calculate the volume of 3M HCl needed to change the pH of 50 mL of the undiluted buffer solution by one pH unit?
To calculate the volume of 3M HCl needed to change the pH of 50 mL of the undiluted buffer solution by one pH unit, you need to consider the volume and concentration of the buffer solution, as well as the pKa value of the buffer system.
Here's an explanation of the steps to calculate the volume:
Step 1: Determine the initial and final pH values:
- Note down the initial pH of the undiluted buffer solution.
- Determine the final pH you want to achieve by changing the pH by one unit. For example, if the initial pH is 7, the desired final pH will be 6 or 8, depending on whether you want to decrease or increase the pH.
Step 2: Identify the buffer system:
- Determine the specific buffer system used in the solution. For example, if it's a phosphate buffer, the pKa will be around 7.2.
Step 3: Calculate the change in concentration of H+ ions:
- pH is a logarithmic scale that indicates the concentration of H+ ions in a solution. To change the pH by one unit, you need a tenfold change in the concentration of H+ ions.
- From the Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.
- The ratio [A-]/[HA] represents the relative concentrations of the acid and its conjugate base. To change the pH by one unit, we need to change this ratio by tenfold.
- Calculate the initial ratio [A-]/[HA] based on the initial pH and pKa value. Then, calculate the final ratio by dividing the initial ratio by ten if you want to decrease the pH or multiplying the initial ratio by ten if you want to increase the pH.
- Finally, calculate the new concentrations [A-] and [HA] using the ratios and the known total volume (50 mL) of the undiluted buffer solution.
Step 4: Calculate the volume of 3M HCl needed:
- Now that you have the final concentrations of [A-] and [HA], you need to calculate the change in concentration of each species.
- Based on the reaction HCl + A- → HA + Cl-, a one-to-one ratio conversion of HCl to A- is assumed.
- Calculate the moles of A- needed by multiplying its final concentration by the final volume.
- Divide the moles of A- by the concentration (3M) of the HCl solution to obtain the required volume of 3M HCl.
Following these steps will help you calculate the volume of 3M HCl needed to change the pH of the 50 mL undiluted buffer solution by one pH unit.