Calculating Standard Gibbs Free Energy Change For TiCl4(g) Reaction With H2O(g)

In this article, we will delve into the fascinating world of thermodynamics and apply its principles to calculate the standard reaction free energy (ΔG°) for a specific chemical reaction. The reaction we will be focusing on is the reaction between gaseous titanium tetrachloride (TiCl4(g)) and gaseous water (H2O(g)) to form solid titanium dioxide (TiO2(s)) and gaseous hydrogen chloride (HCl(g)). This reaction is represented by the following balanced chemical equation:

$$TiCl_4(g) + 2 H_2O(g) \rightarrow TiO_2(s) + 4 HCl(g)$$

The standard reaction free energy, also known as the Gibbs free energy change, is a crucial thermodynamic parameter that determines the spontaneity of a reaction under standard conditions (298 K and 1 atm). A negative ΔG° indicates that the reaction is spontaneous (favors product formation), while a positive ΔG° suggests that the reaction is non-spontaneous (requires energy input). A ΔG° of zero signifies that the reaction is at equilibrium.

To calculate the standard reaction free energy, we will utilize the thermodynamic information available in the ALEKS Data tab. ALEKS (Assessment and LEarning in Knowledge Spaces) is an adaptive learning system that often provides thermodynamic data for various chemical species. This data typically includes the standard enthalpy of formation (ΔH°f) and the standard molar entropy (S°) for each reactant and product involved in the reaction.

The standard reaction free energy can be calculated using the following equation:

$$\Delta G° = \Delta H° - T\Delta S°$$

Where:

• ΔG° is the standard reaction free energy
• ΔH° is the standard enthalpy change of reaction
• T is the temperature in Kelvin (usually 298 K for standard conditions)
• ΔS° is the standard entropy change of reaction

To determine ΔH° and ΔS°, we will use Hess's Law and the following equations:

$$\Delta H° = \sum \Delta H°_f(products) - \sum \Delta H°_f(reactants)$$

$$\Delta S° = \sum S°(products) - \sum S°(reactants)$$

Where:

• ΔH°f represents the standard enthalpy of formation for each species
• S° represents the standard molar entropy for each species

By carefully applying these equations and utilizing the thermodynamic data from ALEKS, we can accurately calculate the standard reaction free energy for the given reaction.

Before we can embark on the calculation, the first crucial step is to gather the necessary thermodynamic data for each chemical species involved in the reaction. This data typically includes the standard enthalpy of formation (ΔH°f) and the standard molar entropy (S°) for each reactant and product under standard conditions (298 K and 1 atm). As mentioned earlier, we will be utilizing the ALEKS Data tab as our primary source of this information.

The ALEKS system is a valuable resource for students as it provides a comprehensive database of thermodynamic properties for a wide range of chemical substances. To access this data, you would typically navigate to the ALEKS Data tab within the platform. The exact location and format of this data may vary slightly depending on the specific ALEKS implementation being used.

Once you have located the thermodynamic data section, you will need to carefully extract the ΔH°f and S° values for each of the following species:

• Titanium tetrachloride (TiCl4(g))
• Water (H2O(g))
• Titanium dioxide (TiO2(s))
• Hydrogen chloride (HCl(g))

The data is usually presented in a tabular format, with the chemical species listed alongside their corresponding ΔH°f and S° values. Pay close attention to the units of these values, as they are critical for accurate calculations. Standard enthalpy of formation is typically expressed in kilojoules per mole (kJ/mol), while standard molar entropy is usually given in joules per mole-kelvin (J/mol·K).

To ensure accuracy, double-check that you have correctly transcribed the values from the ALEKS Data tab. It's a good practice to create a separate table or list to organize the data for easy reference during the calculation process. For example, you might create a table like this:

Species	ΔH°f (kJ/mol)	S° (J/mol·K)
TiCl4(g)	-	-
H2O(g)	-	-
TiO2(s)	-	-
HCl(g)	-	-

Once you have successfully gathered and organized the thermodynamic data for all the species involved, you will be well-prepared to proceed with the next step, which involves calculating the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) for the reaction.

(Note: Since we do not have access to the ALEKS Data tab directly, we will use hypothetical values in the subsequent calculations for illustrative purposes. In a real-world scenario, you would replace these values with the actual data obtained from ALEKS.)

