[asadeghi]

Hello everyone. Assume this reaction in an open container: MgCO₃->MgO+CO₂
If we draw the mol/s-t graph for MgCO₃, it will be a horizontal line since the concentration of a MgCO₃ won't differ. But what about the mol-t graph? Obviously, the amount of MgCO₃ will decrease so the graph will be descending. No problem with that. My problem is, will it be linear or not? A linear graph would mean that the speed of the reaction will be the same all through the reaction. And we know that the speed equation for this reaction is: R=K[MgCO₃] so basically R should be a constant. However, we know that only a few reactions have a constant speed until their completion. Could you please help me with this problem?!

Thanks in advance

[magician4]

look up "first order kinetics" ( and realise your errors)


if there are further questions, pls. come back


regards

Ingo

[asadeghi]

Are you suggesting that it's a first-order reaction? Can you please explain a bit more? And I did look up "first order kinetics".

[magician4]

Are you suggesting that it's a first-order reaction?

if R = K * [MgCO3] , it clearly is, isn't it ?
a reaction where  the speed is proportional to the instantaneous  concentration of only one component with the exponential factor of 1 , by my very understanding of the definition of what a first order reaction should be , is a first order reaction:

if R is d (MgCO₃)/dt  - and I don't see what it possibly could be otherwise - you'll have your well-known differential equation

d([MgCO₃])/dt = K * [MgCO₃] ( i.e. a subtype of dx/dt = k x )

with the well - known solution

[MgCO₃] (t) = [MgCO₃ ]₀ * e^-Kt
(and of course, the graph of this isn't linear at all)

as you see, concentration of magnesiumcarbonate will change over time (as its more and more diluted by MgO), and so will the moles of it (as they're consumed)

regards

Ingo

[asadeghi]

So in that case, both the mol/s-t and mol-t graphs should be curves. Correct me if I'm wrong here. But I don't understand something: Why should MgCO₃'s concentration decrease? I mean, the density of it is always the same, isn't it?

[magician4]

So in that case, both the mol/s-t and mol-t graphs should be curves. Correct me if I'm wrong here.

you're right

Why should MgCO₃'s concentration decrease? I mean, the density of it is always the same, isn't it?

that's reality, and you there probably will find something like a mix of first- and zero order kinetics, yes

however, for this problem given to you, you'll have to consider a MgCO₃ that becomes "diluted" by MgO produced thereof, soon as the reaction starts - which is tantamount to a decreasing "concentration"

regards

Ingo

[asadeghi]

I asked that because as far as I know and our textbook suggests, the concentration of liquids and solids is always the same during a reaction and I'm facing some kind of irony here!

[asadeghi]

You know, in our educational system there is so much attention on books and basically more on "theory" than "experiment". So unfortunately, I haven't even seen this reaction or any other reaction with my eyes. I have no idea how these reactions occur or how, for example, MgCO3 turns into MgO...

[magician4]

I asked that because as far as I know and our textbook suggests, the concentration of liquids and solids is always the same during a reaction and I'm facing some kind of irony here!

this is kind of generalized...
in most reactions you might ignore the change of (excess of) solvent , and the change in (enough) undissolved solids ref. resulting active surface thereof, if you were into LMA calculations (!)

with the example at hand , you've reached the limit of above approximations

So unfortunately, I haven't even seen this reaction or any other reaction with my eyes. I have no idea how these reactions occur or how, for example, MgCO3 turns into MgO...

It's pretty much the same setup you use when you wish to turn CaCO₃ into CaO : "calcination"

talking reality:
- in a technical setup, the speed of the process is next to perfect 0.th order, as it completely depends on energy input
- if it wasn't for energy input running the show, the process would be of "negative" (!) order in the beginning , i.e. increase speed once it started  ( I know, this sounds absurd, but that's how it is: at ~ 800°C with the carbon dioxide forming, the material becomes porous, even might bloat, and will increase it's effective, reactive surface drastically, overcompensating the effect of MgO forming and MgCO₃ loss)
- after that (still without energy input ruling the game) the other effects will beginn to kick in, and you would  switch to first order kinetics incrementally.
- by the end of the day, MgCO₃ "incorporated" in MgO would have a hard time to outgas , which would provoke still another type of kinetics, ruled by the effective outgassing properties of the aggregates forming

so much for reality


Anyway, don't be too harsh with your books here: it's very hard to find a good (pseudo) first order kinetics in school, for teaching purposes.
maybe the reaction of Mg ribbons in aq. HCl , in the beginning of the reaction


regards

Ingo