5. An unknown diatomic X2 exhibits a typical phase diagram in three phases: solid, liquid, and vapor. The triple point of X2 is at 77 Torr and 122 °C. Which of the following statements concerning X2 must be true? A) X2 (€) cannot exist at a pressure of 45 Torr. B) Sublimation only occurs at temperatures above 122 °C. C) X2 (€) cannot have a vapor pressure greater than 77 Torr. D) X2 (£) cannot exist at a pressure of 1 atm. E) X2 (l) cannot exist above 122 °C.

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### Understanding Phase Diagrams: A Case Study on Diatomic \( X_2 \)

**Problem Statement:**

An unknown diatomic molecule \( X_2 \) exhibits a typical phase diagram featuring three phases: solid, liquid, and vapor. The triple point of \( X_2 \) is identified at 77 Torr and 122 °C. Given this information, which of the following statements concerning \( X_2 \) must be true?

**Options:**
- **A)** \( X_2 \) (liquid) cannot exist at a pressure of 45 Torr.
- **B)** Sublimation only occurs at temperatures above 122 °C.
- **C)** \( X_2 \) (liquid) cannot have a vapor pressure greater than 77 Torr.
- **D)** \( X_2 \) (liquid) cannot exist at a pressure of 1 atm.
- **E)** \( X_2 \) (liquid) cannot exist above 122 °C.

### Explanation:

To determine the correct statement, we need to analyze the characteristics of phase diagrams, particularly focusing on the conditions provided for \( X_2 \):

1. **Triple Point**: The triple point is where all three phases (solid, liquid, and vapor) coexist. For \( X_2 \), this occurs at 77 Torr and 122 °C.

#### Evaluation of Statements:

- **A)** \( X_2 \) (liquid) cannot exist at a pressure of 45 Torr.
  - At 45 Torr, a pressure lower than the triple point, the substance can only be in solid or gas phases. Therefore, liquid \( X_2 \) indeed cannot exist at this pressure. **A is true**.
  
- **B)** Sublimation only occurs at temperatures above 122 °C.
  - Sublimation (solid to gas phase transition) can occur at temperatures below the triple-point temperature, provided the pressure is low enough. Therefore, this statement is incorrect because sublimation can happen below 122 °C. **B is false**.
  
- **C)** \( X_2 \) (liquid) cannot have a vapor pressure greater than 77 Torr.
  - The liquid phase can exist at pressures and temperatures above the triple-point conditions, implying that vapor pressure can exceed 77 Torr when conditions permit. **C is false**.
  
- **D)** \( X_2 \
Transcribed Image Text:### Understanding Phase Diagrams: A Case Study on Diatomic \( X_2 \) **Problem Statement:** An unknown diatomic molecule \( X_2 \) exhibits a typical phase diagram featuring three phases: solid, liquid, and vapor. The triple point of \( X_2 \) is identified at 77 Torr and 122 °C. Given this information, which of the following statements concerning \( X_2 \) must be true? **Options:** - **A)** \( X_2 \) (liquid) cannot exist at a pressure of 45 Torr. - **B)** Sublimation only occurs at temperatures above 122 °C. - **C)** \( X_2 \) (liquid) cannot have a vapor pressure greater than 77 Torr. - **D)** \( X_2 \) (liquid) cannot exist at a pressure of 1 atm. - **E)** \( X_2 \) (liquid) cannot exist above 122 °C. ### Explanation: To determine the correct statement, we need to analyze the characteristics of phase diagrams, particularly focusing on the conditions provided for \( X_2 \): 1. **Triple Point**: The triple point is where all three phases (solid, liquid, and vapor) coexist. For \( X_2 \), this occurs at 77 Torr and 122 °C. #### Evaluation of Statements: - **A)** \( X_2 \) (liquid) cannot exist at a pressure of 45 Torr. - At 45 Torr, a pressure lower than the triple point, the substance can only be in solid or gas phases. Therefore, liquid \( X_2 \) indeed cannot exist at this pressure. **A is true**. - **B)** Sublimation only occurs at temperatures above 122 °C. - Sublimation (solid to gas phase transition) can occur at temperatures below the triple-point temperature, provided the pressure is low enough. Therefore, this statement is incorrect because sublimation can happen below 122 °C. **B is false**. - **C)** \( X_2 \) (liquid) cannot have a vapor pressure greater than 77 Torr. - The liquid phase can exist at pressures and temperatures above the triple-point conditions, implying that vapor pressure can exceed 77 Torr when conditions permit. **C is false**. - **D)** \( X_2 \
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