For the sake of this example, let's assume we have obtained the following data from ALEKS:

Species	ΔH°f (kJ/mol)	S° (J/mol·K)
TiCl4(g)	-804.2	354.9
H2O(g)	-241.8	188.8
TiO2(s)	-944.7	50.2
HCl(g)	-92.3	186.9

With this data in hand, we can now move on to the next step of calculating the standard enthalpy and entropy changes.

With the thermodynamic data gathered from ALEKS, our next objective is to calculate the standard enthalpy change (ΔH°) for the reaction. The standard enthalpy change represents the heat absorbed or released during a reaction under standard conditions. We can determine ΔH° using Hess's Law, which states that the enthalpy change for a reaction is independent of the pathway taken and can be calculated by summing the standard enthalpies of formation of the products and subtracting the sum of the standard enthalpies of formation of the reactants. The equation for this calculation is:

$$\Delta H° = \sum \Delta H°_f(products) - \sum \Delta H°_f(reactants)$$

Where:

• ΔH° is the standard enthalpy change of the reaction
• ΔH°f(products) represents the standard enthalpy of formation for each product, multiplied by its stoichiometric coefficient in the balanced chemical equation
• ΔH°f(reactants) represents the standard enthalpy of formation for each reactant, multiplied by its stoichiometric coefficient in the balanced chemical equation

Let's apply this equation to our reaction:

$$TiCl_4(g) + 2 H_2O(g) \rightarrow TiO_2(s) + 4 HCl(g)$$

Based on the balanced equation and the data we gathered from ALEKS, we can write:

$$\Delta H° = [1 imes \Delta H°_f(TiO_2(s)) + 4 imes \Delta H°_f(HCl(g))] - [1 imes \Delta H°_f(TiCl_4(g)) + 2 imes \Delta H°_f(H_2O(g))]$$

Now, we substitute the values from our data table:

$$\Delta H° = [1 imes (-944.7 \text{ kJ/mol}) + 4 imes (-92.3 \text{ kJ/mol})] - [1 imes (-804.2 \text{ kJ/mol}) + 2 imes (-241.8 \text{ kJ/mol})]$$

Performing the calculations:

$$\Delta H° = [-944.7 \text{ kJ/mol} - 369.2 \text{ kJ/mol}] - [-804.2 \text{ kJ/mol} - 483.6 \text{ kJ/mol}]$$

$$\Delta H° = -1313.9 \text{ kJ/mol} - (-1287.8 \text{ kJ/mol})$$

$$\Delta H° = -26.1 \text{ kJ/mol}$$

Therefore, the standard enthalpy change (ΔH°) for the reaction is -26.1 kJ/mol. This negative value indicates that the reaction is exothermic, meaning it releases heat into the surroundings.

Having determined the standard enthalpy change (ΔH°), we now shift our focus to calculating the standard entropy change (ΔS°) for the reaction. Entropy is a measure of the disorder or randomness of a system, and the standard entropy change reflects the change in disorder during a reaction under standard conditions. Similar to the enthalpy calculation, we can calculate ΔS° using the standard molar entropies (S°) of the reactants and products, following the equation:

$$\Delta S° = \sum S°(products) - \sum S°(reactants)$$

Where:

• ΔS° is the standard entropy change of the reaction
• S°(products) represents the standard molar entropy for each product, multiplied by its stoichiometric coefficient in the balanced chemical equation
• S°(reactants) represents the standard molar entropy for each reactant, multiplied by its stoichiometric coefficient in the balanced chemical equation

Applying this equation to our reaction:

$$TiCl_4(g) + 2 H_2O(g) \rightarrow TiO_2(s) + 4 HCl(g)$$

Based on the balanced equation and the standard molar entropy values from the ALEKS data, we can set up the calculation as follows:

$$\Delta S° = [1 imes S°(TiO_2(s)) + 4 imes S°(HCl(g))] - [1 imes S°(TiCl_4(g)) + 2 imes S°(H_2O(g))]$$

Now, we substitute the S° values from our data table:

$$\Delta S° = [1 imes (50.2 \text{ J/mol·K}) + 4 imes (186.9 \text{ J/mol·K})] - [1 imes (354.9 \text{ J/mol·K}) + 2 imes (188.8 \text{ J/mol·K})]$$

