Calculate the pH and the percent dissociation of the hydrated cation in the following solutions. See Appendix C for the value of the equilibrium constant. (a) 0.010 M Cr1NO323

Video transcript

Hello. And this problem we are asked what is the ph percent association of the HYDROcodone in a 0.1 Moeller iron three nitrate solution and were given the acid dissociation constant. For the hydrate form of iron three. Iron three nitrate we call is a soluble salt. So it will dissociate completely In a quick solution form Iron three and nitrate annan's iron three. Then we'll combine with six waters former it's hydrated form. Let's begin then by finding the Initial concentration of our hydrated form of Iron three. So we have 0.015 moles environ three nitrate and every leader and everyone more iron three nitrate. You have one mole of iron And then every one mole of Iron three and will Bind with water to form one more. The hydrated form of Iron three. So our moles of iron three nitrate cancels our molds of iron three cancels. And we're left with moles of iron three. In the hydrate form the concentration 0.15 molar. Knowing the initial concentration of our hydrate form of iron. Let's now generate an ice table. We have our hydrate form of Iron three which is a weak acid. So it will react with water form And two plus hydroxide. And I do any minds. So being a weak acid right? It will donate a proton to the water. We have then initial change in equilibrium. So initially the concentration of our Hydrated Iron three is 0.015 moller and water is ignored. Pure liquid and initially have none of our products present. The change then is minus X plus X and plus X. And then we combine the initial and the change to come up with the equilibrium next step then that's right. Our equation for acid dissociation constant and use it then to find our equilibrium concentration of the mines so are asked association constant then is equal to r product concentrations over reacting concentration and making use of what's provided in the ice table. This is an X times X. All over 0.015 minus six. Given that this is a weak acid. Let's check our simplifying assumption to see if we can then eliminate the minus X. And simplify this equation. So check are simplifying assumption. We're going to take our initial concentration Are hydrated Iron three and divided by our asset association constant. 0.0155, x 6.0 times 10 to the -3. This works out 2.5 which is not greater than 500. So we must make use of Rodrick radic formula. So we'll have then X squared Over 0.015 -1 is equal to 6.0 times 10 to the -3. Just then moving things over we get expert equals 0.006, zero times 0.015 -1. Simplifying this. Get nine times 10 to the -5 -0.0060 x. Bring everything over to the left hand side. We'll set this equal to zero. Then we make use of the quadratic formula we call, then X. Is equal to negative B plus or minus square root of b squared minus or a C. Oliver to A. So in our case an X. Is equal to negative 0.60 plus or minus four of B squared -4 times a. Just one time c. Which is 1.99 Times 10 to the -5. All over two. A. So two times one. Then get using the plus get 0.00695 Mueller. Using the negative sign we get -0.0129 smaller. So the negative doesn't make sense. So we'll eliminate that. Make use of then The value of 0.00695. So this is equal to our concentration of my journey mines. So in the next step step four calculate the ph so the ph is equal to the negative log of our journey mine concentration This works out to 2.16. And we're asked to find that percent association. So that's stick five. So to find a percent association. Take the concentration of our journey minds divided by the initial concentration of Are hydrated Iron three which acts as a weak acid and multiplied by 100%. Our units of concentration cancel and this works out to 46%. And so our ph for our hydrate. Catomine iron three plus is 2. and the percent association Is 46%. Thanks for watching. Oh and sorry, one more thing. This corresponds to answer D. Thanks for watching. Please help.