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What is the sum of magic numbers of all ...

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):}`.

Text Solution

Verified by Experts

The correct Answer is:
D
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`
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Knowledge Check

  • pH of 0.1 M NH_(3) aqueous solution is (K_(b) = 1.8 xx 10^(-5))

    A
    11.13
    B
    12.5
    C
    13.42
    D
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  • K_(b) for NH_(4)OH is 1.8 xx 10^(-5) . The [overset(Theta)OH] of 0.1 M NH_(4)OH is

    A
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    B
    `4.20 xx 10^(-3)`
    C
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    D
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  • When 5.0 mL of a 1.0 M HCl solution is mixed with 5.0 mL of a 0.1 M NaOH solution, temperature of solution is increased by 2^@C predicted accurately from this observation?

    A
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    B
    If 10 mL of 0.05 HCl is mixed with 10 mL of 0.05 M NaCl the temperature rise will be `2^@C`
    C
    If 5 mL of 0.1 M HCl is mixed with 5 mL of 0.1 M `NH_3` solution, the temperature rise will be less than `2^@C`
    D
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