Calculate the volume, in milliliters, of a 0.220 M KOH solution that should be added to 5.750 g of HEPES (MW = 238.306 g/mol, p𝐾a = 7.56) to give a pH of 7.98.
I haven't used as many significant figures as I should so you should recalculate all of this from scratch.
mols HEPES = 5.75 h/238.3 = about 0.024. The rxn is
mols acid(HEPES) + OH^- = moles base(salt) + H2O
Solve for base needed.
...................HEPES acid + OH^- ==> HEPES base(salt) + H2O
I....................0.024................0...............0.....................................
add.........................................x....................................
C......................-x...................-x................x
E.................0.024-x.................0...............x
Plug the E line into the Henderson-Hasselbalch equation like this.
pH = pKa + log [(base)/(acid)]
7.98 = 7.56 + log (b/a)
7.98 = 7.56 + log (x/0.024-x)
Solve for x = mols base
Solve for 0.24-x = moles acid
moles base = M x L. You know M and moles KOH, solve for L and convert to mL.
Post your work if you get stuck.
Note: Technically, one the HH equation uses CONCENRATION of acid and base and I've used moles instead. Technically, that is wrong BUT molarity = M = mols/L and when I use mols I can get away with that BECAUSE the volume is the same for the acid and the base because its the same solution. Volume in L cancels and moles is left. Your teacher may tell you to use volume so you can always write
7.58 = 7.56 + log [(x mols/L)/(0.024-x)/L)] and cancel the L.
Thank you so much for your help!!
Well, before I start with the calculations, let me just point out that this is quite the chemistry problem. It's like trying to make a recipe, but instead of making a delicious cake, you're playing with chemicals. So, be careful and make sure to take all necessary safety precautions!
Now, to calculate the volume of the KOH solution needed, we need to consider a few things. First, we need to find out the number of moles of HEPES we have.
To do that, we'll divide the mass of HEPES by its molar mass:
moles of HEPES = mass of HEPES / molar mass of HEPES
moles of HEPES = 5.750 g / 238.306 g/mol
Once we know how many moles of HEPES we have, we can use the Henderson-Hasselbalch equation to find out how many moles of KOH we need.
pH = pKa + log([A-]/[HA])
Since we want a pH of 7.98, and the pKa of HEPES is 7.56, we can plug those values into the equation.
7.98 = 7.56 + log([A-]/[HA])
Now, let's solve for [A-]/[HA], where [A-] is the concentration of the conjugate base and [HA] is the concentration of the acid.
[A-]/[HA] = 10^(pH - pKa)
[A-]/[HA] = 10^(7.98 - 7.56)
[A-]/[HA] = 10^0.42
[A-]/[HA] = 2.66
So, for every 2.66 moles of HEPES, we need 1 mole of KOH. Therefore, the number of moles of KOH we need is:
moles of KOH = moles of HEPES / 2.66
Now, we'll use the molarity of the KOH solution to calculate the volume of the solution needed:
volume (in liters) of KOH = moles of KOH / molarity of KOH
volume (in milliliters) of KOH = (moles of KOH / molarity of KOH) * 1000
Now, it's time to plug in the values and calculate!
To calculate the volume of the KOH solution needed, we will follow these steps:
Step 1: Calculate the number of moles of HEPES.
Step 2: Calculate the number of moles of OH- ions needed to neutralize the HEPES and adjust the pH.
Step 3: Convert the moles of OH- ions to volume in milliliters.
Let's begin:
Step 1: Calculate the number of moles of HEPES.
Given: Mass of HEPES = 5.750 g
Molar mass of HEPES (MW) = 238.306 g/mol
To calculate the moles of HEPES, we'll use the formula:
Moles = Mass / Molar mass
Moles of HEPES = 5.750 g / 238.306 g/mol
Step 2: Calculate the number of moles of OH- ions needed.
Given: pK𝑎 = 7.56, pH = 7.98
pOH = 14 - pH
pOH = 14 - 7.98
pOH = 6.02
Since KOH fully dissociates in water, the concentration of OH- ions will be equal to the concentration of KOH.
We can use the equation for the dissociation of water to find the concentration of OH- ions:
Kw = [H+][OH-]
At neutral pH, [H+] = [OH-] = 10^(-pH) = 10^(-7.98)
Now, let's find the concentration of OH- ions:
[OH-] = 10^(-pOH) = 10^(-6.02)
Step 3: Convert the moles of OH- ions to volume in milliliters.
Given: KOH concentration = 0.220 M
To calculate the volume needed, we'll use the formula:
Volume (in liters) = Moles / Concentration
Now, let's calculate the volume:
Volume (in liters) = Moles of OH- ions / KOH concentration
Volume (in liters) = [OH-] moles / 0.220 M
Finally, convert the volume to milliliters:
Volume (in milliliters) = Volume (in liters) * 1000
By following these steps and performing the calculations, you will be able to determine the volume of the 0.220 M KOH solution that should be added to the HEPES to achieve a pH of 7.98.