Answer:
12.937 mL
Explanation:
First, we have to start with the <u>hendersson-hasselbach equation</u>:
(Equation 1)
So, from this equation, we already know the desired pH value 9.3. Therefore we have to <u>calculate the pKa value</u>, for this, we need to use the following equations:
(equation 2) and (equation 3) With this in mind we can do the calculations:
Additionally, we have to know the <u>buffer system reaction</u>:
(reaction 1)
With this in mind and . Now if we use the hendersson-hasselbach reaction we can find the <u>ratio</u> () that we need for the desired pH value, so:
(equation 4)
From the problem, we know that we already have a portion of , 30 mL and 0.1 M. Also, the HCl that we are going to add will react with the NH3 (), so:
(reaction 2)
With this in mind, <u>all the HA concentration will come from the addition of the HCl</u> and this addition will consume some A-. Therefore, we have to know the <u>moles of A- before the addition</u>:
So, we can write a new equation that calculates the concentration of <u>before the addition</u>:
(equation 5)
In this case, <u>"X" is the of A- (NH3) consumed</u> in the reaction for the addition of HCl and <u>Y is the volume of HCl (in litters)</u>. Additionally, we can write another equation for the concentration of HA after the addition of HCl:
(equation 6)
Let's remember that we already have 0.03L (30mL) on the beaker, thats why we have to add "0.03" in the bottom. Now, we can <u>include these last two equations on equation 4</u>, so:
(equation 7)
<u>We have 2 unknows and 1 equation</u> we need another equation to solve this. So, all X would be produced by the addition of HCl therefore "X" are the moles of HCl added and Y would be the volume of HCl, if we have a concentration of 0.11M for HCl w<u>e can use the molarity equation to relate "X" and "Y"</u>, so:
(equation 8)
(equation 9)
Now, we can <u>replace equation 9 in equation 7</u>, so:
(equation 10).
If we do some math we will obtain:
(equation 11)
When we solve for "Y" we obtain a value of 0.012937 L or 12.937 mL.
I hope it helps!