How Much Solvent is Used in Moles for a Reaction in a Closed Vessel at 80°C?

[tunabeast]

[SOLVED] Physical chemistry problem

Homework Statement

A closed vessel of 5L volume is kept at 80 degrees celcius and contains a mixture of two liquids A and B dissolved in a solvent, with their initial concentrations [A]=0.1mol/L and =1.0mol/L. The volume of the gas phase is 2L and it initially contains only nitrogen.

Liquids A and B react as follows

A+B <--> C+D

where D is water. It is known the reaction reaches 80% conversion, all liquid components are miscible and only water is volatile.

If the partial pressure of water in the vessel at the end of the reaction is 0.1 bar, calculate the amount of solvent used in moles.

Note: You may need to use the Antoine equation.

Homework Equations

The Attempt at a Solution

Well I'm really stuck with this problem, don't really know where to start - some (any!) guidance would be greatly appreciated.

 

[tunabeast]

After asking my tutor i now know how to work this out.

 

[Blueshift5]

This is a classic example of a physical chemistry problem involving a closed vessel, a chemical reaction, and the use of equations to solve for an unknown quantity. To start, we need to identify the important information given in the problem:

1. Closed vessel of 5L volume
2. Temperature of 80 degrees celcius
3. Mixture of two liquids A and B dissolved in a solvent
4. Initial concentrations of [A]=0.1mol/L and =1.0mol/L
5. Gas phase has initial volume of 2L and contains only nitrogen
6. Reaction between A and B to form C and D
7. Reaction reaches 80% conversion
8. All liquid components are miscible
9. Only water is volatile
10. Partial pressure of water at the end of the reaction is 0.1 bar

From this information, we can create a balanced chemical equation for the reaction:

A+B <--> C+D

We also know that the reaction reaches 80% conversion, meaning that 80% of the initial moles of A and B will be converted to moles of C and D. This can be represented mathematically as:

0.8[A] + 0.8 = [C] + [D]

We also need to use the ideal gas law to relate the moles of gas to the partial pressure of water in the vessel. The ideal gas law is:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. We can rearrange this equation to solve for n:

n = PV/RT

Since we know the initial volume (2L) and temperature (80 degrees celcius = 353K) and the final pressure (0.1 bar), we can plug these values in to solve for n, which represents the moles of water in the gas phase at the end of the reaction.

Next, we need to use the Antoine equation to relate the pressure of the water to its vapor pressure. The Antoine equation is:

log(P) = A - (B/(T+C))

Where P is the vapor pressure, T is the temperature in degrees celcius, and A, B, and C are constants specific to the substance. We can rearrange this equation to solve for P:

P =