What is the sum of magic numbers of all solutions gives below : (Interger value is between 50 and 60)
(Magic numver of a solution `=pH` of solution `xx` Weight factor)
`{:(,"Solution",,"Weight factor"),("I",underset((K_(a)=10^(-10)))(0.1 "M HCN"),,2),("II",underset(underset((K_(a)=10^(-5)))(+0.1 M CH_(3) COONa))(0.1 M CH_(3) COOH),,1),("III",0.1 M HCl,,3),("IV",0.1 M NH_(4)OH (K_(b)=10^(-5)),,2),("V",0.01 M NaOH,,0.5),("VI",underset(+10 "ml of 0.1 M" NH_(4)OH)(10 "mL of" 0.01 M CH_(3)COOH),,1):}`.

Answer

D

Explanation

I. `HCN is W_(A), pH_(W_(A)) = (1)/(2) (pK_(a) - log C)`
`= (1)/(2) (10 - log 10^(-1)) = 5.5`
II. Acidic buffer : `pH_("acidic Buffer") = pK_(a) + "log"(0.1)/(0.1) = 5`
III. HCI is `S_(A) : pH =- log (0.1) = 1`
IV. `NH_(4)OH` is `W_(B): pOH_(W_(B)) = (1)/(2) (pK_(a) - logC)`
`= (1)/(2) (5+1) = 3`
`pH = 14 - 3 = 11`
V. NaOH is `S_(B): pOh =- log (0.01) = 2`,
`pH = 14 - 2 = 12`
VI. Salt of `W_(A)//W_(B): pH = 7`
`:.` Magic number `=5.5 xx2 +5 xx 1xx +1xx3 +11 xx2 +12 xx 0.5 +7 xx1 = 54`