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Calculate the pH of 0.175 M phosphoric acid (H3PO4, a triprotic acid). Ka1 = 7.5 x 10-3, Ka2 = 6.2 x 10-8, and Ka3 = 4.8 x 10-13.
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Of course, I'd be happy to help you with this question!
To calculate the pH of phosphoric acid (H3PO4), you need to consider that it is a triprotic acid, meaning that it can donate three protons (H+ ions). Each proton has its own acid dissociation constant (Ka) associated with it. In this case, you are given the values for Ka1, Ka2, and Ka3.
To calculate the pH, you will need to determine the concentration of the different ion species and use their equilibrium constants to find the concentrations of the H+ ions.
Here's how you can approach this problem step by step:
Step 1: Write out the dissociation reactions for each proton.
H3PO4 ⇌ H+ + H2PO4- (Ka1)
H2PO4- ⇌ H+ + HPO42- (Ka2)
HPO42- ⇌ H+ + PO43- (Ka3)
Step 2: Set up an ICE (Initial, Change, Equilibrium) table for each reaction. Let x be the concentration of H+ ions produced by the dissociation of that proton.
For the first reaction (Ka1):
H3PO4 ⇌ H+ + H2PO4-
Initial: 0.175 M 0 M 0 M
Change: -x +x +x
Equilibrium: 0.175 - x x x
Step 3: Set up ICE tables for the second (Ka2) and third (Ka3) reactions in the same way.
Step 4: Write the equilibrium expressions for each reaction using the given Ka values.
Ka1 = [H+][H2PO4-] / [H3PO4]
Ka2 = [H+][HPO42-] / [H2PO4-]
Ka3 = [H+][PO43-] / [HPO42-]
Step 5: Substitute the equilibrium concentrations from the ICE tables into the equilibrium expressions.
For example, for Ka1:
7.5 x 10^(-3) = (x)(x) / (0.175 - x)
Step 6: Since the value for x is small compared to 0.175, you can assume that (0.175 - x) is approximately equal to 0.175. This simplifies the equation, allowing you to solve for x.
Step 7: Solve for x and determine the concentration of H+ ions. Remember that x corresponds to the concentration of H+ ions.
Step 8: Finally, calculate the pH using the formula: pH = -log[H+].
That's it! By following these steps, you should be able to calculate the pH of 0.175 M phosphoric acid. Good luck with your quiz!