What is H RT?

Updated: 9/26/2023
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To what volume should 100 ml of any weak acid HA with a concentration of 0.2 M be diluted to double the percentage ionization?

For a weak acid HA, Ka = [H+] [A-]/[HA] where Ka is the dissociation constant and the square brackets are the concentrations of the species shown in mol dm-3. Percentage ionization is given by PI = [H+] /[HA] x 100 Let the molarity of the final solution be M. Then we have, for the original solution,PI = [H+] /[HA] x 100 = [H+] x 100/0.2PI= 500 [H+]From the first equation, remembering that the concentrations of the two ions are equal,[H+] = sq rt(0.2 Ka)Thus , original PI = 500 x sq rt (0.2 Ka)For the final solution, PI = [new H+]/M x 100 and as before, [new H+] = sq rt (KaM)So final PI = sq rt (KaM)/M x 100= sqrt (Ka)/sqrtM x100We know this is twice the original PI sosqrt (Ka)/sqrtM x100 = 2 x 500 x sq rt (0.2 Ka)Solving this gives M = 0.05.This is a quarter of the original molarity, ( 0.05/0.2), so the final volume should be 4 times the original, i.e. 400 ml.

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