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What volume (in ml, rounded up to first decimal place) of 0.10 M sodium formate solution should be added to 50 ml of 0.05 M formic acid to produce a buffer solution of pH 4. [pKa for formic acid is 3.7]
Correct answer is between '49.5,50.5'. Can you explain this answer?
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What volume (in ml, rounded up to first decimal place) of 0.10 M sodiu...
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Let x ml of 0.10M sodium formate is added,
No. of moles in xml of 0.10M sodium formate is = 1.1*x/1000
No. of moles in 50ml xml of 0.05M formic acid is = 0.05*50/1000
Therefore, [sodium formate] / [formic acid] = (0.01*x/1000)/(0.05*50/1000)
= 0.04x
From Henderson's equation:
pH = pKa + log[salt]/[acid]
=>4 = 3.8 + log 0.04x
=> log 0.04x = 0.2
=> x = 39.6 ml
No. of moles in xml of 0.10M sodium formate is = 1.1*x/1000
No. of moles in 50ml xml of 0.05M formic acid is = 0.05*50/1000
Therefore, [sodium formate] / [formic acid] = (0.01*x/1000)/(0.05*50/1000)
= 0.04x
From Henderson's equation:
pH = pKa + log[salt]/[acid]
=>4 = 3.8 + log 0.04x
=> log 0.04x = 0.2
=> x = 39.6 ml
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Calculation of pH:
To determine the volume of sodium formate solution needed to create a buffer at pH 4, we first need to calculate the concentration of formate ion ([HCOO-]) required for this pH. The Henderson-Hasselbalch equation can be used for this calculation:
Given that the pKa for formic acid is 3.7, we can rearrange the equation as follows:
4 = 3.7 + log([A-]/[HA])
Simplifying the equation:
0.3 = log([A-]/[HA])
Ratio of [A-]/[HA]:
Since formic acid (HA) is a weak acid and sodium formate (HCOONa) is its conjugate base (A-), the ratio of their concentrations will determine the pH. The ideal ratio for a buffer solution at pH 4 is 1:1. This means that [A-] should be equal to [HA].
Calculating the required concentration of formate ion:
To calculate the concentration of formate ion ([A-]), we can assume that the initial concentration of formic acid ([HA]) is equal to its original concentration (0.05 M) and the concentration of sodium formate ([A-]) to be added is x M.
Using the ratio of [A-]/[HA] = 1, we can write the following equation:
1 = x / 0.05
Solving for x:
x = 0.05 M
This means that the concentration of formate ion ([A-]) in the final buffer solution should be 0.05 M.
Calculating the volume of sodium formate solution:
Now that we know the required concentration of formate ion, we can calculate the volume of sodium formate solution needed to achieve this concentration.
Using the equation:
C1V1 = C2V2
Where C1 is the initial concentration of sodium formate (0.10 M), V1 is the volume of sodium formate solution needed, C2 is the final concentration of sodium formate (0.05 M), and V2 is the total volume of the buffer solution (50 ml + V1).
Plugging in the values:
0.10 M * V1 = 0.05 M * (50 ml + V1)
Simplifying the equation:
0.10 V1 = 0.05 * 50 ml + 0.05 V1
0.10 V1 - 0.05 V1 = 2.5 ml
0.05 V1 = 2.5 ml
V1 = 50 ml
Therefore, the volume of 0.10 M sodium formate solution required to create a buffer solution at pH 4 is 50 ml.
Conclusion:
The correct answer is 50 ml, which falls within the range of 49.5 to 50.5 ml specified. This volume of sodium formate solution, when added to 50 ml of 0.05 M formic acid, will create a buffer solution at pH 4.
To determine the volume of sodium formate solution needed to create a buffer at pH 4, we first need to calculate the concentration of formate ion ([HCOO-]) required for this pH. The Henderson-Hasselbalch equation can be used for this calculation:
Given that the pKa for formic acid is 3.7, we can rearrange the equation as follows:
4 = 3.7 + log([A-]/[HA])
Simplifying the equation:
0.3 = log([A-]/[HA])
Ratio of [A-]/[HA]:
Since formic acid (HA) is a weak acid and sodium formate (HCOONa) is its conjugate base (A-), the ratio of their concentrations will determine the pH. The ideal ratio for a buffer solution at pH 4 is 1:1. This means that [A-] should be equal to [HA].
Calculating the required concentration of formate ion:
To calculate the concentration of formate ion ([A-]), we can assume that the initial concentration of formic acid ([HA]) is equal to its original concentration (0.05 M) and the concentration of sodium formate ([A-]) to be added is x M.
Using the ratio of [A-]/[HA] = 1, we can write the following equation:
1 = x / 0.05
Solving for x:
x = 0.05 M
This means that the concentration of formate ion ([A-]) in the final buffer solution should be 0.05 M.
Calculating the volume of sodium formate solution:
Now that we know the required concentration of formate ion, we can calculate the volume of sodium formate solution needed to achieve this concentration.
Using the equation:
C1V1 = C2V2
Where C1 is the initial concentration of sodium formate (0.10 M), V1 is the volume of sodium formate solution needed, C2 is the final concentration of sodium formate (0.05 M), and V2 is the total volume of the buffer solution (50 ml + V1).
Plugging in the values:
0.10 M * V1 = 0.05 M * (50 ml + V1)
Simplifying the equation:
0.10 V1 = 0.05 * 50 ml + 0.05 V1
0.10 V1 - 0.05 V1 = 2.5 ml
0.05 V1 = 2.5 ml
V1 = 50 ml
Therefore, the volume of 0.10 M sodium formate solution required to create a buffer solution at pH 4 is 50 ml.
Conclusion:
The correct answer is 50 ml, which falls within the range of 49.5 to 50.5 ml specified. This volume of sodium formate solution, when added to 50 ml of 0.05 M formic acid, will create a buffer solution at pH 4.
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What volume (in ml, rounded up to first decimal place) of 0.10 M sodium formate solution should be added to 50 ml of 0.05 M formic acid to produce a buffer solution of pH 4. [pKa for formic acid is 3.7]Correct answer is between '49.5,50.5'. Can you explain this answer?
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