At the elementary decomposition of dinitrogen tetraoxide follows with rate laws…

CHEMISTRY · Multi-part · A Level · Chemistry · Chemical equilibria (Le Chatelier’s principle and Kc) · Chemical equilibria (Le Chatelier’s principle and Kc)

Problem

350\,\text{K}

the elementary decomposition of dinitrogen tetraoxide follows

N_{2}O_{4}(g) \leftrightharpoons 2\,NO_{2}(g)

with rate laws Forward rate =

k_f[N_{2}O_{4}]

and Reverse rate =

k_r[NO_{2}]^{2}

. The rate constants at

350\,\text{K}

are

k_f = 0.082\,\text{s}^{-1}

and

k_r = 1.9 \times 10^{-2}\,\text{kPa}^{-1}\cdot\text{s}^{-1}

when partial pressures are expressed in kPa. A sealed

1.00\,\text{L}

flask initially contains pure

N_{2}O_{4}

15\,\text{kPa}

and no

NO_{2}

. (a) Write expressions for the forward and reverse rates as functions of time in terms of the changing partial pressures of

N_{2}O_{4}

and

NO_{2}

. (b) Assuming that

x\,\text{kPa}

N_{2}O_{4}

has decomposed at time

t

, express the forward and reverse rates in terms of

x

. (c) Determine the value of

x

(in kPa) at which the forward and reverse rates become equal. Show algebraic work and report

x

to two significant figures. (d) Calculate the partial pressure of each species at the moment equilibrium is first established. Does the system necessarily remain at these pressures indefinitely? Explain.

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