In what volume ratio should you mix 1.0 M solutions of NH4Cl and NH3 to produce a buffer solution having pH = 9.80?

Video transcript

Hi everyone for this problem it reads calculate the ratio of the volumes of 1.25 molar sodium glycol eight and 1.25 moller glycolic acid necessary to make a buffer of ph 4.25, the P. K. A. Of glycolic acid is 3.83. So what we're being asked to do here is to calculate a ratio. And then the problem we're given a were given a weak acid which is glycolic acid and were given its conjugate base which is like a late. Okay. And another important piece of information we're given is we're asked to make a buffer of ph 4.25 and were also given P. K. So this is a lot of information that we're given but because we're given a weak acid and its conjugate base and were asked to calculate a ratio. What we need to do here is we need to use the Henderson Hasselbach equation to determine this ratio. And that equation is P H. Is equal to P. K. A plus log of the concentration of conjugate base over the concentration of the weak acid. Okay. And essentially what we want to solve for in this problem specifically the ratio is going to be this part of the Henderson Hasselbach equation. The ratio of conjugate base over weak acid. Okay, so let's go ahead and get started. So let's go ahead and replace the weak acid and the conjugate base into this. Okay, so when we rewrite this, what we get is the p H. Is going to equal P. K. A. Plus the log of the conjugate base. Which is let's see the conjugate base is going to be C two H. Three 03 - over the concentration of the weak acid which is c. two H. 403. Okay so that's the ratio there. So let's go ahead and plug in. We know what the ph is. The ph is 4.25. So we get 4.25 is equal to P. K. A. Which were given the P. K. A. Of the weak acid. And that is 3.83. So this is going to be plus the log of the conjugate base over the concentration of the weak acid. Okay so let's go ahead and simplify. We're going to subtract the 3.83 from both sides. So that leaves us with 0.42 is equal to the log of the concentration of conjugate base over the concentration of weak acid. Okay so now we're going to get rid of the log. Okay so what this is going to be then is 10 log of the conjugate base over the weak acid Is equal to 100.42. We're gonna take we're gonna raise both sides by 10. Okay? So what that then does is cancel this log and what we get is 100.42 is equal to the concentration of conjugate base over the concentration of the weak acid. Okay so then what we'll get is When we take the raise that to the 10, what we get is 2. is equal to 2. 0-6. eight is equal to the concentration of conjugate base over the concentration of weak acid. Okay, so the answer then for this is the ratio of the volumes of 1.2 molar sodium glycol, it and 1.2 molar glycolic acid is 2.63. So let's go ahead and write that here. So the ratio Is equal to 2.63. And we were able to solve that using the Henderson Hasselbach equation. So that is it for this problem. I hope this was helpful.