Gas Laws

Step 1: Partial Pressures of and - Total pressure = 1 atm. - , .

Step 2: Henry's Law and Mole Fractions Hence,

Step 3: Ratio of to Thus, the ratio of the mole fractions is .

In order to determine which elements from the given list have half-filled f-orbitals in their ground state, let's first examine the electronic configurations of the f-block elements. The key to understanding this is recognizing that some elements, particularly in the lanthanide and actinide series, have half-filled or fully filled f-orbitals due to their electron configuration.

Step 1: Analyze Electron Configurations

• Eu (Z = 63): Europium has the electron configuration . The configuration is a half-filled f-orbital configuration, meaning it has 7 electrons in the 4f subshell, which is half of the possible 14 electrons that can fill the 4f subshell.
• Sm (Z = 62): Samarium has the electron configuration . Although the 4f orbital is not completely filled, it is close to a half-filled configuration with 6 electrons in the 4f subshell. However, it is not strictly half-filled as it only has 6 electrons (while half of 14 is 7).
• Cm (Z = 96): Curium has the electron configuration . Similar to Europium, Curium has a configuration, which is half-filled.
• Pu (Z = 94): Plutonium has the electron configuration . Here, the 5f orbital is not half-filled because it has only 6 electrons in the 5f subshell, not 7.
• Gd (Z = 64): Gadolinium has the electron configuration , which is another half-filled f-orbital configuration. Gd has 7 electrons in the 4f subshell.
• Cf (Z = 98): Californium has the electron configuration . It does not have a half-filled f-orbital, as its 5f orbital is completely filled with 10 electrons.

Step 2: Identify Elements with Half-Filled f-Orbitals From the above analysis, the following elements have half-filled f-orbitals in their ground state:

• Eu (Z = 63) with
• Gd (Z = 64) with
• Cm (Z = 96) with

Step 3: Conclusion Thus, the correct answer is:

Step 1: Evaluating Each Statement
- Statement I: Conjugate base of chloric acid
- Chloric acid ( ) ionizes as:
- The conjugate base is , not .
- Statement I is incorrect.
- Statement II: as a Lewis Acid
- has an incomplete octet (6 valence electrons on Al).
- It accepts electron pairs, making it a Lewis acid.
- Statement II is correct.
- Statement III: Conjugate base of
- is a weak base; its conjugate acid is .
- The conjugate base of is .
- Statement III is correct.

Step 2: Conclusion Only Statements II and III are correct. Thus, the correct answer is II, III only.

Step 1: Use the Ideal Gas Equation
The ideal gas equation is: where: - is the pressure (1 atm), - is the volume, - is the number of moles, - is the universal gas constant ( L atm mol K ), - is the temperature (300 K).

Step 2: Express Volume as a Function of
Rearranging the equation: Since , K, and atm:

Step 3: Identify the Slope
The equation is in the form: where (the slope) is 24.6 L mol .

Step 4: Verify the Correct Answer
Thus, the slope of the graph is L mol , which matches Option (2).