How Do You Calculate Equilibrium Conditions After Mixing Two Different Gases?

In summary: If so, then you can use the Clausius-Clapeyron equation which is:$$P_{eq} = P_{T1} + \frac{Q_{T1}}{V_{T1}}$$In summary, the equilibrium pressure and temperature are found by solving the Clausius-Clapeyron equation for pressure and temperature, respectively.
  • #1
jaumzaum
434
33
Consider that I have 2 adiabatic containers, one with a monoatomic gas at pressure P1, volume V1 and temperature T1 and another with pressure P2, volume V2, temperature T2. If I open a valvule and mix the two gases, how do I calculate the equilibrium pressure and temperature?

I know the final quantity of moles, and the final volume, so I need a system of 2 eq to calculate the temperature and pressure. One is the Clapeyron Law, what is the other? I mean, what variable remains constant in this system?

If I try to solve it using conservation of energy:
dU1+dW1+dU2+dW2=0

But how would I calculate the work done by the gases, as this is an irreversible transformation?Thanks!
 
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  • #2
Can I say the entropy is constant?
 
  • #3
You can definitely not assume that entropy is constant. Furthermore, the Clapeyron Law apparently is apparently just another name for the ideal gas law. I never heard the name Clapeyron Law before...

The other equation you need is just the conservation of energy. The internal energy of a monatomic gas is:
$$E = \frac{3}{2}nRT$$
This only depends on temperature. So with this you can compute the temperature, then with the ideal gas law you can compute the pressure.
 
  • #4
jaumzaum said:
Consider that I have 2 adiabatic containers, one with a monoatomic gas at pressure P1, volume V1 and temperature T1 and another with pressure P2, volume V2, temperature T2. If I open a valvule and mix the two gases, how do I calculate the equilibrium pressure and temperature?

I know the final quantity of moles, and the final volume, so I need a system of 2 eq to calculate the temperature and pressure. One is the Clapeyron Law, what is the other? I mean, what variable remains constant in this system?

If I try to solve it using conservation of energy:
dU1+dW1+dU2+dW2=0

But how would I calculate the work done by the gases, as this is an irreversible transformation?Thanks!
Is the gas the same in the two containers? Are you allowing the two containers to equilibrate with one another thermally?
 

Related to How Do You Calculate Equilibrium Conditions After Mixing Two Different Gases?

How do you determine the final pressure after mixing two different gases?

To determine the final pressure after mixing two different gases, you can use Dalton's Law of Partial Pressures. According to this law, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. Calculate the partial pressure of each gas using the ideal gas law (P = nRT/V) and then sum them up to get the final pressure.

What is the role of temperature in calculating equilibrium conditions?

Temperature plays a crucial role in calculating equilibrium conditions because it affects the kinetic energy of the gas molecules. When mixing gases, assuming no heat exchange with the surroundings, the final temperature will be the same for both gases. Use the combined gas law to relate the initial and final states of the gases, ensuring that temperature is consistent throughout your calculations.

How do you find the final volume of the gas mixture?

The final volume of the gas mixture can be determined by assuming that the gases are ideal and that they expand to fill the container they are in. If the gases are mixed in a rigid container, the volume remains constant. If the container is flexible, you can use the ideal gas law to find the new volume based on the total number of moles, the temperature, and the pressure.

How do you calculate the final number of moles in the gas mixture?

The final number of moles in the gas mixture is simply the sum of the moles of each individual gas before mixing. This is because the mixing process does not change the amount of substance, only the distribution and possibly the volume and pressure of the gases involved.

What assumptions are made when calculating equilibrium conditions for gas mixtures?

Several assumptions are typically made when calculating equilibrium conditions for gas mixtures: (1) The gases behave ideally, following the ideal gas law (PV = nRT). (2) The mixing process is isothermal (constant temperature) and isobaric (constant pressure) if not otherwise specified. (3) There are no chemical reactions occurring between the gases. (4) The gases are uniformly distributed throughout the container.

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