You are instructed to create 800. mL of a 0.69 M phosphate buffer with a pH of 7.6. You have phosphoric acid and the sodium salts NaH2PO4, Na2HPO4, and Na3PO4 available. what is the molarity needed for the acid component of the buffer?What is the molarity needed for the base component of the buffer? How many moles of acid are needed for the buffer?How many moles of base are needed for the buffer? How many grams of acid are needed for the buffer? How many grams of base are needed for the buffer?
You want 800 x 0.69 = approx (you need to do it) 552 mmols total. I may have different K values than you. I will use 7.20 for pK2.
7.6 = 7.2 + log (base)/(acid)
Solve for b/a and I get approx
b/a = 2.5 (in millimols--not concn)
a + b = 552 (in millimols).
Solve these two equations simultaneously to determine millimils a and mmols b. I think you can go from there. Post your work if you get stuck and explain your trouble.
To create a phosphate buffer solution, we will use the following equations:
H3PO4 ⇌ H+ + H2PO4-
H2PO4- ⇌ H+ + HPO42-
HPO42- ⇌ H+ + PO43-
To find the molarity needed for the acid component of the buffer, we need to calculate the concentrations required for each species.
Step 1: Calculate the concentration of H2PO4- (the acid component) using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Given pH = 7.6 and pKa (phosphoric acid) = 2.12, we can rearrange the equation as:
7.6 = 2.12 + log([HPO42-]/[H2PO4-])
Let x be the concentration of H2PO4-. Then, [HPO42-] = x and [H2PO4-] = 0.69 M - x.
7.6 = 2.12 + log(x/(0.69 - x))
Using logarithmic properties, we can solve for x:
5.48 = log(x/(0.69 - x))
10^5.48 = x/(0.69 - x)
x = 10^5.48 * 0.69 - 10^5.48 * x
x + 10^5.48 * x = 10^5.48 * 0.69
1 x * (1 + 10^5.48) = 0.69 x 10^5.48
x = (0.69 * 10^5.48) / (1 + 10^5.48)
Calculating this equation, we find x ≈ 5.60 x 10^-3 M.
Therefore, the molarity needed for the acid component of the buffer is approximately 5.60 x 10^-3 M.
To find the molarity needed for the base component of the buffer, we use the equation:
[HPO42-] = 0.69 M - [H2PO4-]
Given that [H2PO4-] = 5.60 x 10^-3 M, we can calculate:
[HPO42-] = 0.69 M - 5.60 x 10^-3 M
[HPO42-] ≈ 0.6844 M
Therefore, the molarity needed for the base component of the buffer is approximately 0.6844 M.
To determine the number of moles of acid needed for the buffer, we use the equation:
moles of acid = concentration of acid (H2PO4-) * volume of buffer solution
moles of acid = 5.60 x 10^-3 M * 0.800 L
moles of acid ≈ 4.48 x 10^-3 mol
Therefore, the buffer requires approximately 4.48 x 10^-3 moles of acid.
To find the number of moles of base needed for the buffer, we use the equation:
moles of base = concentration of base (HPO42-) * volume of buffer solution
moles of base = 0.6844 M * 0.800 L
moles of base ≈ 0.5475 mol
Therefore, the buffer requires approximately 0.5475 moles of base.
To calculate the grams of acid needed for the buffer, we use the equation:
grams of acid = moles of acid * molar mass of acid (H3PO4)
The molar mass of H3PO4 is approximately 98 g/mol.
grams of acid = 4.48 x 10^-3 mol * 98 g/mol
grams of acid ≈ 0.44 g
Therefore, the buffer requires approximately 0.44 grams of acid.
To calculate the grams of base needed for the buffer, we use the equation:
grams of base = moles of base * molar mass of base (NaH2PO4)
The molar mass of NaH2PO4 is approximately 120 g/mol.
grams of base = 0.5475 mol * 120 g/mol
grams of base ≈ 65.7 g
Therefore, the buffer requires approximately 65.7 grams of base.
