General Chemistry Homework Problem

Question

4. At 100 degrees celsius, Kc = 4.72 for the reaction 2NO2(g) ⇌ N2O4(g). An empty 10.0 L flask is filled with 3.45 g of NO2 at 100 degrees celsius.

A) Calculate the equilibrium concentrations

.

B) Calculate the equilibrium partial pressures. (Use ideal gas law).

C) Calculate the total pressure of the flask when the reaction reaches equilibrium. (Total pressure = sum of partial pressures: Dalton’s law).

Answer 1

A) To figure out the concentrations at equilibrium, we should use an ICE (Initial, Change, Equilibrium) Table. To start, we need to convert grams of NO₂ to moles and divide by the volume to get concentration.

3.45 g of NO₂ * ( 1 mol NO₂ / 46.0 g NO₂) = 0.0750 mol

Then divide by 10 L to get Molarity --> 0.00750 M <-- this is our initial concentration

Initially, we only have NO₂ and no N₂O₄. Therefore, the reaction must go in the forward direction to achieve equilibrium. When the reaction moves forward, the concentration of NO₂ will decrease while N₂O₄ will increase. The rate of decrease of NO₂ will be twice as fast as the rate of increase of N₂O₄ due to the stoichiometry (coefficients in the reaction). So my ICE table looks as follows:

NO₂ <-> N₂O₄

Initial (M) 0.00750 0

Change -2x +x

Equilibrium (M) 0.00750-2x x

In this reaction, Kc = [N₂O₄] / [NO₂]²

Substituting in values, we get:

4.72 = (x) / (0.00750-2x)²

Solving for x using the quadratic equation, x = 2.33x10^-4 M

Therefore, [NO₂] = 0.00750 - 2*2.33x10^-4 = 0.00703 M

[N₂O₄] = 2.33x10^-4 M

B) Converting molarity to partial pressure is relatively straightforward. Remember that concentration is moles over volume (n/V). If we take our ideal gas law: PV = nRT and solve for pressure, we get:

P = (n/V) RT

or

P = MRT; where M = the molarity

From this, we can see that the conversion from Molarity to atm just requires us to multiply by RT. Don't forget to convert Celsius to Kelvin!

Partial Pressure of NO₂ = 0.00703*0.0821*373 = 0.215 atm

Partial Pressure of N₂O₄ = 2.33*10^-4*0.0821*373 = 0.00714 atm

C) Total pressure = sum of partial pressures.

Total Pressure = 0.215 atm + 0.00714 atm = 0.222 atm