GATE CY format:nat PYQs & Answers — Page 13

Questions 121–130 of 166. Imported answers require independent review unless marked reviewed.

Topic practice 166 questionsPage 13 of 17

Consider the following equilibrium

At 298 K, the standard molar Gibbs energies of formation, ΔfG°, of SO₂(g) and SO₃(g) are −300 and −371 kJ mol⁻¹, respectively. The value of the equilibrium constant, Kₚ, at this temperature is ______ × 10¹⁰. (Round off to the nearest integer)

(Gas constant R = 8.31 J mol⁻¹ K⁻¹)

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Consider the electrochemical cell

M(s)|M₂(s)|M₂(aq)|M(s)

where ‘M’ is a metal. At 298 K, the standard reduction potentials are E°M²⁺(aq)/M(s) = −0.12 V, E°M₂(s)/M(s) = 0.36 V and the temperature coefficient is (∂E°cell/∂T)ₚ = 1.5 × 10⁻⁴ V K⁻¹. At this temperature the standard enthalpy change for the overall cell reaction, ΔrH°, is ______ kJ mol⁻¹. (Round off to two decimal places)

(Faraday constant F = 96500 C mol⁻¹)

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The normal boiling point of a compound (X) is 350 K (heat of vaporization, ΔvapH = 30 kJ mol⁻¹). The pressure required to boil ‘X’ at 300 K is ______ Torr. (Round off to two decimal places)

(Ignore the temperature variation of ΔvapH; Gas constant R = 8.31 J mol⁻¹ K⁻¹ and 1 atm = 760 Torr)

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For a bimolecular gas phase reaction P + Q → R, the pre-exponential factor is 1 × 10¹³ dm³ mol⁻¹ s⁻¹. The standard entropy of activation at 25 °C is ______ J K⁻¹ mol⁻¹. (Round off to two decimal points)

(The standard concentration c° = 1 mol dm⁻³, Planck constant h = 6.62 × 10⁻³⁴ J s; Boltzmann constant kB = 1.38 × 10⁻²³ J K⁻¹; Gas constant R = 8.31 J mol⁻¹ K⁻¹)

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Character table of point group D₈ is given below.

D₈	E	2C₈	2C₄	2C₈³	C₂	4C₂′	4C₂″
A₁	a	1	1	1	1	1	1
A₂	b	1	1	1	1	h	i
B₁	c	−1	1	−1	1	1	j
B₂	d	−1	1	−1	1	−1	1
E₁	e	√2	0	−√2	−2	0	0
E₂	f	0	−2	0	k	0	0
E₃	g	−√2	0	√2	−2	0	0

Value of (a + b + c + d + e + f + g + h + i + j + k) is equal to ________

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, where

and

are spin angular momentum operators and

is spin up eigen function, then the value of ‘a’ is ________. (Round off to one decimal place)

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A particle in one dimensional box of length

with potential energy

is perturbed by the potential

eV, where

is a constant. The 1st order correction to the 1st excited state of the system is __________ ×

eV.

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Consider a two dimensional harmonic oscillator with angular frequency

. The wavelength of x polarized light required for the excitation of a particle from its ground state to the next allowed excited state is ________ ×

m. (Round off to one decimal place)

(Speed of light

)

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The molar heat capacity of a substance is represented in the temperature range 298 K to 400 K by the empirical relation

, where b is a constant. The molar enthalpy change when the substance is heated from 300 K to 350 K is 2 kJ mol⁻¹. The value of b is __________ J K⁻² mol⁻¹. (Up to two decimal places)

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For low partial pressure of ozone (O₃), the adsorption of ozone on graphite surface is fully dissociative in nature, and follows Langmuir isotherm. Under these conditions, the dependence of the surface coverage of graphite (θ) on partial pressure of ozone (P₍O₃₎) is given by θ ∝ (P₍O₃₎)ˣ, the value of x is____________. (Up to two decimal places)

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GATE CY format:nat PYQs

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