To determine the molarity needed for the acid component of the buffer, we can utilize the Henderson-Hasselbalch equation, which relates the pH of a buffer to the pKa and the ratio of the conjugate base (CB) to the weak acid (WA):
pH = pKa + log [CB]/[WA]
In this case, the acid component will be the weak acid, which is phosphoric acid (H3PO4). The corresponding conjugate bases are H2PO4-, HPO42-, and PO43-, which are derived from the sodium salts NaH2PO4, Na2HPO4, and Na3PO4, respectively.
Given that the desired pH is 7.6, we can plug in the values into the Henderson-Hasselbalch equation to determine the ratio [CB]/[WA]. However, we first need to determine the pKa value for phosphoric acid.
The pKa values for phosphoric acid are as follows:
pKa1 = 2.15
pKa2 = 7.20
pKa3 = 12.37
Since the desired pH is closer to pKa2 (7.20), we will use this value to determine the ratio [CB]/[WA].
pH = pKa + log [CB]/[WA]
7.6 = 7.20 + log [CB]/[WA]
Next, we need to consider the acid-base equilibrium for phosphoric acid:
H3PO4 ⇌ H2PO4- + H+
Since 1 mole of H3PO4 dissociates to yield 1 mole of H+, the ratio [CB]/[WA] can be deduced:
[CB]/[WA] = [H2PO4-]/[H3PO4] = 10^(pH - pKa)
= 10^(7.6 - 7.20)
Now we can calculate the ratio [CB]/[WA]:
[CB]/[WA] = 10^(7.6 - 7.20)
To determine the molarity needed for the acid component of the buffer, we need to know the total volume (800 mL) and the desired molarity (0.69 M) of the buffer.
Let x be the molarity of the acid component (H3PO4). Since the concentration of H3PO4 equals the concentration of H2PO4- (CB) and NaH2PO4 (the acid form), we can write the following equation:
x * 800 mL = 0.69 M * 800 mL
Solving for x:
x = (0.69 M * 800 mL) / 800 mL
Now, let's calculate the molarity needed for the acid component of the buffer:
x = 0.69 M
Therefore, the molarity needed for the acid component of the buffer is 0.69 M.
To determine the molarity needed for the base component of the buffer, we can subtract the molarity of the acid component from the desired buffer molarity:
Molarity of base component = Desired buffer molarity - Molarity of acid component
= 0.69 M - 0.69 M
= 0 M
Therefore, the molarity needed for the base component of the buffer is 0 M.
To calculate the number of moles of acid needed for the buffer, we can use the formula:
moles = Molarity * Volume (in liters)
Given that the volume is 800 mL (or 0.8 L), and the molarity of the acid component is 0.69 M, we can substitute these values into the formula:
moles = 0.69 M * 0.8 L
Now, let's calculate the number of moles of acid needed for the buffer:
moles = 0.55 mol
Therefore, the number of moles of acid needed for the buffer is 0.55 mol.
Since the molarity of the base component is 0 M, no moles of base are needed for the buffer.
To determine the mass (in grams) of the acid needed for the buffer, we need to know the molar mass of phosphoric acid (H3PO4).
The molar mass of phosphoric acid can be calculated as follows:
Molar mass = (mass of H atoms) + (mass of P atom) + (mass of O atoms)
The atomic masses are:
H (hydrogen) = 1.01 g/mol
P (phosphorus) = 31.00 g/mol
O (oxygen) = 16.00 g/mol
Mass of H atoms = 3 * (1.01 g/mol)
Mass of P atom = 1 * (31.00 g/mol)
Mass of O atoms = 4 * (16.00 g/mol)
Now, we can calculate the molar mass of phosphoric acid:
Molar mass = (3 * (1.01 g/mol)) + (1 * (31.00 g/mol)) + (4 * (16.00 g/mol))
Next, we can calculate the mass of the acid needed for the buffer using the formula:
mass = moles * molar mass
Substituting the values for moles (0.55 mol) and the molar mass of phosphoric acid, we can calculate the mass of acid needed for the buffer:
mass = 0.55 mol * (molar mass of H3PO4)
Therefore, the grams of acid needed for the buffer can be calculated by multiplying the number of moles by the molar mass of phosphoric acid.
Finally, to determine the grams of base needed for the buffer, we can calculate it using the formula:
grams = moles * molar mass
Since no moles of base are needed for the buffer (as the molarity of the base component is 0 M), there are 0 grams of base needed for the buffer.