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The rate expression for a heterogenous catalytic reaction is given by, - rA = K.KA PA(1 + KA.PA + Kr.PR), where K is surface reaction rate constant and KA and KR are absorption equilibrium constants of A and R respectively. If KR PR >> (1 + KA PA), the apparent activation energy EA is equal to (given E is the activation energy for the reaction and ΔHR and ΔHA are the activation energies of adsorption of R and A)
V1, V2, V3 and V4 are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4 cm respectively. Some statements regarding these volumes are given below :
(i) V1 + V2 + 2V3 4
(ii) V1 + 4V2 + V3 4
(iii) 2(V1 + V3) + V2 = V4
Which of these statements area correct ?
Letx(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, P3, P4.
Properties
P1 : Linear but NOT time-invariant
P2 : Time-invariant but NOT linear
P3 : Linear and time-invariant
Relations
R1 : y(t) = t2x(t)
R2 : y(t) = t |x(t)|
R3 : y(t) = |x(t)|
R4 : y(t) = x(t - 5)
Given,
3H2 + CO = CH4 + H2O, KP = 101.84 and 4H2 + CO2 = CH4 + 2H2O, KP = 101.17
the KP for the reaction CO + H2O = CO2 + H2 is
Pick out the wrong statement below:
I. For the same conversion, the holding time required in a batch reactor, is always equal to the space time required in a PFR.
II. Two mixed reactors of unequal size are available for producing a specified product, formed by a homogenous second order reaction. To achieve maximum production rate, the smaller reactor should be placed in series before the larger reactor.
III. Arrehenius equation describing the effect of temperature on rate constant is given by, $${\text{K}} = {\text{A}}.{{\text{e}}^{ - \frac{{{\text{Ea}}}}{{{\text{RT}}}}}}$$
IV. The mechanism for the decomposition of CH3CHO into CH4 and CO in presence of I2 is:
CH3CHO + I2 → CH3I + HI + CO; slow
CH3I + HI → CH4 + I2; fast
Then the rate of disappearance CH3CHO is equal to K.CCH3l.CHl and acts as a catalyst.
Consider the following system of equations in three real variables x1, x2 and x3
2x1 - x2 + 3x3 = 1
3x1 - 2x2 + 5x3 = 2
-x1 - 4x2 + x3 = 3
This system of equations has
Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations σ1, σ2 respectively. Consider Y = X1 - X2; μ1 = μ2 = 1, σ1 = 1, σ2 = 2, Then,
Let $$\overrightarrow {\bf{L}} $$ = (Lx, Ly, Lz) denotes the orbital angular momentum operators of a particle and let L+ = Lx + i Ly and L- = Lx - i Ly. The particle is in aneigen state of L2 and Lz eigen values $${\hbar ^2}\left( {l + 1} \right)$$   and $$\hbar l$$  respectively. The expectation value of L+L- in this state is
In the hydrodealkylation of toluene to benzene, the following reactions occur:
C7H8 + H2 → C6H6 + CH4
2C6H6 ⇋ C12H10 + H2
Toluene and hydrogen are fed to a reactor in a molar ratio 1 : 5.80% of the toluene gets converted and the selectivity of benzene (defined as moles of benzene formed/moles of toluene converted) is 90%. The fractional conversion of hydrogen is
There are 4 consecutive odd numbers (x1, x2, x3 and x4) and three consecutive even numbers (y1, y2 and y3). The average of the odd numbers is 6 less than the average of the even numbers. If the sum of the three even numbers is 16 less than the sum of the four odd numbers, what is the average of x1, x2, x3 and x4?