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Chapter 15: Problem 82

A sealed glass bulb contains a mixture of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) gases. When the bulb is heated from \(20^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\), what happens to these properties of the gases: (a) color, (b) pressure, (c) average molar mass, (d) degree of dissociation (from \(\mathrm{N}_{2} \mathrm{O}_{4}\) to \(\mathrm{NO}_{2}\) ), (e) density? Assume that volume remains constant. (Hint: \(\mathrm{NO}_{2}\) is a brown gas; \(\mathrm{N}_{2} \mathrm{O}_{4}\) is colorless.)

Short Answer

Expert verified
With the increase in temperature, the color of the gas mixture will become browner, the pressure and the degree of dissociation will increase, while the average molar mass and the density will decrease.

Step by step solution

01

Determine the change in color

The change in color depends on the degree of dissociation. As the temperature increases, \(\mathrm{N}_{2} \mathrm{O}_{4}\) dissociates into \(\mathrm{NO}_{2}\). Since \(\mathrm{NO}_{2}\) is a brown gas, the color of the gas mixture will become browner.
02

Determine the change in pressure

The pressure of a gas is directly proportional to the temperature, as per the ideal gas law. If the volume remains constant, and the moles of the gas does not change, then an increase in temperature will result in an increase in pressure.
03

Determine the change in average molar mass

The average molar mass depends upon the relative amount of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) in the mixture, which changes as the \(\mathrm{N}_{2} \mathrm{O}_{4}\) dissociates into \(\mathrm{NO}_{2}\). Since the molar mass of \(\mathrm{NO}_{2}\) is lower than that of \(\mathrm{N}_{2} \mathrm{O}_{4}\), the average molar mass of the gas mixture will decrease.
04

Determine the change in the degree of dissociation

The degree of dissociation increases with increase in temperature. Since the temperature increases, more of the \(\mathrm{N}_{2} \mathrm{O}_{4}\) will dissociate into \(\mathrm{NO}_{2}\). Therefore, the degree of dissociation will increase.
05

Determine the change in density

The density of a gas at constant pressure is inversely proportional to the temperature. If the pressure changes (which it does in this case), then the change in temperature and the change in molar mass both impact the density. Since both the temperature and the molar mass are increasing, the density will decrease.

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Most popular questions from this chapter

Iodine is sparingly soluble in water but much more so in carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right)\). The equilibrium constant, also called the partition coefficient, for the distribution of \(\mathrm{I}_{2}\) between these two phases $$ \mathrm{I}_{2}(a q) \rightleftharpoons \mathrm{I}_{2}\left(\mathrm{CCl}_{4}\right) $$ is 83 at \(20^{\circ} \mathrm{C}\). (a) A student adds \(0.030 \mathrm{~L}\) of \(\mathrm{CCl}_{4}\) to \(0.200 \mathrm{~L}\) of an aqueous solution containing \(0.032 \mathrm{~g}\) \(\mathrm{I}_{2} .\) The mixture is shaken and the two phases are then allowed to separate. Calculate the fraction of \(\mathrm{I}_{2}\) remaining in the aqueous phase. (b) The student now repeats the extraction of \(I_{2}\) with another 0.030 \(\mathrm{L}\) of \(\mathrm{CCl}_{4}\). Calculate the fraction of the \(\mathrm{I}_{2}\) from the original solution that remains in the aqueous phase. (c) Compare the result in (b) with a single extraction using \(0.060 \mathrm{~L}\) of \(\mathrm{CCl}_{4}\). Comment on the difference.

A mixture containing 3.9 moles of \(\mathrm{NO}\) and 0.88 mole of \(\mathrm{CO}_{2}\) was allowed to react in a flask at a certain temperature according to the equation $$ \mathrm{NO}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{CO}(g) $$ At equilibrium, 0.11 mole of \(\mathrm{CO}_{2}\) was present. Calculate the equilibrium constant \(K_{\mathrm{c}}\) of this reaction.

Define reaction quotient. How does it differ from equilibrium constant?

A mixture of 0.47 mole of \(H_{2}\) and 3.59 moles of \(H C l\) is heated to \(2800^{\circ} \mathrm{C}\). Calculate the equilibrium partial pressures of \(\mathrm{H}_{2}, \mathrm{Cl}_{2}\), and \(\mathrm{HCl}\) if the total pressure is 2.00 atm. The \(K_{P}\) for the reaction \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\) is 193 at \(2800^{\circ} \mathrm{C}.\)

The equilibrium constant \(K_{\mathrm{c}}\) for the decomposition of phosgene, \(\mathrm{COCl}_{2}\), is \(4.63 \times 10^{-3}\) at \(527^{\circ} \mathrm{C}\) : $$ \mathrm{COCl}_{2}(g) \rightleftharpoons \mathrm{CO}(g)+\mathrm{Cl}_{2}(g) $$ Calculate the equilibrium partial pressure of all the components, starting with pure phosgene at 0.760 atm.
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