An 0.0284 aqueous solution of lactic acid is found to be 6.7% ionized. Determine Ka for lactic acid.
HC3H5O3 + H2O <-- --> H3O^+ + C3H5O3^- Ka =?
Thanks.
Ka=[H3O+][C3H5O3-]/[acid]
= .067^2*conc^2/conc= .067^2*.0284
check my thinking.
Just wondering, why do you square the numerators?
Oh, lactic acid, you're such a rebel. Not wanting to conform to the rules of society, huh? Well, let's find your Ka and try to make some sense out of this rebellious behavior.
First, we need to understand what "6.7% ionized" means. Imagine you're at a party with 100 people. If only 6.7 of them start dancing like crazy on the dance floor, then you can say there's a 6.7% dance party going on. Same idea here, but with ions instead of dance moves.
So, if we have an 0.0284 M solution of lactic acid, and 6.7% of it is ionized, that means only 6.7% of H3C3H5O3 breaks apart into H3O+ and C3H5O3-.
Now, let's do a little math. If only 6.7% of lactic acid breaks apart, that means 93.3% remains un-ionized. So, the concentration of the un-ionized form is 0.0284 M multiplied by 0.933.
The concentration of the ionized form, H3O+ and C3H5O3-, is 0.0284 M multiplied by 0.067.
Now, we can set up the equation for Ka:
Ka = [H3O+][C3H5O3-] / [HC3H5O3]
Plug in the values we calculated, and you'll find your Ka. Good luck, lactic acid! Don't party too hard on the dance floor.
To determine the Ka for lactic acid, we need to use the information that it is 6.7% ionized in a 0.0284 M aqueous solution.
Step 1: Calculate the concentration of H3O^+ ions and C3H5O3^- ions in the solution. Since lactic acid is 6.7% ionized, we can calculate the concentration of the ionized form (H3O^+ and C3H5O3^-) by multiplying the concentration of lactic acid (0.0284 M) by the ionization percentage (6.7% or 0.067):
[H3O^+] = (6.7/100) * 0.0284 M
[C3H5O3^-] = (6.7/100) * 0.0284 M
Step 2: Write the equilibrium expression for the ionization of lactic acid:
Ka = [H3O^+][C3H5O3^-] / [HC3H5O3]
Step 3: Substitute the concentrations into the equilibrium expression:
Ka = ([H3O^+][C3H5O3^-]) / [HC3H5O3]
Ka = ([(6.7/100) * 0.0284 M][(6.7/100) * 0.0284 M]) / 0.0284 M
Step 4: Simplify the expression:
Ka = ([0.067 * 0.0284] * [0.067 * 0.0284]) / 0.0284
Ka = (0.0000538296 * 0.0000538296) / 0.0284
Ka ≈ 1.02008 × 10^-7
Therefore, the Ka value for lactic acid is approximately 1.02008 × 10^-7.
Ka = [H3O^+][C3H5O3^- ] / [HC3H5O3]
Let [H3O^+] = [C3H5O3^- ] = x
Ka = [x][x ] / [conc. - x] (exact)
Ka = [x][x ] / [conc.] (approximate if x is much smaller than cocnetration)
I assume conc. = 0.0284 is moles/liter
[H3O^+] = [C3H5O3^- ] = (0.067)(0.0284)
Ka = {[(0.067)(0.0284)][(0.067)(0.0284)]} / [0.0284] (approx)
Pay close attention how the values were substituted in the last expression.