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Correct choice is (a) \(\frac {de_{VIB}}{dt} = \frac {1}{τ}\)(e\(_{vib}^{EQ}\) – evib)

Best explanation: The vibrational rate equation gives a RELATION between evib which is the time rate change with the difference between the equilibrium and the local instantaneous NON – equilibrium value (e\(_{vib}^{eq}\) – evib). It is given by the following relation which is a differential equation:

\(\frac {de_{vib}}{dt} = \frac {1}{τ}\)(e\(_{vib}^{eq}\) – evib)

The correct ANSWER is (b) 7.91

To elaborate: Given, KF = 1.85 × 10^-4 , kb= 2.34 × 10^-5

The EQUILIBRIUM constant based on concentrations for non – equilibrium is same as derived for the equilibrium condition SINCE it relates the forward and reverse rate constants. It is given by:

kc = \(\frac {k_f}{k_b}\)

Substituting the values, we get,

kc = \(\frac {1.85 × 10^{- 4}}{2.34 × 10^{- 5}}\) = 7.91

The CORRECT OPTION is (a) Number of transitions PER particle per second

Explanation: The COLLISION frequency (Z) when multiplied with the transition probability (Pi, i + 1) yield the number of transitions per particle per second. Since the collision frequency is the number of collisions taking place per particle and the transition probability gives the number of transitions taking place per collision per particle.

Right option is (d) High TEMPERATURE, low pressure

Best explanation: Molecular collision FREQUENCY is directly proportional to the pressure of the molecule and inversely proportional to the square root of the temperature. Therefore, for OBTAINING low collision frequency, the pressure should be low and the temperature should be high.

Correct answer is (d) Dissociative – recombination reaction of nitrogen and oxygen

Easy explanation: The reaction taking place below 9000 K for the formation of nitric OXIDE are dissociation reaction and BIMOLECULAR exchange reaction ALSO KNOWN as shuffle reaction. They are as follows:

Correct ANSWER is (a) True

For explanation: When a molecule undergoes a translation-vibration transfer also known as T – V transfer, molecules tend to lose or gain vibrational energy. This energy is reflected in the form of an increase or DECREASE in the KINETIC energy of the molecule UNDERGOING collision.

Correct choice is (B) Decreases

Explanation: The molecular COLLISION frequency (Z) is given by the relation:

Z ∝ \(\FRAC {p}{\sqrt {T}}\)

THEREFORE, molecular collision frequency is inversely proportional to the square root of temperature which means that as the temperature INCREASES, collision frequency decreases.

The CORRECT CHOICE is (a) Molecular COLLISION frequency

To EXPLAIN: The amount of time taken by the molecules for collision depends on the molecular collision frequency. Thus parameter tells how many collisions take PLACE with a neighboring particle in a second for a single particle.

Right choice is (b) Kinetic ENERGY between the molecules

The EXPLANATION is: For a molecule to become vibrationally excited, it has to undergo several NUMBER of collisions which is affected by the kinetic energy PRESENT between these colliding particles. HIGHER kinetic energy results in higher gas temperature which eventually leads to lesser number of collisions required for the molecule to become vibrationally excited.

Right option is (b) No change in chemical composition spontaneously

To EXPLAIN: In a mixture of gases (AIR), when there is no SUDDEN change in the chemical composition spontaneously or over a short period of TIME, the SYSTEM is known to be in chemical equilibrium. There are no changes in temperature, velocity, pressure in the system.

Right ANSWER is (c) Oxygen is dissociated COMPLETELY, nitrogen begins to dissociate

The explanation: Up to 2500 K, there is no reaction taking place and oxygen starts to dissociated. At 4000 K, oxygen gets completely dissociated and nitrogen begins the PROCESS of DISSOCIATION. The reaction is as follows:

The correct answer is (b) Even number

To explain: There are certain atoms and molecules which have even number (2, 4, 6, ..) of ELEMENTARY particles (quarks, leptons) that OBEY Bose – Einstein statistical distribution. These particles are KNOWN as Bosons.

Right choice is (c) Total pressure is EQUAL to sum of partial pressures

The EXPLANATION: Dalton’s LAW of partial pressure was formulated to FIND out the total pressure of the chemically reactive mixture. This is the sum of partial pressures of individual components in the mixture. Dalton’s law is only applicable or perfect gases which means that the INTERMOLECULAR forces between individual molecules is negligible.

The correct answer is (C) Reverse reaction

Easiest explanation: The reaction quotient gives the same expression as the equilibrium constant for a reaction that is at CHEMICAL equilibrium. But, for a reaction when the reaction quotient (Q) is GREATER than the equilibrium constant (k), there’s more PRODUCT than the reactant and reverse reaction takes place.

The correct choice is (a) True

For EXPLANATION I would say: At higher temperatures, the MOLECULES are spread over different STATES in several energy levels but the same trend is not observed at lower temperatures. At temperatures below 5K, molecules are NEAR or at the ground STATE thus making it overly populated.

