How Does Rainfall Affect the pH of Unbuffered and Buffered Lakes?

[lananh]

Homework Statement

Im having issues with two parts of this problem, not sure what I'm doing wrong...

A lake with a surface area of 12.2 acres (1 acre = 4.840 103 yd2) receives 1.67 in. of rain of pH 4.82. (Assume that the acidity of the rain is due to a strong, monoprotic acid.) How many moles of H3O+ are in the rain falling on the lake? I solved that the mols are 32 H3O.

If the lake is unbuffered (assume pH = 7.00) and its average depth is 9.20 ft before the rain, calculate the pH after the rain has been thoroughly mixed with lake water. (Ignore runoff from the surrounding land.)

New pH = IM HAVING ISSUES WITH THIS ONE

Natural waters are typically buffered by dissolved carbonates. If the lake originally contains 0.96 mM HCO3- and 0.28 mM H2CO3, what is the pH of the lake water before and after the rain? (Ignore runoff).

pH = (before rain) I solved it for 6.90
pH = (after rain) IM HAVING ISSUES WITH THIS ONE

any help or guidance would be greatly appreciated.

Homework Equations

ph=pka + log (a/ha)
ph=-log[h]

The Attempt at a Solution

above

 

[Gokul43201]

You've calculated the moles of H3O+ in the given volume of rainwater from the pH of rainwater. Next, you just need to work backwards. You know the number of moles of H3O+ from rain. Add to this the number of moles of H3O+ in the lake (pH=7), to get the total number of moles of H3O+. With this number and the final volume of the lake, you can calculate the final (unbuffered) pH.

 

[Blueshift5]

It looks like you have correctly calculated the moles of H3O+ in the rain falling on the lake. For the second part, you can use the Henderson-Hasselbalch equation to calculate the new pH of the lake after the rain has been mixed in. The equation is:

pH = pKa + log ([A-]/[HA])

Where pKa is the acid dissociation constant, [A-] is the concentration of the conjugate base (in this case, HCO3-), and [HA] is the concentration of the acid (in this case, H2CO3).

For the third part, you can use the same Henderson-Hasselbalch equation, but this time you will need to calculate the new concentrations of HCO3- and H2CO3 after the rain has been mixed in. You can do this by using the initial concentrations and the fact that the total moles of each species must remain constant. Then, you can plug those new concentrations into the equation to calculate the pH of the lake after the rain has been mixed in.

Remember to double check your units and make sure they are consistent throughout your calculations. Also, be sure to use the correct pKa values for HCO3- and H2CO3. I hope this helps!