you need to prepare 100 ml of ph=3.50 buffer solution using 0.100 M formic acid and 0.200 M sodium formate. how much of each solution shoudl be mixed to prepare this buffer?
To prepare a 100 mL buffer solution with a pH of 3.50 using 0.100 M formic acid (HCOOH) and 0.200 M sodium formate (HCOONa), follow these steps:
Step 1: Calculate the number of moles of formic acid (HCOOH) needed for the buffer solution using the Henderson-Hasselbalch equation:
pH = pKa + log([salt]/[acid])
Since the pH is given as 3.50, and the pKa of formic acid is 3.75, we can rearrange the equation to solve for the ratio [salt]/[acid]:
3.50 = 3.75 + log([salt]/[acid])
log([salt]/[acid]) = 3.50 - 3.75
log([salt]/[acid]) = -0.25
Now, calculate the antilog (inverse logarithm) of -0.25:
[salt]/[acid] = 10^(-0.25)
[salt]/[acid] = 0.56
This means that the ratio of sodium formate (salt) to formic acid (acid) in the buffer solution should be 0.56.
Step 2: Calculate the volume of each solution needed:
Let x represent the volume (in mL) of 0.100 M formic acid needed.
Since the total volume of the buffer solution is 100 mL, the volume of 0.200 M sodium formate needed will be (100 - x) mL.
Step 3: Convert volumes to moles:
Moles of formic acid (HCOOH) = concentration (M) x volume (L)
Moles of sodium formate (HCOONa) = concentration (M) x volume (L)
In this case, since we're given the concentrations in Molarity (M) and the volumes in milliliters (mL), we need to convert milliliters to liters by dividing by 1000:
Moles of formic acid (HCOOH) = 0.100 M x (x/1000) L
Moles of sodium formate (HCOONa) = 0.200 M x [(100 - x)/1000] L
Step 4: Set up the equation based on the mole ratios:
Since the ratio of sodium formate (salt) to formic acid (acid) is 0.56, we can set up the following equation:
0.56 = (moles of sodium formate) / (moles of formic acid)
Replacing the moles from Step 3, the equation becomes:
0.56 = (0.200 x [(100 - x)/1000] L) / (0.100 x (x/1000) L)
Simplifying the equation:
0.56 = (0.200 / 0.100) x [(100 - x)/x]
0.56 = 2 x [(100 - x)/x]
0.56 = (200 - 2x) / x
Cross-multiply:
0.56x = 200 - 2x
2.56x = 200
x = 200 / 2.56
x ≈ 78.13
Step 5: Calculate the volumes of each solution:
The volume of formic acid needed is approximately 78.13 mL, and the volume of sodium formate needed is approximately 100 - 78.13 = 21.87 mL.
Therefore, you will need to mix approximately 78.13 mL of 0.100 M formic acid and 21.87 mL of 0.200 M sodium formate to prepare a 100 mL buffer solution with a pH of 3.50.
To prepare a buffer solution of a specific pH, you'll need to calculate the quantities of your acid and its conjugate base needed. In this case, formic acid (HCOOH) acts as the acid, and sodium formate (HCOONa) acts as the conjugate base.
Let's break down the steps to calculate the volumes of the 0.100 M formic acid and 0.200 M sodium formate solutions needed to prepare a 100 ml buffer solution at pH 3.50.
Step 1: Calculate the ratio of conjugate base to acid needed for the desired pH.
The Henderson-Hasselbalch equation relates the pH, pKa (the negative logarithm of the acid dissociation constant), and the ratio of the concentration of the conjugate base (A-) to the concentration of the acid (HA) in the buffer solution:
pH = pKa + log10([A-]/[HA])
Given that pH = 3.50 and the pKa of formic acid is 3.75 (approximately), the equation becomes:
3.50 = 3.75 + log10([A-]/[HA])
Rearranging the equation, we get:
log10([A-]/[HA]) = 3.50 - 3.75
log10([A-]/[HA]) = -0.25
Taking the antilog (inverse logarithm) of both sides gives:
[A-]/[HA] = 10^(-0.25)
[A-]/[HA] = 0.5623
Step 2: Determine the required concentrations of the acid and conjugate base.
Since we know the concentrations of the acid and conjugate base solutions, we can use the ratio derived in the previous step to calculate their concentrations in the buffer solution.
Let x be the volume (in milliliters) of the 0.100 M formic acid solution required.
The volume of the sodium formate solution needed will be 100 - x ml.
Using the concentration formula (C = n/V), where C is concentration, n is the number of moles, and V is volume in liters, we can determine the number of moles of the acid and conjugate base:
Moles of acid (HA) = (0.100 M) * (x ml / 1000 ml) = 0.100x/1000
Moles of conjugate base (A-) = (0.200 M) * ((100 - x) ml / 1000 ml) = 0.200(100 - x)/1000
Step 3: Implement the ratio to find the values of x and (100 - x).
According to the ratio derived in Step 1, we can set up the equation:
[A-]/[HA] = 0.5623
Substitute the moles of the acid and conjugate base from Step 2 into the equation:
(0.200(100 - x)/1000) / (0.100x/1000) = 0.5623
Simplifying the equation further:
0.200(100 - x) / 0.100x = 0.5623
Now, cross-multiply and solve the equation for x:
0.200(100 - x) = 0.5623(0.100x)
20 - 0.200x = 0.05623x
Collect like terms:
0.05623x + 0.200x = 20
0.25623x = 20
x = 20 / 0.25623
x ≈ 78.04 ml
Therefore, you need approximately 78.04 ml of the 0.100 M formic acid solution and (100 - 78.04) ≈ 21.96 ml of the 0.200 M sodium formate solution to prepare a 100 ml buffer solution at pH 3.50.