How much 6.0M NaoH must be added to 0.5L of a buffer that is 0.0200M acetic acid and 0.0250M sodium acetate to raise the PH to 5.75
To answer this question, we need to understand the concept of pH and the Henderson-Hasselbalch equation.
The pH is a measure of the acidity or alkalinity of a solution. It is defined as the negative logarithm (base 10) of the concentration of hydrogen ions (H+). A pH of 7 is considered neutral, while values below 7 are acidic and values above 7 are basic.
The Henderson-Hasselbalch equation is used to calculate the pH of a buffer solution. The equation is given by:
pH = pKa + log([A-]/[HA])
Where:
- pH is the desired pH of the buffer solution.
- pKa is the dissociation constant of the weak acid (acetic acid in this case).
- [A-] is the concentration of the conjugate base (sodium acetate in this case).
- [HA] is the concentration of the weak acid (acetic acid in this case).
Given:
- pH = 5.75
- [HA] = 0.0200 M
- [A-] = 0.0250 M
Let's solve the equation for pKa:
pH = pKa + log([A-]/[HA])
5.75 = pKa + log(0.0250/0.0200)
Now, we need to rearrange the equation to solve for pKa:
pKa = 5.75 - log(0.0250/0.0200)
Now, we have the pKa value. From the pKa value, we can calculate the ratio [A-]/[HA]. In a buffer solution, the ratio [A-]/[HA] must be equal to 10^(pH - pKa). So:
[A-]/[HA] = 10^(pH - pKa)
Now, calculate [A-]/[HA]:
[A-]/[HA] = 10^(5.75 - pKa)
Next, we need to determine the amount of NaOH required to raise the pH to 5.75. NaOH is a strong base that reacts with acetic acid (HA) to form water (H2O) and sodium acetate (A-). The reaction between NaOH and acetic acid is given by:
NaOH + HA → H2O + A-
From the balanced equation, we can see that one mole of NaOH reacts with one mole of HA to produce one mole of A-. Therefore, the number of moles of NaOH needed will be equal to the number of moles of HA in the buffer solution.
To calculate the number of moles of HA, we use the formula:
moles of HA = concentration of HA * volume of solution (in liters)
Given that the volume of the buffer solution is 0.5 L and the concentration of HA is 0.0200 M, we can calculate the moles of HA:
moles of HA = 0.0200 M * 0.5 L
Now, we have the moles of HA. This will be the same as the moles of NaOH needed to react with HA and raise the pH to 5.75.
Finally, we convert the moles of NaOH to grams using its molar mass, which is 39.997 g/mol. Multiply the moles of NaOH by its molar mass to obtain the required mass of NaOH.
mass of NaOH = moles of NaOH * molar mass of NaOH
By following these steps, you should be able to determine the amount of 6.0 M NaOH required to raise the pH of the buffer solution to 5.75.