1.Suppose you had a buffer containing 0.5 moles of sodium monobasic phosphate and 0.5 moles of sodium dibasic phosphate. How many moles of hydrochloric acid would this phosphate buffer be able to accept before the pH of the solution began to change drastically?
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5 mol with 1 point PH
To determine how many moles of hydrochloric acid the phosphate buffer can accept before the pH changes drastically, we need to consider the acid-base equilibrium reactions that occur between the buffer components and the hydrochloric acid.
The equilibrium reactions involved in this buffer system are:
Sodium monobasic phosphate (NaH2PO4) ↔ sodium ion (Na+) + dihydrogen phosphate ion (H2PO4-)
Sodium dibasic phosphate (Na2HPO4) ↔ 2 sodium ions (2Na+) + hydrogen phosphate ion (HPO4-)
In an acidic solution, the basic form (HPO4-) accepts protons to form the acidic form (H2PO4-).
Since the buffer contains equal amounts of sodium monobasic phosphate and sodium dibasic phosphate, the moles of dihydrogen phosphate ions (H2PO4-) are equal to the moles of hydrogen phosphate ions (HPO4-).
So, let's calculate the concentration of dihydrogen phosphate ions (H2PO4-) in the buffer:
Given:
Moles of sodium monobasic phosphate = 0.5 moles
Moles of sodium dibasic phosphate = 0.5 moles
The total volume of the buffer is not specified, but it is not needed in this calculation since we are only concerned with the moles of the buffer components.
Since the moles of dihydrogen phosphate ions (H2PO4-) are equal to the moles of hydrogen phosphate ions (HPO4-), we can use the moles of sodium monobasic phosphate (NaH2PO4) as the total moles of dihydrogen phosphate ions (H2PO4-).
Therefore, the concentration of dihydrogen phosphate ions (H2PO4-) is 0.5 moles.
To calculate the moles of hydrochloric acid that the phosphate buffer can accept, we need to consider the acid-base reaction between hydrochloric acid (HCl) and dihydrogen phosphate ions (H2PO4-):
HCl + H2PO4- ↔ Cl- + H3PO4
This reaction consumes 1 mole of HCl per mole of H2PO4-.
Therefore, the buffer can accept 0.5 moles of hydrochloric acid (HCl) before the pH of the solution begins to change drastically.
To determine how many moles of hydrochloric acid (HCl) a phosphate buffer can accept before the pH of the solution changes drastically, you need to consider the buffering capacity of the buffer system. In this case, we have a mixture of sodium monobasic phosphate (NaH2PO4) and sodium dibasic phosphate (Na2HPO4), which can act as a buffer.
The buffering capacity of a buffer system depends on the equilibrium constants (Ka1 and Ka2) of the acidic and basic components. These equilibrium constants represent the extent to which the acidic and basic components donate or accept protons (H+).
To calculate the buffering capacity, we determine the equivalent concentration (Ceq) of the buffer solution, which is the sum of the concentrations of the acidic and basic components:
Ceq = [NaH2PO4] + [Na2HPO4]
Given that we have 0.5 moles of both NaH2PO4 and Na2HPO4, the equivalent concentration is:
Ceq = 0.5 + 0.5 = 1 mole
The buffering capacity is expressed as the moles of acid or base that can be added or removed per liter of the buffer solution while maintaining the pH within a specific range.
To calculate the buffering capacity per liter, we need to consider the pKa values of the two acid-base equilibria:
NaH2PO4 ⇌ Na+ + H2PO4- (pKa1)
Na2HPO4 ⇌ 2Na+ + HPO4^2- (pKa2)
For calculating the buffering capacity, we use the Henderson-Hasselbalch equation:
pH = pKa + log([base]/[acid])
Let's assume the desired pH range for the buffer solution is ±1 unit around the pKa values of the two acid-base equilibria.
For pKa1:
pH1 = pKa1 + 1
pH2 = pKa1 - 1
Calculating the base-to-acid ratios using the Henderson-Hasselbalch equation:
(pKa1 + 1) = log([Na2HPO4]/[NaH2PO4])
(pKa1 - 1) = log([Na2HPO4]/[NaH2PO4])
Since we have the same concentration of NaH2PO4 and Na2HPO4 (0.5 moles each):
2 = log([Na2HPO4]/[NaH2PO4])
Taking the antilog, we get:
[Na2HPO4]/[NaH2PO4] = 10^2
[Na2HPO4]/[NaH2PO4] = 100
So, for pKa1, the base-to-acid ratio is 100.
Similarly, for pKa2:
(pKa2 + 1) = log([NaH2PO4]/[Na2HPO4])
(pKa2 - 1) = log([NaH2PO4]/[Na2HPO4])
Again, assuming equal concentration (0.5 moles each):
1 = log([NaH2PO4]/[Na2HPO4])
Taking the antilog:
[NaH2PO4]/[Na2HPO4] = 10^1
[NaH2PO4]/[Na2HPO4] = 10
So, for pKa2, the base-to-acid ratio is 10.
Now, we can calculate the moles of HCl that the buffer can accept before the pH changes drastically. We assume that HCl ionizes completely, so one mole of HCl releases one mole of H+.
For pKa1:
Buffer capacity = Ceq * (base-to-acid ratio)
= 1 * (100 moles H+ / 1 mole base)
For pKa2:
Buffer capacity = Ceq * (base-to-acid ratio)
= 1 * (10 moles H+ / 1 mole base)
Adding the buffer capacities from both pKa values:
Total buffer capacity = Buffer capacity of pKa1 + Buffer capacity of pKa2
Keep in mind that these calculations assume ideal behavior and that the pH change is considered drastic when it deviates beyond the desired ±1 unit range.
By following this method, you can determine the moles of hydrochloric acid a phosphate buffer can accept before the pH of the solution changes significantly.