Can someone work out this concentration PLEASE IM DYING (1 Viewer)

[C2H6O]

PLEASE HELP ME FIND [HCO3-] IVE DONE IT 50 TIMES BUT IM GETTING A VALUE THATS SLIGHTLY GREATER THAN [H2CO3]
Reaction is H2CO3 <=> HCO3- + H+
Ka is 2.5*10^-4
initial [H2CO3] is 5.69902916800219*10^-14 M
if you get pretty much the same concentration for [HCO3-] as [H2CO3] or even higher somehow can someone explain why??? (also i cannot approximate so must use quadratic formula)

 

[cheesynooby]

i put it into bing math solver and i got slightly lower
also im confused why is it a problem that ur getting a value slightly greater? at this point itd probably just depend on what calculator ur using
(also y cant u approximate? does that mean u have to factor self ionisation of water as well...)

 

[cheesynooby]

PLEASE HELP ME FIND [HCO3-] IVE DONE IT 50 TIMES BUT IM GETTING A VALUE THATS SLIGHTLY GREATER THAN [H2CO3]
Reaction is H2CO3 <=> HCO3- + H+
Ka is 2.5*10^-4
initial [H2CO3] is 5.69902916800219*10^-14 M
if you get pretty much the same concentration for [HCO3-] as [H2CO3] or even higher somehow can someone explain why??? (also i cannot approximate so must use quadratic formula)

i just realised i put it in wrong and i got slightly higher
but also surely they dont expect an answer to use that exact of a value considering the Ka is probably not very precise

 

[C2H6O]

i put it into bing math solver and i got slightly lower
also im confused why is it a problem that ur getting a value slightly greater? at this point itd probably just depend on what calculator ur using
(also y cant u approximate? does that mean u have to factor self ionisation of water as well...)

idk these are just the parameters I got given for this task so I gotta work with them. Also I’m using excel so surely there shouldn’t be any approximation errors. To me it doesn’t make sense that the concentrations are almost the same cause the ka is small meaning it should be favoured to the reactants, and given that there are TWO products this difference should be more dramatic no? And how could it be greater it would have more moles of product than reactant when the molar ratio is 1:1:1 which doesn’t feel possible. My brain I fried from working on this for 2 hours though so maybe I’m missing sometnjng

 

[Sorghum Sneedley]

15 sig figs of precision is crazy

 

[Sorghum Sneedley]

Also I’m using excel so surely there shouldn’t be any approximation errors.

could it be a floating point error with that many sig figs?

 

[C2H6O]

15 sig figs of precision is crazy

nah i just put 15 bc in excel the [HCO3-] is greater by a tiny difference

 

[C2H6O]

Can someone with a fresh brain just verify whether it should be possible that [H2CO3] could approximately equal to or be slightly less than [HCO3-]?

 

[cheesynooby]

ok yeah theres no way that [HCO3] should go up it should at the very least be almost equal
also uhhh this happened

 

[C2H6O]

ok yeah theres no way that [HCO3] should go up it should at the very least be almost equal
also uhhh this happened
View attachment 46994

oh lmao yeah i tried desmos as well earlier and got really whacky stuff. i think youll have to graph that green function in desmos 3d cause you should have z=*quadratic with x and y*

 

[C2H6O]

ok well to be frank idk what to do with this

 

[C2H6O]

i kinda forgot what the point of graphing this was?

 

[C2H6O]

ok well the point of intersection of the red green and blue functions is on the border of the purple area so that means the values are indeed really close

 

[cheesynooby]

View attachment 46996
i kinda forgot what the point of graphing this was?

based on the math for my blue function where y is the Ka and x is the [HCO3] it seems that its pretty impossible for x to exceed [H2CO3] cuz theres an asymptote there and then Ka goes negative
but for Ka to reach 10^-4 it would have to go rlly far up the graph so x would be really close
(ignoring self ionisation also my brain is too fried to comprehend ur 3d graphs)

 

[C2H6O]

Why does that not make any sense to me it feels like this method with the quadratic equation must have an error cause how can the ka be a small number but [H2CO3]=[HCO3-]=[H+] cause that would mean ka=[HCO3-][H+]/[H2CO3] = x^2/x=x ????

 

[cheesynooby]

but [H2CO3] would be the original concentration - x (and since x ~= original concentration its very close to 0 like 0.0000001) which brings Ka wayy up (yea it makes no sense but the math works)

 

[C2H6O]

wait that implies ka approx= [HCO3-]???

 

[C2H6O]

but [H2CO3] would be the original concentration - x (and since x ~= original concentration its very close to 0 like 0.0000001) which brings Ka wayy up (yea it makes no sense but the math works)

ohhh fk

 

[C2H6O]

Why does that not make any sense to me it feels like this method with the quadratic equation must have an error cause how can the ka be a small number but [H2CO3]=[HCO3-]=[H+] cause that would mean ka=[HCO3-][H+]/[H2CO3] = x^2/x=x ????

so ka=[HCO3][H+]/([H2CO3]-x)=x^2/(x-x) that's a div 0 error fml

 

[C2H6O]

Since Ka has to be positive that means [H2CO3] must be greater than [HCO3-], which is contradictory to what excel spat out, so im going to assume even excel reached its limit of accuracy??