Calculate for [H+] please?

Question

H(C4H7O2) <-> C4H7O2- + H+

Given that [C4H7O2-] = 3.8 x 10^-2 M and [HC4H7O2] = 1 M, calculate the concentration of H+.

Ka = 1.444 x 10^-5

Answer 1

Ka=( [C4H7O2][H+] )/ [H(C4H7O2)]=( [3.8x10^-2][H+] )/ [1]=1.444x10^-5
[3.8x10^-2][H+]=[1][1.444x10^-5]
[H+]=[1][1.444x10^-5] / [ 3.8x10^-2]

Answer 2

It all depends on what your concentrations stand for.

If they are the concentrations at equilibrium then it is a very simple problem-just substitute the values in the equation for Ka like Natasha B is showing you.

If you are referring to a buffering system and the initial concentrations (and not at equilibrium) then Nickytheknight is right, though I prefer solving the quadratic equation.
The way the question is formulated I guess it refers to the first case.

Nickytheknight you should think the answers through before judging them.

Answer 3

I assume those two are inital conc.s, so

HA--------->A-.............+ H+....... (equation)
1.0M..........3.8E-2M......... 0........ (inital concentrations)
-x............... +x ............... +x........ (delta concentrations)
1.0-x.........3.8E-2 + x..... x........ (final concentrations)

[just ignore the dots, they dont mean anything]

so

(3.8E-2 +x)x/(1.0-x) = Ka = 1.444E-5

solve for x,

you probably noticed this is a quadratic equation, and I hate solving those equations, so a math trick here, let's assume x<< 3.8E-2<1, so 3.8E-2 +x = 3.8E-2 and 1.0-x = 1.0, the above equation could be simplified to this

(3.8E-2)*x/1 = 1.444E-5

solve for x, x = 3.8E-4, but is our assumption accurate? Let's check it out, we assume x is far less than 3.8E-2 and get x = 3.8E-4, so

x/3.8E-2 = 0.01<5%

our assumption is fine, but if this number is greater than 5%, we have to solve quadratic equation. Please notice, this checkup is VERY important and has to be done EVERY TIME you are making such mathematical assumptions. Anyhow, the final conc of H+ is [look at our table, the final conc of H+ is x] 3.8E-4 M

****
strategy of the person above me is not appropriate if the two conc. are initial concs; elsewise, he/she would be correct.