The molar mass of HCl is 1x1 + 35.5x1 = 36.5. The given solution contains 18.25g of HCl gas. The number of moles is 18.25/36.5 = 0.5 mol. The molality is calculated by the formula

Molality (m) = No. of moles of solute / Mass of solvent in kg

Molality = 0.5/0.5 = 1m.

The average speed of gas molecules is related to the temperature and molar mass by the following formula: where:
is the average speed of the gas molecules,
is the ideal gas constant (8.314 J K mol ),
is the temperature in Kelvin,
is the molar mass of the gas in kg/mol.
Given:
Temperature ( ) = 27 C = 27 + 273.15 = 300.15 K
Molar mass of argon ( ) = 40 u = 40 g/mol = 40 10 kg/mol
Substituting these values into the formula:
Squaring this value to get the square of the average speed:
Therefore, the square of the average speed of argon gas at 27 C is approximately .
The closest value among the given options is (B) 1.59 10 .
Therefore, the answer is (B).

Step 1: Use the relation between molar enthalpy of fusion and cryoscopic constant. The formula relating the enthalpy of fusion ( ) to the cryoscopic constant ( ) is: where: - J mol K (universal gas constant), - K (freezing point of water), - K kg mol .
Step 2: Substitute the values into the equation. Approximating, we get 6 kJ/mol. Thus, the correct answer is 6 kJ/mol.

Step 1: Using the Gibbs Free Energy and Equilibrium Constant Relation
The standard Gibbs free energy change is related to the equilibrium constant by: where: - J mol K = kJ mol K ,
- K,
- kJ mol .
Step 2: Rearranging for Substituting values: Step 3: Finding
Taking the exponent: Approximating: Final Answer: The equilibrium constant is approximately , which matches Option (2).

Step 1: In a thermodynamic process, the work done is represented by the area under the curve on the P-V diagram. From the given graph, the path correctly represents the work done in the system as the area under this curve.

Step 2: The other paths do not enclose the area under the curve in the correct manner to represent the work done during this thermodynamic process. Therefore, the correct path for the work done is . Thus, the correct answer is option (3).

1. Given data:

• Initial state: atm, L, K
• Final state: atm, L, K
• Change in internal energy ( ) = 60 L-atm
• 1 L-atm = 101 J

2. Calculate the change in enthalpy ( ):

3. Convert L-atm to Joules (J):

4. Convert Joules to Kilojoules (kJ):

Therefore, the change in enthalpy of the process is 7.77 kJ.

Final Answer: 7.77 kJ.

Step 1: Analyze each process for entropy change

• : Entropy increases as gas has more disorder than liquid.
• : Entropy decreases as the number of gas molecules decreases.
• : Entropy decreases as diamond is more ordered than graphite.
• : Entropy decreases as pressure increases, reducing volume and disorder.
• : Entropy increases as the number of gas molecules increases.
• Temperature of a crystalline solid is raised from 0 K to 115 K: Entropy increases as temperature increases, increasing molecular motion.

Step 2: Count the processes with negative entropy change

Processes II, III, and IV have negative entropy changes.

Final Answer: 3

Step 1: Convert from to . Step 2: Use the relationship between and . The relationship is given by the equation: Where and .
Step 3: Solve for .
Step 4: Convert to (common logarithm).

Analysis of Each Statement:
Statement-I Analysis: A bomb calorimeter is designed to measure the change in internal energy ( ) of a reaction that occurs at constant volume. Since no work is done by volume expansion, the heat change measured represents the change in internal energy.
Statement-II Analysis: In a bomb calorimeter, the system is designed to be adiabatic, meaning that ideally, no heat is transferred to or from the surroundings during the measurement. This isolation ensures that the heat measured is only due to the reaction itself.