Determine the pH of an HF solution of each concentration. In which cases can you

Question

Determine the pH of an HF solution of each concentration. In which cases can you not make the simplifying assumption that x is small? ("x is small" means less than 5%)

(a) 0.230 M

   using the assumption:__________

   without the assumption:_________

   assumption ratio:________%

b) 0.0460 M

   using the assumption:________

   without the assumption: _______

   assumption ratio: _________%

C) 0.0230 M

   using the assumption:________

   without the assumption: _______

   assumption ratio: _________%

Explanation / Answer

HF is weak acid and undergoes ionization as

HF+ H2O ------>H3O++F-

Ka= [H3O+] [F-]/[HF]= 6.6*10-4

let x= drop in concentration of HF to reach equilibrium

at Equilibrium, [H3O+]= [F-]= x and [HF] = M-x, where M is iniitial concentration of HF

when M= 0.230, x2/(2.3-x)= 4.6*10-4, since RHS of equation is very small, it is reasonable to assume 2.3-x= 2.3

x2/2.3= 4.6*10-4, x = 0.033, hence 2.3-0.033 =2.267 and it is reasonable to assume 2.3-x= 2.3

pH= -log (0.033)= 1.48

% ionization = 100*0.033/2.3=1.4%, so the assumption of 2.3-x is justified here

when M= 0.0460, x2/(0.0460-x)= 4.6*10-4, when solved for x, x=4.4*10-3M, pH= 2.35

% ionization is 100*(4.4*10-3/0.046)=9.5%, so the assumption of 0.046-x =0.046 is not valid since the initial concentration of HF itself is very small,

when M=0.0230, x2/(0.0230-x)= 4.6*10-4, when sovled for x, x= 3.05*10-3, % ionization = 100*3.05*10-3/0.0230=13.3%. more than 5%. pH= -log (3.05*10-3)= 2.51

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