A gaseous molecule (g) decomposes on a clean metal surface at 400 K by the overall…

CHEMISTRY · Multi-part · AP · Chemistry · Kinetics · Kinetics

Problem

A gaseous molecule

X_2

(g) decomposes on a clean metal surface at 400 K by the overall reaction

X_2

(g)

\to

2\,X

(g). Experimental studies show the following elementary steps occur on the surface, where

*

represents a free site: 1.

X_2

(g) +

*

\rightleftharpoons

X_2^*

(ads) 2.

X_2^*

(ads)

\to

2\,X^*

(ads) (rate-determining) 3.

X^*

(ads)

\rightleftharpoons

X

(g) +

*

Initial-rate data collected at 400 K are listed below.

$P_{X_2}$ (mbar)	Initial rate $r_0$ (mol m $^{-2}$ s $^{-1}$ )
10	$5.2 \times 10^{-6}$
25	$1.3 \times 10^{-5}$
50	$2.4 \times 10^{-5}$

Assume that adsorption in step 1 is quasi-equilibrated and that each surface site can hold at most one adsorbate. (1) Part 1: (a) Derive an expression for the initial rate

r_0

in terms of the intrinsic surface rate constant

k_s

for step 2, the equilibrium adsorption constant

K_{\text{ads}}

for step 1, the partial pressure

P_{X_2}

, and the total number of surface sites

N_s

. (2) Part 2: (b) Use the data in the table to determine a numerical value for

K_{\text{ads}}

at 400 K. Show all reasoning and clearly state any additional assumptions you make. (3) Part 3: (c) Predict the initial rate when

P_{X_2}

is increased to 80 mbar, keeping temperature and total site density unchanged. Provide your answer in mol m

^{-2}

^{-1}

. (4) Part 4: (d) A trace impurity

Y

(g) adsorbs competitively on the same sites with an equilibrium constant

K_Y

that is one-tenth of

K_{\text{ads}}

. Qualitatively discuss how a

5\,\text{mbar}

partial pressure of

Y

will alter the rate you predicted in part (c) and justify your reasoning with reference to surface coverage.

Related theory

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