Equilibrium Question 893
Question: pH of an aqueous solution of HCl is 5. if 1 c.c. of this solution is diluted to 1000 times. The pH will become
Options:
A) 8
B) 5
C) 6.9
D) None
Show Answer
Answer:
Correct Answer: C
Solution:
pH of HCl solution = 5 $ {{[{H^{+}}]} _{initial}}={10^{-5}} $
$ {{[{H^{+}}]} _{initial}}\times V_1={{[{H^{+}}]} _{final}}\times V_2 $
$ {{[{H^{+}}]} _{final}}\times {10^{-8}} $
Let the $ {H^{+}} $ from water be x. $ H_2O\rightarrow \underset{x+{10^{-8}}}{\mathop{{H^{+}}}},+\underset{x}{\mathop{O{H^{-}}}}, $
$ x(x+{10^{-8}})={10^{-14}} $
$ x^{2}+{10^{-8}}-{10^{-14}}=0 $
$ x=\frac{-{10^{-8}}\pm \sqrt{{10^{-16}}=4\times {10^{-14}}}}{2} $
$ \Rightarrow $ $x=\frac{-{10^{-8}}+{10^{-8}}\sqrt{401}}{2}=19\times {10^{-8}}=9.5\times {10^{-8}} $
$ {{[{H^{+}}]} _{Total}}={{[{H^{+}}]} _{HCl}}+{{[{H^{+}}]} _{Water}} $
$ ={10^{-8}}+{10^{-8}}\times 9.5=10.5\times {10^{-8}} $
$ pH=8-\log ,10.5 $
Slightly less then 7 Hence [c].
