Consider the high‐temperature decomposition equilibrium of sulfur trioxide: at

CHEMISTRY · Multi-part · A Level · Chemistry · Gaseous equilibria (Kp) · Gaseous equilibria (Kp)

Problem

Consider the high‐temperature decomposition equilibrium of sulfur trioxide:

2\,\text{SO}_{3}(g) \rightleftharpoons 2\,\text{SO}_{2}(g) + \text{O}_{2}(g)

K_{p} = 0.010

700\,\text{K}

. You will design a particulate representation of this equilibrium in a container that must contain exactly 100 gaseous particles of the three reactive species (

\text{SO}_{3}

\text{SO}_{2}

\text{O}_{2}

) combined. No inert species are present. Respond to the following prompts. (a) Write the equilibrium‐constant expression for

K_{p}

for this reaction. (b) Let

y

be the number of

\text{O}_{2}

particles in the final diagram. Using stoichiometry, express the numbers of

\text{SO}_{3}

and

\text{SO}_{2}

particles in terms of

y

such that the total particle count equals 100. (c) Substitute the expressions from part (b) into the

K_{p}

expression from part (a) and solve for the value of

y

that satisfies

K_{p} = 0.010

. Round

y

to the nearest whole number and determine the corresponding whole‐number counts of

\text{SO}_{3}

and

\text{SO}_{2}

. (d) Verify quantitatively that your particle counts reproduce the equilibrium constant within a reasonable rounding tolerance, showing all calculations. (e) Describe the principal visual differences you would expect between the regions of the diagram populated by reactant and product particles, and explain how these differences communicate the magnitude of

K_{p}

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