A solution containing 22.18 mL of a .1212 M H2CO3 solution is mixed with 17.22 mL of a .1234 M Na2CO3 solution. What is the pH of the final mixture? Ka1 = 6.2x10-7 Ka2 = 4.4x10-11. If you diluted the mixture up to 100 mL, would the pH change? If it does change, what would the new pH be?
To solve this problem, we need to consider the chemical reaction that occurs when H2CO3 and Na2CO3 are mixed. H2CO3 is a weak acid, while Na2CO3 is composed of the sodium salt of a weak acid, making it a basic solution. When they react, H2CO3 will donate a hydrogen ion (H+) to the CO3^2- ion, forming HCO3-.
Step 1: Calculate the amount of moles of H2CO3 and Na2CO3 in the given solutions.
To do this, we'll use the formula: moles = concentration (M) * volume (L).
For H2CO3:
moles of H2CO3 = 0.1212 M * (22.18 mL / 1000 mL/L) = 0.002705 moles
For Na2CO3:
moles of Na2CO3 = 0.1234 M * (17.22 mL / 1000 mL/L) = 0.002125 moles
Step 2: Determine the limiting reactant.
Since the balanced equation between H2CO3 and Na2CO3 is 1:1, the limiting reactant will be the one with fewer moles. In this case, Na2CO3 is the limiting reactant.
Step 3: Calculate the moles of HCO3- formed.
Since Na2CO3 is the limiting reactant, it will react completely to produce the same number of moles of HCO3- ions. Therefore, the moles of HCO3- formed will also be 0.002125 moles.
Step 4: Calculate the concentration of HCO3- in the final mixture.
The volume of the final mixture is the sum of the volumes of the two solutions used. Therefore, the final volume is 22.18 mL + 17.22 mL = 39.4 mL = 0.0394 L.
Since moles = concentration * volume, the concentration of HCO3- in the final mixture is:
concentration of HCO3- = (0.002125 moles) / (0.0394 L) = 0.054 moles/L = 0.054 M
Step 5: Calculate the pH of the final mixture.
HCO3- is the conjugate base of H2CO3, and the pH of a solution containing a weak base can be calculated using the Henderson-Hasselbalch equation: pH = pKa + log([base]/[acid]), where [base] is the concentration of the conjugate base and [acid] is the concentration of the weak acid.
The pKa values given are for the dissociation of H2CO3, with HCO3- as its conjugate base. We will use the second pKa value, which corresponds to the dissociation of HCO3- to CO3^2-.
pH = 10.6 + log([HCO3-]/[H2CO3])
= 10.6 + log(0.054/0.1212)
= 10.6 + log(0.4459)
= 10.6 + (-0.350)
= 10.250
Therefore, the pH of the final mixture is approximately 10.250.
To answer the second part of the question, if you dilute the mixture up to 100 mL, the concentration of the HCO3- ions will remain the same. Therefore, the pH will also remain the same since it is determined by the dissociation of HCO3-.