ODE question, appreciate your help

[zibb3r]

Can anyone give me a hand with this question? I honestly have no idea how to do it?

I was thinking for d(A)/dt=-d(B)/dt= -k₁(A)+k_-1(B) because the 2 on both sides cancels out? But this was completely wrong...

Any ideas? :)

 

[epenguin]

View attachment 62034

Can anyone give me a hand with this question? I honestly have no idea how to do it?

I was thinking for d(A)/dt=-d(B)/dt= -k₁(A)+k_-1(B) because the 2 on both sides cancels out? But this was completely wrong...

Any ideas? :)

The equation of the most elementary reversible chemical reaction. Your equation is OK. Just use conservation of mass which enables you to get the equation in one dependent variable only.

I don't see the point of the 2 either*. I suggest you reframe it as A ⇔ B with the rate constants half those given.

Since this seems meant to trip students up, I suggest you placate them by using the symbols they ask, a and b.


* Unless by any chance the context suggests they mean a mechanism in which two molecules of A collide and transform into something that rapidly dissociates into two molecules of B, in which case the d.e. would be different. However if you have never done the more elementary one before then are unlikely to mean this.

 

[zibb3r]

Thanks but apprantley I have to show it fully as in can't can have it that way/have to show the 2s. Do you have any clue how Id write it that way?

 

[epenguin]

Thanks but apprantley I have to show it fully as in can't can have it that way/have to show the 2s. Do you have any clue how Id write it that way?

I can't offer more than

I don't see the point of the 2 either*. I suggest you reframe it as A ⇔ B with the rate constants half those given.
.

plus my *footnote in post.

Sometimes here we have to spend too much time on exegesis, working out what a question could possibly mean. This looks like a printed text, if we saw more of where it came from, e.g. the textbook section, or the section on which it is an exercise, we'd know better what the problem is.