Acetic acid tends to form dimers, (CH₃CO₂H₂), because of hydrogen bonding: The equilibrium constant Kc for this reaction is 1.51⨉10² in benzene solution but only 3.7⨉10^-2 in water solution. (a) Calculate the ratio of dimers to monomers for 0.100 M acetic acid in benzene.

Video transcript

Hello. In this problem, we are told that a settling undergoes demonization to produce final settling or be time. We're told in a water solution. The equilibrium constant for the reaction is 3.50 times 10 to minus two. We are asked to determine the ratio monitor two timer 4.75 molar settling in water solution. So settling our reactant as a formula C. Two H two and a product, vinyl settling has a formula C four H. Four. So a settling is our monomer. And vinyl settling is our timer. If we write a balanced reaction in terms of the monomer and dime er we have two moles of our monomer. In equilibrium with our timer, let's now generate an ice table. We're told that we initially have .750 Mueller settling which is our monomer and we initially have none of the diner present. The change then is minus two X. And plus X equilibrium. We're combining the initial and the change this is 0.750 minus two X. And then X. Our equilibrium constant expression written in terms of the dimmer and the monomer is equal to the concentration of our product, which is the dimmer. All over. The concentration of our monomer reactant squared And this is equal to 3.50 times 10 to the -2. So, plugging in the information from the ice table, we have the timer concentration is X. And that of the monomer is .750 -2 x. When we square that set it equal to 3.50 times 10 to the -2. We're gonna move our denominator over to the right hand side. We now have X. Is equal to 3.50 times 10 to minus two Times 0.750 -2 x times itself. Sometimes it's helpful to write it out to see what's going on. So X. N is equal to 0.0350 times 0.5625 minus three X plus four X squared simplifying this further, X is equal to 0.0196, -0.105 x plus 0.14 x squared. We'll move our X over to the right hand side. You then get 0.14 x squared -1.105 x plus 0.01969. And we said this all equal to zero. So we're going to determine whether or not we have to make use of the quadratic equation or if we can simplify things. So if the monomer concentration initially divided by our equilibrium constant is greater than 500. We can avoid using the quadratic formula in this case, our initial monomer concentration is 0. And our equilibrium constant is 3.50 times 10 - -2. This works out to 21 Which is not greater than 500. So we'll need to make use of the quadratic formula. Rewriting our quadratic equation. We have 0.14 X squared minus 1. X plus 0.1969 is equal to zero. Remember the quadratic formula X. N. Is equal to negative B plus or minus square root of B squared minus four A. C. Oliver to A. So in our case then X is equal to a negative negative 1.105. That makes it a positive plus or minus square root of B squared. So negative 1.105 squared minus four times 0.14 which is a times C. Which is 0.1969. All over To a. So two times 0.14. So working out what's under the square root X. Then works out to 1.105 plus or minus 1.999 divided by 0.28. So our positive route works out to 7.875. And the negative works out to 0.0182. And so based on our initial concentration of 0. we know that this route is not possible. We'd end up with a negative concentration which is impossible. And so we're gonna make use of then the negative. So looking at our ice table X. Is equal to the concentration of our diver Which is the vinyl acetate. Final settling. Excuse me, which is 0.018 to Mueller. And the concentration of our monomer, which is settling Is equal to 0.750 -2X. This works out to 0.750 -2 times 0.0182. So our monomer concentration is 0. Moeller. So we are asked to determine the ratio of monomer two timer. So our ratio then is 0. Moller divided by 0. Polar. And this works out to 39.2. So our ratio of monomer to dimmer, which is settling to finally settling Is 39.2. Thanks for watching. Hope this help.