Chemical Kinetics

The graph shows the distribution of velocities for gas molecules at three different temperatures: and .

Step 1: The curve with the highest peak corresponds to the temperature at which most molecules have velocities near the average velocity. This is because at higher temperatures, the molecules have higher average velocities.

Step 2: Looking at the graph, we can observe that: - The curve for is the highest, indicating that has the highest number of molecules at higher velocities. - The curve for lies below , showing that has a lower number of molecules at higher velocities. - The curve for is the lowest, indicating that has the least number of molecules with high velocities.

Step 3: From the above observations, we can conclude that the correct order of temperature is , which corresponds to option (1).

Step 1: Let's evaluate each statement.

Statement I: For an ideal gas, the compressibility factor is defined as: For an ideal gas, this value is 1.0, so Statement I is true.

Step 2: Now consider Statement II. The kinetic energy of a gas molecule is given by: The kinetic energy is directly proportional to temperature for a given substance. The relationship given in the question, where the kinetic energy of N_2O_4 is twice that of NO at the same temperature, is consistent with this law. So Statement II is also true.

Step 3: Statement III states that the rate of diffusion of a gas is inversely proportional to the square root of its density. This is a correct statement according to Graham's law of diffusion: Thus, Statement III is also true.

Step 4: All statements I, II, and III are true. Therefore, the correct answer is option (3), which includes statements I and III.

In a first-order reaction, the instantaneous rate of reaction is given by the equation: The slope of the graph at point C represents the rate constant , and thus, the instantaneous rate is directly related to the slope. The slope of the graph represents the rate.

Step 1: Determine the molecular formula of hydrocarbon
- Since the hydrocarbon contains 92.3\% carbon, the remaining 7.7\% is hydrogen.
- Let the molecular formula be .

Step 2: Find from given data
- The given condition states that the hydrocarbon produces moles of water, which releases 0.75 moles of with sodium.
- Since 1 mole of releases 1 mole of hydrogen atoms:
So, , leading to .

Step 3: Calculate oxygen consumption - The balanced combustion reaction:
- Molar mass of hydrocarbon = 39 g, and the oxygen required per mole is:

Step 1: For isothermal processes, the change in internal energy of an ideal gas is zero. The first law of thermodynamics gives the relationship . The work done during an isothermal irreversible process can be calculated as , which matches Statement-I. Therefore, Statement-I is correct.

Step 2: For an adiabatic process, there is no heat exchange ( ), and the change in internal energy is equal to the work done, , which matches Statement-II. Therefore, Statement-II is also correct. Thus, both Statement-I and Statement-II are correct.

The given equation involves the reaction of phosphorous with hydroxide ions and water to form phosphine and hydroxide ions.

Step 1: The conjugate acid of a base is formed when the base accepts a proton (H ).

Step 2: In the reaction, is a base because it can accept a proton to form . Therefore, the conjugate acid of is , which reacts to form hypophosphorous acid.

Step 3: From the options provided, the correct conjugate acid of is , as it is related to the reaction in the equation. Thus, the correct answer is option (2), Hypophosphorous acid.

Step 1: Understanding viscosity behavior
- Viscosity is a measure of a fluid’s resistance to flow.
- As temperature increases, the intermolecular forces weaken, decreasing viscosity.
- This applies to liquids, whereas for gases, viscosity increases with temperature due to molecular kinetic energy increase.

Step 2: Understanding viscosity units
- The SI unit of viscosity is the Pascal-second (Pa·s), which is equivalent to N·s/m²
- This can be written as: Pa·s = kg/m·s
- The given unit (kg m^-1 s^-2) is incorrect for viscosity but correct for pressure.

Step 1: Using the relation between heat and entropy
- From thermodynamics, where is heat absorbed, is temperature, and is entropy change.

Step 2: Substituting values