GATE CY exam:gate PYQs & Answers — Page 52

Questions 511–520 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 52 of 65

The specific rotation of optically pure (R)-2-bromobutane is −112.00. A given sample of 2-bromobutane exhibited a specific rotation of −82.88. The percentage of (S)-(+)-enantiomer present in this sample is ________.

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Consider the following two parallel irreversible first order reactions at temperature T,

P → Q (k₁) P → R (k₂)

where k₁ and k₂ are the rate constants and their values are 5 × 10⁻² and 15 × 10⁻² min⁻¹, respectively, at temperature T. If the initial concentration of the reactant ‘P’ is 4 mol L⁻¹, then the concentration of product ‘R’ after 10 min of reaction is ______ mol L⁻¹. (Round off to two decimal places)

(Assume only P is present at the beginning of the reaction.)

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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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GATE CY exam:gate PYQs

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