At a certain temperature the dimerization of nitrogen dioxide is represented by 2 ,…

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

Problem

At a certain temperature the dimerization of nitrogen dioxide is represented by

2\,\mathrm{NO_2(g)}\;\rightleftharpoons\;\mathrm{N_2O_4(g)}

A rigid 2.00 L container is filled with the gases at this temperature. A particulate-level snapshot shows • 60 individual red spheres, each labeled NO₂ • 20 bonded pairs of red spheres, each labeled N₂O₄ • 40 yellow spheres representing Ar (an inert gas) Each colored particle in the diagram corresponds to

5.00\times10^{20}

molecules of the indicated species. Avogadro’s number is

N_{A}=6.022\times10^{23}\,\text{mol}^{-1}

. Answer the following questions about the equilibrium mixture. (a) Write the equilibrium-constant expression

K_c

for the reaction. (b) Using the information provided, calculate the numerical value of

K_c

for this reaction at the stated temperature. Show all work, including unit analysis. (c) The volume of the container is suddenly doubled to 4.00 L while the temperature remains constant. After a new equilibrium is established, will the value of

K_c

increase, decrease, or remain the same? Justify your answer. (d) Predict qualitatively how the relative numbers of

\mathrm{NO_2}

and

\mathrm{N_2O_4}

particles would change if the temperature were increased at constant volume. Explain your reasoning in terms of equilibrium and molecular bonding.

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