Performing the calculations:

$$\Delta S° = [50.2 \text{ J/mol·K} + 747.6 \text{ J/mol·K}] - [354.9 \text{ J/mol·K} + 377.6 \text{ J/mol·K}]$$

$$\Delta S° = 797.8 \text{ J/mol·K} - 732.5 \text{ J/mol·K}$$

$$\Delta S° = 65.3 \text{ J/mol·K}$$

Thus, the standard entropy change (ΔS°) for the reaction is 65.3 J/mol·K. This positive value indicates that the reaction leads to an increase in disorder or randomness in the system, which is expected as we are forming more gaseous molecules (4 moles of HCl) from fewer gaseous molecules (1 mole of TiCl4 and 2 moles of H2O) and a solid (TiO2).

With both the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) calculated, we are now in a position to determine the standard Gibbs free energy change (ΔG°) for the reaction. As mentioned earlier, the Gibbs free energy change is a crucial thermodynamic parameter that predicts the spontaneity of a reaction under standard conditions. The relationship between ΔG°, ΔH°, and ΔS° is given by the equation:

$$\Delta G° = \Delta H° - T\Delta S°$$

Where:

• ΔG° is the standard Gibbs free energy change
• ΔH° is the standard enthalpy change of the reaction
• T is the temperature in Kelvin (usually 298 K for standard conditions)
• ΔS° is the standard entropy change of the reaction

For standard conditions, the temperature (T) is typically 298 K (25 °C). We have already calculated ΔH° as -26.1 kJ/mol and ΔS° as 65.3 J/mol·K. Before we can plug these values into the equation, we need to ensure that the units are consistent. Since ΔH° is in kJ/mol, we will convert ΔS° from J/mol·K to kJ/mol·K by dividing by 1000:

$$\Delta S° = 65.3 \frac{\text{J}}{\text{mol·K}} imes \frac{1 \text{ kJ}}{1000 \text{ J}} = 0.0653 \frac{\text{kJ}}{\text{mol·K}}$$

Now we can substitute the values into the Gibbs free energy equation:

$$\Delta G° = -26.1 \text{ kJ/mol} - (298 \text{ K} imes 0.0653 \frac{\text{kJ}}{\text{mol·K}})$$

Performing the calculation:

$$\Delta G° = -26.1 \text{ kJ/mol} - 19.46 \text{ kJ/mol}$$

$$\Delta G° = -45.56 \text{ kJ/mol}$$

Rounding our answer to zero decimal places, as requested, we get:

$$\Delta G° ≈ -46 \text{ kJ/mol}$$

Therefore, the standard Gibbs free energy change (ΔG°) for the reaction is approximately -46 kJ/mol. This negative value indicates that the reaction is spontaneous or thermodynamically favorable under standard conditions, meaning it will tend to proceed in the forward direction to form products.

In this comprehensive article, we have successfully calculated the standard Gibbs free energy change (ΔG°) for the reaction between titanium tetrachloride (TiCl4(g)) and water (H2O(g)) to form titanium dioxide (TiO2(s)) and hydrogen chloride (HCl(g)). We began by gathering the necessary thermodynamic data, including standard enthalpies of formation (ΔH°f) and standard molar entropies (S°), from the ALEKS Data tab.

We then applied Hess's Law to calculate the standard enthalpy change (ΔH°) for the reaction, which turned out to be -26.1 kJ/mol, indicating an exothermic process. Next, we calculated the standard entropy change (ΔS°) as 65.3 J/mol·K, signifying an increase in disorder during the reaction.

Finally, we utilized the Gibbs free energy equation (ΔG° = ΔH° - TΔS°) to determine the standard Gibbs free energy change, which we found to be approximately -46 kJ/mol after rounding to zero decimal places. The negative value of ΔG° confirms that the reaction is spontaneous under standard conditions.

This exercise demonstrates the power of thermodynamics in predicting the feasibility and spontaneity of chemical reactions. By understanding and applying thermodynamic principles, we can gain valuable insights into the behavior of chemical systems and make informed predictions about their reactivity.

Standard Gibbs Free Energy, Thermodynamics, Enthalpy, Entropy, Chemical Reaction, ALEKS, Titanium Tetrachloride, Titanium Dioxide, Hydrogen Chloride, Spontaneity, Hess's Law