How do gas reactions affect volume in a fixed container?

[gfd43tg]

Hello,

I am looking at reactions that change volume during the reaction, for example ammonia synthesis

$$N_{2} + 3H_{2} \rightleftharpoons 2NH_{3}$$

where it is clear that the products are less moles than the reactants. However, I am thinking of a scenario in a plug flow reactor where this is happening. How can it be that the volume is changing? Aren't the gases just going to occupy the space in the PFR, therefore the volume is constant? Same thing really for a batch reactor too, I mean just because a gas reacts to form less moles, it should still have the volume of its vessel, therefore not change??

 

[Chestermiller]

I'll give you the answer for a batch reactor, and then, maybe you can figure it out for a PFR.

If the number of moles changes, it doesn't have to be the volume that is affected. It can also be the pressure. In a batch reactor, the mass density remains constant, but the molar density changes. This causes a change in the pressure.

Chet

 

[gfd43tg]

So again, I suppose the molar density would change just as well in a PFR, so the pressure and/or temperature would change. If the volume of a PFR is a fixed vessel, and should be constant, then all I see is a change in moles to maintain the equality PV = nRT requires either P or T to change. But the lecture/book is actually talking about a change in volume, very specifically. I don't get how the volume of a gas in a fixed container can change, no matter what the reaction is.

 

[Chestermiller]

So again, I suppose the molar density would change just as well in a PFR, so the pressure and/or temperature would change. If the volume of a PFR is a fixed vessel, and should be constant, then all I see is a change in moles to maintain the equality PV = nRT requires either P or T to change. But the lecture/book is actually talking about a change in volume, very specifically. I don't get how the volume of a gas in a fixed container can change, no matter what the reaction is.

Well, a PFR for a reaction like this is very different from the case of a batch reactor. But, we can figure out what is going on in the PFR by letting the mathematics help us.

Suppose we have a PFR with the reaction B + 3C --> 2D, where B, C, and D are gaseous species. We are going to assume that the shear stress at the wall is very small so that the pressure gradient along the tube is very low, in which case the total pressure P is constant at the inlet pressure throughout the reactor. We are also going to assume that the heat of reaction is zero, so that the temperature throughout the reactor is constant at the inlet temperature T. We are going to assume ideal gas behavior, and that B, C, and D comprise the entire flow stream. Let x be the axial position along the reactor, and let v(x) represent the axial velocity a position x. Let A be the cross sectional area of the tube. Let y_B(x), y_c(x), and y_d(x) represent the mole fractions of the three species, and let M_b, M_c, and M_d represent the molecular weights of the three species.

For an ideal gas, in terms of the mole fractions, what are the partial pressures of B, C, and D at a given location x along the reactor? What are the molar densities of the three species at a given location x along the reactor? What are the mass densities of the three species at a given location x along the reactor? What is the total mass density $\rho (x)$of the gas at a given location x along the reactor?

TO BE CONTINUED

Chet

 

[alphy]

Dear researcher,

Thank you for your inquiry about gas reactions and their effect on volume in a fixed container. I can provide some insights into this topic.

Firstly, it is important to understand that in a fixed container, the volume remains constant. However, the volume of the gases within the container can change due to the gas reactions that are occurring.

In the example you mentioned, the ammonia synthesis reaction, the number of moles of the products is less than the number of moles of the reactants. This means that the total volume of gases in the container will decrease during the reaction. This is because the molecules of nitrogen and hydrogen are combining to form larger molecules of ammonia, resulting in a decrease in the total number of gas molecules.

In a plug flow reactor, the gases are continuously flowing through the reactor, and as the reaction takes place, the volume of gases will decrease. This is because the gases are being consumed and converted into ammonia, which has a smaller volume compared to the reactants.

In a batch reactor, the volume of the gases may not change as drastically as in a plug flow reactor. This is because in a batch reactor, the gases are not continuously flowing, and the reaction takes place in a closed system. However, there will still be a decrease in volume as the reaction progresses and the gases are consumed.

It is also important to consider the temperature and pressure of the system, as these factors can affect the volume of gases. For instance, an increase in temperature can cause gases to expand, resulting in an increase in volume, while an increase in pressure can cause gases to compress, resulting in a decrease in volume.

In conclusion, gas reactions can indeed affect the volume in a fixed container, as the number of moles of gases can change during the reaction. However, the overall volume of the container will remain constant. I hope this explanation helps to clarify your doubts. Thank you.