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Salt of Strong Acid and Weak Base

Calculate the...

Question

Calculate the $p H$ of a $2.0 M$ solution of ${N H}_{4} C l . [K_{b} ({N H}_{3}) = 1.8 \times 10^{- 5}]$

p H = 4.477

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p H = 7.455

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p H = 9.53

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p H = 11.46

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Solution

The correct option is A $p H = 4.477$
Using the above relation for $N H_{4} C l$ ,
$p H = 1 / 2 [p K_{w} - p K_{b} - l o g_{10} C]$
$p K_{w} = - l o g_{10} (10^{- 14}) = 14$
$l o g_{10} C = l o g_{10} 2 = 0.301$
$p K_{b} = - l o g_{10} (1.8 \times 10^{- 5}) = 5 - 0.255 = 4.745$
Hence,
$p H = 1 / 2 [14 - 4.745 - 0.301] = 4.477$

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