What volume, in liters, of 1.09 M KOH solution should be added to a 0.102 L solution containing 9.35 g of glutamic acid hydrochloride (Glu, FW = 183.59 g/mol; pKa1 = 2.23, pKa2 = 4.42, pKa3 = 9.95) to get to pH 10.26?
Should I start with molar concentrations in the beginning (because of the 0.102 L of Glu) or stick with moles?
To solve this problem, it's often helpful to work with molar concentrations. However, in this case, it might be easier to stick with moles.
Let's break down the problem into steps:
Step 1: Calculate the number of moles of glutamic acid hydrochloride (Glu) present in the 0.102 L solution.
To do this, we need to convert the mass of Glu to moles using its molar mass.
Molar mass of Glu = 183.59 g/mol
Mass of Glu = 9.35 g
Number of moles of Glu = Mass of Glu / Molar mass of Glu
Step 2: Determine the ratio of Glu to KOH needed to reach the desired pH.
Using the given pKa values, we can determine the protonation state of Glu at pH 10.26.
At pH 10.26, only the third ionization (protonation) of Glu is relevant:
pH > pKa3, Glu will be deprotonated (will have a negative charge).
This means that Glu will act as a base and react with KOH according to the balanced equation:
Glu + KOH → Glu- + K+ + H2O
From the balanced equation, we can see that for every 1 mole of Glu, we need 1 mole of KOH.
Step 3: Calculate the number of moles of KOH required.
Since the ratio of Glu to KOH is 1:1, the number of moles of KOH needed will be the same as the moles of Glu.
Step 4: Calculate the volume of 1.09 M KOH solution needed.
We now have the number of moles of KOH and its concentration. We can use this information to calculate the volume of KOH solution required.
Molar concentration (M) = Moles / Volume (in liters)
We can rearrange the equation to solve for Volume:
Volume (in liters) = Moles / Molar concentration (M)
Substituting the values:
Volume (in liters) = Number of moles of KOH / Molar concentration of KOH
Step 5: Calculate the molar concentration of KOH.
The molar concentration of KOH is given as 1.09 M in the problem statement.
Now, you have all the steps to solve the problem. Plug in the values obtained in each step to get the final answer, the volume of 1.09 M KOH solution required.