At 55 degree centigrade and 1 atmosphere,N2O4 was found to decompose 50.3%.At what pressure and same temperature the equilibrium

N2O4↔ 2NO2

will give the ratio of N2O4:NO2 as 8:1

To determine the pressure at which the equilibrium ratio of N2O4 to NO2 is 8:1 at 55 degrees Celsius, we can use the principles of chemical equilibrium and the ideal gas law. Let's break this down step by step.

Understanding the Reaction

The decomposition of dinitrogen tetroxide (N2O4) into nitrogen dioxide (NO2) can be represented by the following equilibrium reaction:

N2O4 (g) ⇌ 2 NO2 (g)

Initial Conditions

At 55 degrees Celsius and 1 atmosphere, we know that N2O4 decomposes to 50.3%. This means that if we start with 1 mole of N2O4, after decomposition, we would have:

• 0.497 moles of N2O4 remaining
• 0.503 moles of NO2 formed (since 1 mole of N2O4 produces 2 moles of NO2)

Calculating the Equilibrium Constant (Kp)

The equilibrium constant (Kp) for the reaction can be expressed as:

Kp = (P_NO2^2) / (P_N2O4)

At 1 atmosphere, the partial pressures can be calculated as follows:

• Let the initial pressure of N2O4 be P_N2O4 = 1 atm.
• After decomposition, the partial pressures are:
• P_N2O4 = 0.497 atm
• P_NO2 = 0.503 atm × 2 = 1.006 atm (since 1 mole of N2O4 produces 2 moles of NO2)

Now, substituting these values into the Kp expression:

Kp = (1.006^2) / 0.497

Calculating this gives:

Kp ≈ 2.03

Finding the New Pressure for the Desired Ratio

We want to find the pressure at which the ratio of N2O4 to NO2 is 8:1. This means:

• P_N2O4 = 8x
• P_NO2 = x

Substituting these into the Kp expression gives:

Kp = (x^2) / (8x) = x / 8

Setting this equal to the previously calculated Kp:

x / 8 = 2.03

Solving for x gives:

x = 16.24 atm

Calculating the Total Pressure

Now, substituting back to find the pressures:

• P_N2O4 = 8x = 8 * 16.24 atm = 129.92 atm
• P_NO2 = x = 16.24 atm

The total pressure (P_total) is the sum of the partial pressures:

P_total = P_N2O4 + P_NO2 = 129.92 atm + 16.24 atm = 146.16 atm

Final Result

Therefore, at 55 degrees Celsius, to achieve an equilibrium ratio of N2O4 to NO2 of 8:1, the pressure must be approximately 146.16 atm.