How Does the Ideal Gas Law Apply to Chemical Reactions?

[Qube]

Homework Statement

1. When the following reaction proceeds, what will be true? 2A(g) + 3B(g) -> 4C(g)

(1) The temperature will increase at constant P and V.
(2) The volume will increase at constant T and P.
(3) The pressure will increase at constant T and V.
(4) The density will increase at constant T and P.
(5) The moles will increase at constant T and V.

Homework Equations

PV=nRT

The Attempt at a Solution

PV=nT. I removed the constant R. This is the equation I'll be considering when evaluating how each variable in the ideal gas equation is related to another variable.

We know from the equation in the question that the number of moles of gas decreases from 5 to 4. There are 5 moles of reactants and 4 moles of products. So n changes.

The choices present one variable as increasing along with two other variables held constant. So let's consider the choices.

1) Temperature will increase if P and V are held constant. Temperature is INVERSELY proportional to n. N decreases. T increases. Yes. Well, that was quick, but let's consider the other choices.

2) Volume is directly proportional to n because the two variables are on opposite sides of the equation PV=nRT and there aren't any fractions. N decreases. V also decreases. We can generalize this rule: any variable directly proportional to n will decreases as n is decreasing and if this variable decreases this variable will contradict any answer choices (since they all peg the variable as increasing).

3) P is directly proportional to n. Wrong choice in the context of the problem.

4) Density = Molar Mass (M) multiplied by P (pressure) over RT, where R is the gas constant and T is temperature. T and P are held constant, so looks like density is proportional to molar mass. We don't know any molar masses. The identities of the gases is unknown. Can't be right.

5) This directly contradicts what's going on in the problem in the first place.

Questions:

1) I'm fairly confident my answer is correct; are my lines of reasoning similarly correct?

2) Also this is a test question from a test I just took and this question got thrown out without explanation. Any answer choice chosen was considered correct. Why might this be? Am I overlooking something?

 

[Chestermiller]

The only thing I can think of is #4. You already correctly said in #2 that, at constant T and P, the volume decreases. Irrespective of the molar masses, the total mass of material in the reactor doesn't change. So the mass density must increase. However, if you are referring to the molar density, the volume decreases in proportion to the number of moles. So the molar density doesn't change.

 

[Qube]

Thanks! Prof agreed. There is an argument to be made regarding molar density and mass density.