Let's begin this problem by examining what kind of solution we have. And it tells us right here at the beginning that we have a buffer, so let's underline that word. And when we have a buffer, we know that the Henderson–Hasselbalch equation is a good way to calculate the pH of a buffer. So let's write the Henderson–Hasselbalch equation, pH = pka + log [B]/[A]. Now you can also use instead of concentrations, you can put moles of base over moles of acid. And this problem, one way is about as easy as the other. We are trying to calculate the PH so we need to know the PKA. Well the PKA is the negative log of the KA value but I don't have the KA value, I have the KB of ammonia. To get the KA we will take KW divided by KB which is 1.76 times 10 to -5. Okay, then plus the log of the concentration of the base over the concentration of the acid. NH3, nitrogen with three things attached, that's my base. The acid is this portion of the salt. So the acid is NH4 plus. So I need a concentration of those two items. They gave me the concentration of the base where I can put 0.750 molar right there. Now I need to know the concentration of the acid. To get the concentration of the acid, I need to know the moles of the acid over the volume in liters. Well it's 500 millilitres,so that bottom number was easy enough to determine. 500 millilitres or let's write it this way, 0.5 liters, 500 milliliters is 0.5 liters. What I need to know is the moles of that acid. And they gave me grams of it. And they gave me the formula of the salt which is ammonium chloride. So I'll get the molar mass of ammonium chloride, one nitrogen, look at the formula there. One nitrogen, four hydrogens, and a chlorine, because it's the mass of the whole salt, so we need to use the molar mass of the whole salt. When you add those values together, you get 53.50. I would go with the grams and the moles. So 20 grams divided by the molar mass will give me moles of this acid, divided by the volume will give me moles per liter, or molarity of this acid. And when you divide those values out, you obtain a number of 0.748. It's almost as concentrated as the base, but not quite. So when I take the negative log of this ratio, I have 9.246. Since there is, I'll go ahead and write this out, log of 0.750 / 0.748. Since there is a slight more base than there is acid, then this may be a little bit higher in pH. And when you actually work the numbers out it does raise it up to that third decimal point to 9.247. So that is the pH of this buffer solution. And it's very common when you've got a buffer based upon a base and its conjugate acid salt that you would have a pH greater than 7.
