(A) At 25 C, K = 81 for the reaction A( g ) + B( g ) ? C( g ) + D( g ). Initiall

Question

(A) At 25 C, K = 81 for the reaction

A(g) + B(g) ? C(g) + D(g).

Initially, 0.100 mol of C(g) and 0.100 mol of D(g) are injected into a 1.00 L reaction vessel. What is the concentration of A(g) when the reaction has come to equilibrium at 25C?

The equation below was determined to be the best fit to a straight line for the Arrhenius plot of first-order reaction. What is the activation energy of the reaction? y =-1 1283x + 28.964 30 25 20 10 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 A. 343.3 kJ/mol B. 112.8 kJ/mol C. 135.7 kJ/mol D. 93.81 kJ/mol

Explanation / Answer

A(g) + B(g)     C(g) + D(g)

0……..0…….0.1mol….0.1 mol    (initial state)

x……..x……..0.1-x …..0.1-x         (equilibrium state)

The equilibrium constant K = [C][D]/([A][B]) = (0.1-x)2/x2 = (0.1/x – 1)2

81 = (0.1/x – 1)2

9 =0.1/x – 1

10 = 0.1/x

X = 0.01 mol = [A]

……………………………..

Arrhenius plot is

lnk = (-Ea/R) (1/T) + lnA

-Ea/R = - 11283 (see the equation of your plot, y = lnk, 28.964 = lnA, x = 1/T)

Ea = 11283 x R = 11283 x 8.314x10-3 kJ/mol = 93.81 kJ/mol

R is the constant in gas law.

Answer D.

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