Two elementary gas-phase equilibria are tabulated at the same temperature: (1) 2…

CHEMISTRY · Multi-part · AP · Chemistry · Equilibrium · Equilibrium

Problem

Two elementary gas-phase equilibria are tabulated at the same temperature: (1) 2 NO(g) + O₂(g) ⇌ 2 NO₂(g)

K_1 = 1.1 \times 10^{3}

(2) NO₂(g) + NO(g) ⇌ N₂O₃(g)

K_2 = 4.6 \times 10^{-2}

A reaction vessel at this temperature contains the following partial pressures:

P_{\text{NO}} = 0.25\,\text{atm}

P_{\text{O}_2} = 0.40\,\text{atm}

P_{\text{NO}_2} = 0.10\,\text{atm}

P_{\text{N}_2\text{O}_3} = 0.05\,\text{atm}

(a) Combine reactions (1) and (2) algebraically to obtain a single overall chemical equation that relates the four species present in the vessel. Write the balanced overall equation. (b) Derive an expression for the equilibrium constant

K_{\text{overall}}

for the equation obtained in part (a) in terms of

K_1

and

K_2

. Then compute the numerical value of

K_{\text{overall}}

. (c) Write the reaction quotient

Q_{\text{overall}}

for the overall equation from part (a) and calculate its value using the measured partial pressures. (d) Compare

Q_{\text{overall}}

with

K_{\text{overall}}

and predict the spontaneous direction of change for the vessel. Provide a quantitative justification that explicitly references your calculations in parts (b) and (c).

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