Calculate the percent association of 4.10 * 10 to the -1 molar of acetic acid. Here we're told that the KA value for acetic acid is 1.8 * 10 to the -5. All right, since it's a weak acid, we need to set up an ice chart, and we know it's a weak acid because its KA is less than one. So here we're going to use steps one to three to set up the ice chart.
So first, we're going to react the weak acid with water. In this case, water will be in its liquid form following the Bronsted-Lowry acid definition that we know. We know that the acid is acetic acid and therefore the water would be the base. The acid donates an H plus and the basic subset. Doing this would create as our products the acetate ion and the hydronium ion.
This is an ice chart. So which stands for initial change equilibrium. Now we place the initial amount given to us for the weak acid, which we're told is 4.10 * 10 to the -1, which is just basically 0.410 molar. Remember, ice charts ignore solids and liquids, so the water will be ignored. We're not told anything initially about our product, so initially there's zero for the change row. Remember, we lose reactants in order to make products, so minus X + X + X. For the equilibrium row we bring down everything, so .410 -, X + X + X.
So we filled out our ice chart. Now using the equilibrium row, set up the equilibrium constant expression and solve for X. Check if a shortcut can be utilized to avoid the quadratic formula. So here we're going to say what the quadratic formula we have it. Here we say we use the 500 approximation method. When the ratio of initial concentration to the KA value in this case is greater than 500, we can ignore the minus X.
So our initial concentration of acetic acid is 4.1 * 10 to -1 molar. Its KA value was 1.8 * 10 to the -5. When we punch that in, it gives us 22,777.8, a number much greater than 500. That means that our in our equilibrium expression we can ignore the minus X. So remember our equilibrium expression is products over reactants, so it's ka equals my two products divided by the weak asset. Again, water is a liquid so we ignore it.
So 1.8 * 10 to the -5 = X ^2 divided by. Remember using the 500 approximation method below, we saw that we can ignore the minus X. So this is just .410 on the bottom and we didn't include the minus X here. Cross multiply these two When we do that X ^2 = 7.38 * 10 to the -6. Take the square root of both sides X = 2.717 * 10 to the -3. We just found out what X is and it says use the X variable.
Now to calculate the percent ionization association. Here we're going to say that the X that we found is equal to my hydronium ion concentration. So we just found out what H3O plus concentration is. Remember for weak acid, percent ionization or dissociation equals the concentration of H3O plus at equilibrium divided by the initial concentration of the acid times 100. So at equilibrium HDL plus was 2.717 * 10 to the -3 molar. Our initial concentration was 0.410 molar and then multiply that by 100. When we do that, we get oh .66%. So that's the amount of acetic acid that basically ionized when placed in an aqueous solution. It's a weak acid, so we should expect a number that's much smaller than 100%. In this case it .66%.