Determine the volume (in mL) of 1.18 M perchloric acid (HClO4) that must be added to 747 mL of 0.976 M sodium hydrogen citrate (Na2C6H6O7) to yield a pH of 4.77.
http://www.egr.msu.edu/scb-group/tools/citric/cit.htm
To determine the volume of perchloric acid (HClO4) needed to achieve the desired pH, we can utilize the concept of acid-base titration. In this case, we are aiming to achieve a certain pH by mixing two solutions with known concentrations. Here's how you can calculate the volume needed:
Step 1: Start by writing the balanced equation for the reaction between perchloric acid and sodium hydrogen citrate. In this case, it will be:
HClO4 + Na2C6H6O7 → NaClO4 + H3C6H5O7
Step 2: Next, calculate the number of moles of sodium hydrogen citrate (Na2C6H6O7) using its given concentration and volume.
Number of moles = concentration (M) × volume (L)
Convert the given volume of sodium hydrogen citrate from mL to L:
Volume (L) = 747 mL × (1 L/1000 mL) = 0.747 L
Number of moles of sodium hydrogen citrate = 0.976 M × 0.747 L
Step 3: Use the balanced equation to find the moles of perchloric acid required to neutralize the sodium hydrogen citrate. According to the balanced equation, the mole ratio between perchloric acid and sodium hydrogen citrate is 1:1.
Number of moles of perchloric acid = number of moles of sodium hydrogen citrate
Step 4: Calculate the volume of perchloric acid needed to achieve the desired pH by dividing the number of moles obtained in Step 3 by its concentration.
Volume (L) = number of moles / concentration
Convert the volume obtained from L to mL:
Volume (mL) = Volume (L) × 1000
Step 5: Now, you need to know the concentration of the perchloric acid (HClO4) solution to proceed with the calculation. Once you have that information, substitute the concentration in Step 4 to calculate the volume in mL.
With the information provided, unfortunately, the concentration of the perchloric acid is not given. You would need to know the concentration of the perchloric acid solution to determine the volume required to achieve the desired pH.