Titanium(IV) chloride can be made from titanium(IV) oxide as shown in the equation. TiO₂(s) + 2C(s) + 2Cl₂(g) → 2CO(g) + TiCl₄(l) ΔHº = -60.0 kJ mol⁻¹ Some entropy data are shown in Table 3. | Substance | Sº / J K⁻¹ mol⁻¹ | |------------|-------------------| | TiO₂(s) | 50.2 | | Cl₂(g) | 5.70 | | CO(g) | 223 | | TiCl₄(l) | 253 | Use the equation and the data in Table 3 to calculate the Gibbs free-energy change for this reaction at 989 °C. Give your answer to the appropriate number of significant figures. Use your answer to explain whether this reaction is feasible. Gibbs free-energy change ______ kJ mol⁻¹ Explanation

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Titanium(IV) chloride can be made from titanium(IV) oxide as shown in the equation - AQA - A-Level Chemistry - Question 5 - 2017 - Paper 1

Question 5

Titanium(IV) chloride can be made from titanium(IV) oxide as shown in the equation. TiO₂(s) + 2C(s) + 2Cl₂(g) → 2CO(g) + TiCl₄(l) ΔHº = -60.0 kJ mol⁻¹ Some entrop... show full transcript

Worked Solution & Example Answer:Titanium(IV) chloride can be made from titanium(IV) oxide as shown in the equation - AQA - A-Level Chemistry - Question 5 - 2017 - Paper 1

Step 1

Calculate ΔS for Reaction

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Answer

To calculate the total entropy change (ΔS) for the reaction, use the formula:

$ΔS = S_{products} - S_{reactants}$

Substituting the values from Table 3:

$ΔS = [2(Sº_{CO}) + Sº_{TiCl₄}] - [Sº_{TiO₂} + 2Sº_{Cl₂}]$

This results in:

$ΔS = [2(223) + 253] - [50.2 + 2(5.70)]$

Calculating this gives:

$ΔS = [446 + 253] - [50.2 + 11.4]$

$ΔS = 699 - 61.6 = 637.4 ext{ J K}^{-1} ext{ mol}^{-1}$

Convert this to kJ:

$ΔS = 0.6374 ext{ kJ K}^{-1} ext{ mol}^{-1}$

Step 2

Calculate Gibbs Free-Energy Change (ΔG)

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Answer

To calculate the Gibbs free-energy change (ΔG), the equation is:

$ΔG = ΔH - TΔS$

Where:

ΔH = -60.0 kJ mol⁻¹ (given)
T = 989 °C = 1262 K (conversion from Celsius to Kelvin: T(K) = T(°C) + 273)
ΔS = 0.6374 kJ K⁻¹ mol⁻¹ (calculated above)

Now substitute the values into the equation:

$ΔG = -60.0 - (1262 * 0.6374)$

Calculating this:

$ΔG = -60.0 - 804.5 = -864.5 ext{ kJ mol}^{-1}$

Considering significant figures, we round ΔG to -864 kJ mol⁻¹.

Step 3

Explain feasibility of the reaction

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Answer

The reaction is feasible since the Gibbs free-energy change (ΔG) is negative:

$ΔG = -864 ext{ kJ mol}^{-1} < 0$

A negative ΔG indicates that the reaction occurs spontaneously under the given conditions (at 989 °C). Therefore, the formation of titanium(IV) chloride from titanium(IV) oxide and the other reactants is thermodynamically favored.

Titanium(IV) chloride can be made from titanium(IV) oxide as shown in the equation - AQA - A-Level Chemistry - Question 5 - 2017 - Paper 1

Worked Solution & Example Answer:Titanium(IV) chloride can be made from titanium(IV) oxide as shown in the equation - AQA - A-Level Chemistry - Question 5 - 2017 - Paper 1

Calculate ΔS for Reaction

Calculate Gibbs Free-Energy Change (ΔG)

Explain feasibility of the reaction

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