Question

nitrogen forms a surprising number of compounds with oxygen. a number of these, often given the collective symbol nox (for
itrogen + x oxygens\) are serious contributors to air pollution. they can often be interconverted, sometimes by reaction with oxygen or ozone (o₃) in the air.
an atmospheric scientist decides to study the reaction between nitrogen trioxide and nitrogen monoxide that produces nitrogen dioxide. he fills a stainless steel reaction chamber with 7.3 atm of nitrogen trioxide gas and 5.2 atm of nitrogen monoxide gas and raises the temperature considerably. at equilibrium he measures the mole fraction of nitrogen dioxide to be 0.46.
calculate the pressure equilibrium constant ( k_p ) for the equilibrium between nitrogen trioxide, nitrogen monoxide, and nitrogen dioxide at the final temperature of the mixture.
round your answer to 2 significant digits.
( k_p = square )

Explanation:

Step1: Write the balanced chemical equation

The reaction between nitrogen trioxide (\(NO_3\)) and nitrogen monoxide (\(NO\)) to form nitrogen dioxide (\(NO_2\)) is \(NO_3+NO
ightleftharpoons 2NO_2\).

Step2: Set up the ICE table

Let \(x\) be the change in pressure.

	\(NO_3\)	\(NO\)	\(NO_2\)
Change (\(P\))	\(-x\)	\(-x\)	\(+2x\)
Equilibrium (\(P\))	\(7.3 - x\)	\(5.2 - x\)	\(2x\)

The total pressure at equilibrium \(P_{total}=(7.3 - x)+(5.2 - x)+2x=12.5\) atm.

Since the mole - fraction of \(NO_2\), \(y_{NO_2}=\frac{P_{NO_2}}{P_{total}}\), and \(y_{NO_2} = 0.46\), then \(P_{NO_2}=y_{NO_2}\times P_{total}\).

\(2x=0.46\times12.5\)
\(2x = 5.75\)
\(x = 2.875\)

Step3: Calculate the equilibrium pressures

\(P_{NO_3}=7.3−x=7.3 - 2.875 = 4.425\) atm
\(P_{NO}=5.2−x=5.2 - 2.875 = 2.325\) atm
\(P_{NO_2}=5.75\) atm

Step4: Calculate \(K_p\)

The formula for \(K_p\) for the reaction \(aA + bB
ightleftharpoons cC\) is \(K_p=\frac{P_C^c}{P_A^aP_B^b}\).

For the reaction \(NO_3+NO
ightleftharpoons 2NO_2\), \(K_p=\frac{P_{NO_2}^2}{P_{NO_3}P_{NO}}\)

Substitute the values: \(K_p=\frac{(5.75)^2}{(4.425)(2.325)}\)

\(K_p=\frac{33.0625}{10.398125}\approx3.2\)

Answer:

\(3.2\)