2) Phosphorus trihydride (PH3) is a chemical compound that is isoelectronic with ammonia (NH3). It is a precursor in the synthesis of a variety of organophosphorus compounds that are used as insecticides and pesticides. PH3 can be formed by the following reaction: P.(g) + 6 H2(g) 5 4 PH:(g) (2.1) a) Give the expression for K, the thermodynamic equilibrium constant for the above reaction. b) Using the information below, find the numerical value for K for the above reaction. Assume T = 25. °C, the temperature at which the thermodynamic data are given. substance AH°; (kJ/mol) AG°: (kJ/mol) S° (J/mol·K) H2(g) P.(g) PH:(g) 0.0 58.9 5.4 0.0 130.6 279.9 24.5 13.4 210.1 c) If the temperature is increased to T = 50.0 °C, will the numerical value for K increase, decrease, or stay the same? Briefly justify your answer.

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**Phosphorus Trihydride (PH₃) Formation and Equilibrium**

Phosphorus trihydride (PH₃) is a chemical compound isoelectronic with ammonia (NH₃). It serves as a precursor in synthesizing various organophosphorus compounds used as insecticides and pesticides. PH₃ can be formed by the following reaction:

\[ 
\text{P}_4(g) + 6 \text{H}_2(g) \rightleftharpoons 4 \text{PH}_3(g) \quad (2.1) 
\]

**a) Expression for K, the Thermodynamic Equilibrium Constant**

To find the expression for the equilibrium constant \( K \) for the reaction:

\[ K = \frac{[\text{PH}_3]^4}{[\text{P}_4][\text{H}_2]^6} \]

**b) Calculation of Numerical Value for K**

Assume \( T = 25.0^\circ C \), the temperature at which the thermodynamic data are provided:

| Substance | \( \Delta H_f^\circ \) (kJ/mol) | \( \Delta G_f^\circ \) (kJ/mol) | \( S^\circ \) (J/mol·K) |
|-----------|---------------------------------|---------------------------------|------------------------|
| H₂(g)     | 0.0                             | 0.0                             | 130.6                  |
| P₄(g)     | 58.9                            | 24.5                            | 279.9                  |
| PH₃(g)    | 5.4                             | 13.4                            | 210.1                  |

**c) Effect of Temperature Increase on Equilibrium Constant**

**Prompt:** If the temperature is increased to \( T = 50.0^\circ C \), will the numerical value for \( K \) increase, decrease, or stay the same? Briefly justify your answer.

**Answer:** 

The equilibrium constant \( K \) is influenced by temperature changes according to the van 't Hoff equation. If the reaction is exothermic, increasing the temperature will decrease the value of \( K \). If it is endothermic, \( K \) will increase. In this case, you would apply the reaction enthalpies to determine whether the reaction is endothermic or exothermic, which is suggested by
Transcribed Image Text:**Phosphorus Trihydride (PH₃) Formation and Equilibrium** Phosphorus trihydride (PH₃) is a chemical compound isoelectronic with ammonia (NH₃). It serves as a precursor in synthesizing various organophosphorus compounds used as insecticides and pesticides. PH₃ can be formed by the following reaction: \[ \text{P}_4(g) + 6 \text{H}_2(g) \rightleftharpoons 4 \text{PH}_3(g) \quad (2.1) \] **a) Expression for K, the Thermodynamic Equilibrium Constant** To find the expression for the equilibrium constant \( K \) for the reaction: \[ K = \frac{[\text{PH}_3]^4}{[\text{P}_4][\text{H}_2]^6} \] **b) Calculation of Numerical Value for K** Assume \( T = 25.0^\circ C \), the temperature at which the thermodynamic data are provided: | Substance | \( \Delta H_f^\circ \) (kJ/mol) | \( \Delta G_f^\circ \) (kJ/mol) | \( S^\circ \) (J/mol·K) | |-----------|---------------------------------|---------------------------------|------------------------| | H₂(g) | 0.0 | 0.0 | 130.6 | | P₄(g) | 58.9 | 24.5 | 279.9 | | PH₃(g) | 5.4 | 13.4 | 210.1 | **c) Effect of Temperature Increase on Equilibrium Constant** **Prompt:** If the temperature is increased to \( T = 50.0^\circ C \), will the numerical value for \( K \) increase, decrease, or stay the same? Briefly justify your answer. **Answer:** The equilibrium constant \( K \) is influenced by temperature changes according to the van 't Hoff equation. If the reaction is exothermic, increasing the temperature will decrease the value of \( K \). If it is endothermic, \( K \) will increase. In this case, you would apply the reaction enthalpies to determine whether the reaction is endothermic or exothermic, which is suggested by
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