How many grams of NaHCO3 should be added to one liter of 0.100 M H2CO3 (Ka = 4.2 x 10-7) to prepare a buffer with pH = 7.00?
I got molefrom.100/1L equal .100mole. where do I go from here?
There are a mistake in the calculation. The correct calculation
4.2x.100=.42mole now NaHCO3=.42mole
7th: multiply molar mass: .42x84g/mole=?
answer: 35gram not39gram
1st:7= -log( 4.2x10^-7)+log(NaHCO3÷.100)
2nd: 7=6.3767+log(NaHCO3÷.100)
3rd: minus6.3767 on both side which equal .6232 lead to -->.6232= log(NaHCO3÷.100)
4th: 10^.6232=10^log(NaHCO3÷100)
5th: 4.2= (NaHCO3÷100)
6th: cross multiply:4.2x.100=4.2mole now NaHCO3=4.2mole
7th: multiply molar mass: 4.2x94g/mole=?
answer: 39gram
To determine how many grams of NaHCO3 should be added, you need to follow these steps:
1. Calculate the concentration of HCO3- ions required in the buffer solution using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where:
pH is the desired pH (7.00 in this case)
pKa is the acid dissociation constant (-log(Ka), which is -log(4.2 x 10^-7) in this case)
[A-] is the concentration of the conjugate base (HCO3-)
[HA] is the concentration of the acid (H2CO3, which is the initial concentration of H2CO3 in this case)
Rearrange the equation to solve for [A-]:
[A-] = 10^(pH - pKa) * [HA]
2. Convert the calculated concentration of HCO3- ions to moles by multiplying it by the volume of the buffer solution (1 liter in this case).
3. Finally, calculate the mass of NaHCO3 needed to supply the moles of HCO3- ions. Since the molar mass of NaHCO3 is 84.01 g/mol, you can use the following formula:
Mass (g) = Moles * Molar mass
Let's calculate it step-by-step:
Step 1:
pH = 7.00
pKa = -log(4.2 x 10^-7) ≈ 6.38
[HA] = 0.100 M (given)
[A-] = 10^(7.00 - 6.38) * 0.100
[A-] = 3.59 * 0.100
[A-] ≈ 0.359 M
Step 2:
Moles of HCO3- = [A-] * Volume of buffer solution
Moles of HCO3- = 0.359 * 1 (liters)
Moles of HCO3- = 0.359 moles
Step 3:
Mass (g) = Moles * Molar mass
Mass (g) = 0.359 * 84.01
Mass (g) ≈ 30.30 g
Therefore, approximately 30.30 grams of NaHCO3 should be added to make a buffer solution with a pH of 7.00.
To prepare a buffer with a specific pH, you need to use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is given as:
pH = pKa + log([A-]/[HA])
In this case, the acid is H2CO3 and the conjugate base is HCO3-. The pKa of H2CO3 can be calculated using the equilibrium constant (Ka). To find pKa, you take the negative logarithm of Ka:
pKa = -log(Ka)
So, first, you need to calculate the pKa of H2CO3 using the given Ka value:
pKa = -log(4.2 x 10^-7)
Now that you have the pKa, you can plug it into the Henderson-Hasselbalch equation along with the pH you want to achieve (pH = 7.00). The [A-]/[HA] ratio is the ratio of the concentration of the conjugate base to the concentration of the acid. In this case, the conjugate base is HCO3- and the acid is H2CO3. To calculate this ratio, we need to use the molarity (M) and the volume (V) of the solution.
Given:
pH = 7.00
pKa = calculated value
Now, let's rearrange the Henderson-Hasselbalch equation to solve for the ratio [A-]/[HA]:
[A-]/[HA] = 10^(pH - pKa)
Now substitute the given values:
[A-]/[HA] = 10^(7.00 - pKa)
Now, if you want to prepare a buffer in one liter (V = 1L), you need to consider the moles of H2CO3 required for the desired concentration. You correctly calculated the moles as 0.100 mole.
To find the amount of HCO3- (conjugate base) in grams that you need to add, you need to multiply the moles of HCO3- by its molar mass:
Mass = moles x molar mass
The molar mass of NaHCO3 is approximately 84.01 g/mol.
So, to calculate the mass of NaHCO3 needed, you can multiply the moles you found earlier by the molar mass:
Mass of NaHCO3 = Moles of HCO3- x Molar mass of NaHCO3
Mass of NaHCO3 = 0.100 mole x 84.01 g/mol
Therefore, you should add approximately 8.401 grams of NaHCO3 to one liter of 0.100 M H2CO3 to prepare a buffer with a pH of 7.00.