate of the reaction?

A: No, the standard free energy change of a reaction is not a direct measure of the rate of the reaction. While a negative standard free energy change indicates that the reaction is spontaneous, it does not provide any information about the rate at which the reaction will occur.

Q: Can I use the standard free energy change of a reaction to predict the equilibrium constant of the reaction?

A: Yes, the standard free energy change of a reaction is related to the equilibrium constant of the reaction through the equation:

\Delta G_{\text{reaction}} = -RT \ln K

where $R$ is the gas constant, $T$ is the temperature in Kelvin, and $K$ is the equilibrium constant.

Q: Can I use the standard free energy change of a reaction to predict the thermodynamic properties of the reaction?

A: Yes, the standard free energy change of a reaction can be used to predict the thermodynamic properties of the reaction, such as the enthalpy change and the entropy change.