Question

For the second order reaction:
A --> products
the plot of what term versus time would yield a straight line?

Answer 1

@Photon336 @Prathamesh_M @Preetha @sweetburger

Answer 2

[A]


1/[A]


ln[A]/[A]


ln[A]

Answer 3

try solving the differential equation:
\[-\frac{ d[A] }{ dt }=[A]^{2}\]

Answer 4

u will eventually end up with a relation between [A], i.e., concentration of A, and time

Answer 5

Okay I think the answer is either C or D.

Answer 6

What do you think?

Answer 7

@Prathamesh_M

Answer 8

What equation did u end up with finally?

Answer 9

I think u should try again i got B

Answer 10

\[-\frac{ d[A] }{ [A]^{2} }=dt\]

Answer 11

Now integrate on both sides applying appropriate limits

Answer 12

Okay, I got B now.
@Photon336 what do you think, is that right?

Answer 13

well. first a second order rate law would probably look like this

\[[A] \rightarrow products \]

since we've got only reactant A becoming a product. we automatically know that the reaction must be second order with respect to A.

\[r = k[A]^{2}\]

but I believe that the rate is like how fast your reaction rate is. but it also means that [A] is disappearing at some rate.

like we know the rate constant depends on time right?

\[[A_{0}]^{2}k~dt = -d[A_{0}]\]

so like what we're trying to say here is that I think that the rate of formation of products is equal to the rate we're losing A

\[\frac{ -d[A_{0}] }{ [A_{0}]^{2} } = k~dt \]

\[\int\limits \frac{ -d[A_{0}] }{ [A_{0}]^{2} } = \int\limits k~dt \]

\[-\int\limits \frac{ 1 }{ u^{2} } = -1*-1 \frac{ 1 }{ u }~du => \frac{ 1 }{ [A_{0}] }\]

hmm yeah this is what i'm getting.

\[\frac{ 1 }{ [A_{0}] } = k~t\]

Answer 14

@shall29 I forgot to include something

i put in the initial concentration but didn't take into consideration the final one.

\[\int\limits_{[A]_{0}}^{[A]} \frac{ 1 }{ [A]^{2} } = \frac{ 1 }{ [A] }-\frac{ 1 }{ [A_{0}] }\]

\[\frac{ 1 }{ [A] }-\frac{ 1 }{ [A_{0}] } = kt\]


\[kt+\frac{ 1 }{ [A]_{0} } = \frac{ 1 }{ [A] }\]

Answer 15

Sorry about that. Okay I understand that now

Answer 16

So the answer is B, yes?

Answer 17

yes its 1/[A]