Barbituric acid, HC4H3N2O3, is used to prepare various barbiturate drugs (used as sedatives). Calculate the concentrations of hydronium ion and barbiturate ion in a 0.15 M solution of the acid. The value of Ka is 9.8 105.
Find the hydronium ion concentration.
Find the hydronium ion concentration.

Ka, being the dissociation constant for an acid in water, would have the equation
HC4H3N2O3 > H3O+ + C4H3N2O3
Ka = 9.8 105 = [H3O+][C4H3N2O3]/ [HC4H3N2O3]
Since you know the molarity of the acid, that's the bottom half of your expression! Next, since you know for each mole of acid that splits up into the two products, there will be equal moles of the products (given by the balancing of the equation), you can call the top half x * x or, x^2.
The bottom will now become 0.15M  x, because when H3O+ and C4H3N2O3 are formed, there is that much LESS acid.
Plug in all those cool things into the original expression...
x^2/ 0.15M x = 9.8 105
Because I'm never in the mood to deal with a quadratic equation in my quest to solve for x, I think the Ka value is sufficiently small enough to neglect the x in the denominator. (The rule of thumb is when the power of ten is 5 on Ka or smaller, you can do this.)
You haaaaave...0.15M * 9.8 105 = x^2
Then you get x, and you win. Yay!
HC4H3N2O3 > H3O+ + C4H3N2O3
Ka = 9.8 105 = [H3O+][C4H3N2O3]/ [HC4H3N2O3]
Since you know the molarity of the acid, that's the bottom half of your expression! Next, since you know for each mole of acid that splits up into the two products, there will be equal moles of the products (given by the balancing of the equation), you can call the top half x * x or, x^2.
The bottom will now become 0.15M  x, because when H3O+ and C4H3N2O3 are formed, there is that much LESS acid.
Plug in all those cool things into the original expression...
x^2/ 0.15M x = 9.8 105
Because I'm never in the mood to deal with a quadratic equation in my quest to solve for x, I think the Ka value is sufficiently small enough to neglect the x in the denominator. (The rule of thumb is when the power of ten is 5 on Ka or smaller, you can do this.)
You haaaaave...0.15M * 9.8 105 = x^2
Then you get x, and you win. Yay!