Correct option is (b) False

To EXPLAIN: While analyzing the chemical composition of AIR at normal temperature and pressure, the major composition is of oxygen and nitrogen molecules. Presence of water vapor, argon, helium ETC. are very less THUS they can be neglected. Although, at higher temperature (2500K – 9000K), oxygen and nitrogen undergo chemical reaction and there is presence of O, N, NO, NO^+ etc.

Right option is (b) Temperature

Explanation: The vibrational motion of the molecules becomes significant by absorbing some of the energy that would otherwise GO into the translational and rotational molecular motion as the temperature of a diatomic or polyatomic GAS is raised above normal conditions. The EXCITATION of vibrational energy, ALLOWS the specific heat to become a function of temperature function making it THERMALLY perfect rather than calorically perfect.

Correct option is (c) Temperature and volume

Best EXPLANATION: The partition function Q is ALSO known as the state sum. It is defined by the formula:

Q = ∑jgje\(^{- \frac {ε_j^{‘}}{KT}}\)

This partition function has its USE in statistical thermodynamics and is a function of both temperature and volume.

Correct option is (a) Energy when GAS is at ABSOLUTE zero

The explanation: The MOLECULE’s ground state refers to the energy that the molecule WOULD have if the gas were theoretically at absolute zero temperature. Therefore, the values for the translational, rotational, vibrational, and electronic modes are often referred to as zero – point ENERGIES.

Right ANSWER is (a) True

Best explanation: Electrons revolve around the NUCLEUS of an atom which makes up the molecule. This molecule POSSESSES ELECTRICAL energy. This is a result of TWO factors – kinetic energy due to translation motion and potential energy.

The correct option is (C) Less than 1

Explanation: Transition PROBABILITY is the probability that a molecule will jump to ANOTHER i + 1 level after the molecular COLLISION. The transition of the molecule moving to a higher energy level requires several number of collisions. This probability value is ALWAYS less than 1.

Right answer is (a) ATOMS break away from molecular structure

Easiest explanation: At HIGHER temperature molecules dissociate or ionize depending on the temperature RANGE. Dissociation is a process where the atoms which are a part of the molecule break away from the molecular structure. This leads to the gas BECOMING highly chemically reactive.

The correct option is (a) \(\FRAC {dN_i}{DT}\) = Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1 – Pi, i + 1 ZNi – Pi, i – 1 ZNi

The EXPLANATION: The rate of CHANGE of population of the molecules in i^th level is computed by adding rate of increase of NI (population of i^th level) and rate of decrease of Ni. Thus the formula is:

\(\frac {dN_i}{dt}\) = Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1 – Pi, i + 1 ZNi – Pi, i – 1 ZNi

Where, Pi + 1, i ZNi + 1 + Pi – 1, i ZNi – 1 is the rate of increase of population in i^th level due to the molecules jumping up from i – 1 and down from i + 1 levels.

Pi, i + 1 ZNi – Pi, i – 1 ZNi is the rate of decrease of population in the i^th level due to the molecules jumping from i^th level to i + 1 and i – 1 levels.

The correct answer is (b) False

The EXPLANATION: For studying MODERN compressible flow, the ASSUMPTION of calorically perfect has is not valid at high temperature because the gases become highly reactive. The molecules of the gas vibrate as the temperature rises causing deviation from the calorically perfect gas BEHAVIOR.

Right choice is (b) Partial temperature

For explanation I would say: There are several WAYS to describe the composition of air which is at a CHEMICAL equilibrium. These are – partial fraction, CONCENTRATION, mole fraction, mole – mass fraction and mass fraction. These HELP in determining the composition of the reacting GAS.

Correct option is (B) False

To explain I WOULD say: The reaction between hydrogen and oxygen molecule to form water molecule involves a SERIES of chemical reactions instead of one single step. THUS, it is not an elementary chemical reaction.

The correct choice is (B) Distribution of molecules at DIFFERENT ENERGY levels

To ELABORATE: The Boltzmann distribution is a probability distribution of how molecules are at different energy levels. It is given by:

N\(_j^*\) = N\(\frac {g_j e^{- \frac {ε_j^{‘}}{kT}}}{∑_jg_j e^{ – \frac {ε_j^{‘}}{kT}}} \)

Where, ε\(_j^{‘}\) is total energy

gj are the degenerate states

N are the number of molecules

The correct ANSWER is (B) False

To explain: Boltzmann distribution helps in ANALYZING the ENERGY state εj in which the molecule or atom lies within a system of N – molecules. This distribution is provided for a system of molecules/atoms which is in thermodynamic equilibrium.

Right choice is (b) 3

The explanation is: For a diatomic molecule having translation ENERGY, there are three thermal degrees of freedom. This energy is at the center of mass PRESENT due to the translation kinetic energy. The velocity components are in X, y, Z direction of the Cartesian space.

The correct OPTION is (b) 2

The best explanation: CO2 is a linear POLYATOMIC molecule that has similar properties as the diatomic molecule having rotational kinetic energy. The MOMENT of inertia for the molecule in z – axis is negligible SMALL compared to x and y – axis. Due to this reason, diatomic and even linear polyatomic molecules have only two thermal degrees of freedom.