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The ionization constant of HF is 3.2xx10^(-4). Calculate the degree of dissociation of HF in its 0.02 M solution.Calculate the concentration of all species present (H_3O^(+), F^- and HF ) in the solution and its pH.

Answer»

Solution :In aqueous solution of HF, two proton transfer reactions occurs like,
(i)Ionization of HF (ii) Self ionization of water.
(i)`HF_((aq))+H_2O_((ll)) hArr H_3O_((aq))^(+) + F_((aq))^(-)`
(ii)`H_2O_((l)) + H_2O_((l)) hArr H_3O_((aq))^(+)+ OH_((aq))^(-)`
`K_a (i) =3.2xx10^(-4)` and `K_w`(ii) = `1.0xx10^(-14)`
At `K_a (i) gt gt K_w (ii)`, So, main EQUILIBRIUM in solution is ionization of HF.
Suppose , dissociation amount of HF= `alpha`
Initial [HF]=0.02 M
`therefore` Dissociated [HF]=`(0.02alpha)M`
` therefore` At equilibrium [HF]=(Initial - Dissociated )
=(0.02 - 0.02 `alpha`)
`=0.02 (1-alpha)M`
`H_3O^+` and `F^-` produce equal to the amount of the HF dissociate .
`therefore` At equilibrium `[H_3O^+]=[F^-] 0.02 alpha M`
These are SHOWN in the following table.
`{:("Equilibrium :",HF_((aq))+,H_2O_((l)) hArr, H_3O_((aq))^(+) +, F_((aq))^(-)),("Initial M:", 0.02, -,Zero,Zero),("Change:", -0.02alpha,-,+0.02alpha,+0.02 alpha),("Equili (M)", 0.02 - 0.02 alpha, , 0.02 alpha,0.02 alpha):}`
Equilibrium constant for ionization of HF.
`K_a=([H_3O^+][F^-])/"[HF]"`
`therefore 3.2 xx10^(-4) = ((0.02 alpha)(0.02alpha))/(0.02 (1-alpha))=(0.02 alpha^2)/(1-alpha)`
`therefore 3.2xx10^(-4) (1-alpha)=0.02 alpha^2`
`therefore 0.02 alpha^2 + 3.2 xx10^(-4) alpha -3.2 xx10^(-4) = 0.0`
`therefore alpha^2 + 0.016 alpha - 0.016 =0.0`
For this quadratic equation a=1,b=0.016 and c=-0.16
`therefore alpha =(-b+sqrt(b^2-4ac))/(2a)`
`=(-0.016 pm sqrt((0.016)^2 - 4(1)(-0.016)))/(2(1))`
`=(-0.016 pm sqrt(0.000256+0.064))/2`
`=(-0.016 pm 0.2535)/2`
`=0.2375/2`
`-0.2695/2`
=0.1187 OR -0.1347
`approx` Dissociation degree or negative value is not possible .
At equilibrium `[H_3O^+] = [F^-]=0.02alpha`
`=0.02xx0.1187` = 0.002374
`=2.374xx10^(-3)` M
`approx 2.4 XX 10^(-3)` M
At equilibrium [HF]=`(0.02-0.02 alpha)`
=0.02-0.02(0.12)=(0.02-0.0024)
=0.0176 `=1.76xx10^(-2)` M
pH=log `[H_3^+O]`=log `(2.4xx10^(-3))`
=-(0.3802-3)=-(-2.6198)
=+2.6198 `approx` 2.62
OR
`K_a=(H_3O^+)^2/C_o=3.2xx10^(-4)`
`[H_3O^+]=sqrt(K_aC_o)=sqrt(3.2xx10^(-4)xx0.02)`
`=sqrt(6.4xx10^(-6))= 2.53xx10^(-3)` M
So, `[H_3O^+]=[F^-]=2.53xx10^(-3)` M = 0.00253 M
[HF]=(0.02-0.00253)=0.01747 `approx` 0.017 M
pH=-log `(2.53xx10^(-3))` = 2.5969 `approx` 2.6


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