Question

Problem PageQuestion Nitrogen forms a surprising number of compounds with oxygen. A number of these, often given the collective symbol (for "nitrogen oxygens") are serious contributors to air pollution. They can often be interconverted, sometimes by reaction with oxygen or ozone () in the air. An atmospheric scientist decides to study the reaction between nitrogen trioxide and oxygen that produces nitrogen dioxide and ozone. She fills a stainless steel reaction chamber with of nitrogen trioxide gas and of oxygen gas and raises the temperature considerably. At equilibrium she measures the mole fraction of ozone to be . Calculate the pressure equilibrium constant for the equilibrium between nitrogen trioxide, oxygen, nitrogen dioxide and ozone at the final temperature of the mixture. Round your answer to significant digits.

Answer 1

The given question is incomplete. The complete question is :

Nitrogen forms a surprising number of compounds with oxygen. A number of these, often given the collective symbol NOx (for "nitrogen + 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 oxygen that produces nitrogen dioxide and ozone. He fills a stainless steel reaction chamber with 7.4atm of nitrogen trioxide gas and 3.6atm of oxygen gas and raises the temperature considerably. At equilibrium he measures the mole fraction of ozone to be 0.17. Calculate the pressure equilibrium constant Kp for the equilibrium between nitrogen trioxide, oxygen, nitrogen dioxide and ozone at the final temperature of the mixture. Round your answer to 2 significant digits.

Answer: Thus the pressure equilibrium constant for the equilibrium between nitrogen trioxide, oxygen, nitrogen dioxide and ozone at the final temperature of the mixture is 0.365

Explanation:

The balanced chemical reaction is:

 $NO_3(g)+O_2(g)\rightarrow NO_2(g)+O_3(g)$

initial :   7.4 atm   3.6 atm          0 atm      0 atm

At eqm:   (7.4-x) atm  (3.6-x)atm    x atm   x atm

Total pressure at equilibrium  $P_T$ = (7.4-x) + (3.6-x) + x + x = 11 atm

Given : mole fraction of ozone = 0.17

Thus $p_{O_3}=\chi_{O_3}\times P_T=0.17\times 11=1.87$

Thus x = 1.87

Equilibrium constant is defined as the ratio of concentration of products to the concentration of reactants each raised to the power their stoichiometric ratios.

The expression for $K_p$ is written as:

$Kp=\frac{(p_{O_3})\times (p_{NO_2})}{(p_{NO_3})\times (p_{O_2})}$

$K_p=\frac{x\times x}{(7.4-x)\times (3.6-x)}$

$K_p=\frac{1.87\times 1.87}{(7.4-1.87)\times (3.6-1.87)}$

$K_p=\frac{1.87\times 1.87}{(5.53)\times (1.73)}=0.365$

Thus the pressure equilibrium constant for the equilibrium between nitrogen trioxide, oxygen, nitrogen dioxide and ozone at the final temperature of the mixture is 0.365