
Originally Posted by
jrmonroe
Let’s say the two volumes contain 10^7 molecules, so an acid with pH 5 contains 100 H3O+ ions, and water with pH 7 contains 1 H3O+ ion. Together they contain 2 × 10^7 molecules with 101 H3O+ ions. Half the solution would contain 10^7 molecules with 50.5 H3O+ ions. The pH =–log(50½/10^7) = 5.30. Diluting this with water and halving would yield 10^7 molecules with 25.75 H3O+ ions, giving a pH of 5.59. Repeated dilutions yields pH’s of: 5.30, 5.59, 5.874, 6.143, 6.388, 6.594, 6.751, 6.858, 6.923, 6.960, 6.979, 6.990, 6.995, 6.9974, 6.9987, 6.9993, 6.9997, 6.9998, and 6.9999.
Let an Excel spreadsheet do these calculations for you instead of doing them by hand. Start with 100 in A1, and with =–LOG(A1/10000000) in B1. Then put =(A1+1)/2 into A2, and fill down B1 into B2 (Ctrl+D). Then fill down A2 and B2 into A3 and B3 through A20 and B20. You’ll see how the diluted pH approaches, but never reaches, a pH of 7. Then go back to A2 and change it to your original thinking by changing the function simply =A1/2 (meaning no H3O+ ions in the “water”). Fill down A2 into A3 through A20, and you’ll see the dilutions approach a pH of 11.