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Equilibrium

Question
CBSEENCH11006551

Calculate the pH of a solution obtained by mixing 150 mL of 0.1 N - NaOH and 150 ml of 0.2 N - HCl.

Solution
In such problems of acid and base mixture solution, we should determine the volume of each having unit normality (or molarity).
Now 150 ml of 0.1 space straight N space minus space NaOH
                       identical to space 150 space cross times space 0.1 space mL space of space straight N minus NaOH
identical to space 15 space mL space of space straight N minus NaOH
150 space mL space of space 0.2 space straight N space minus space HCl
space space space space space space space space space space space space space space space space space space space space space space space space space space space identical to space 150 space cross times space 0.2 space mL space of space straight N minus HCl
space space space space space space space space space space space space space space space space space space space space space space space space space space space identical to space space space space 30 space mL space of space straight N minus HCl

space space space space space space space space space space space space space space space space space space space space space space space space
15 space mL space of space straight N minus space NaOH  are neutralised by 15 mL of N-HCl
HCl left unused after mixing the two solutions
                                   = (30 - 15) i.e. 15 mL of N-solution
  Total , volume of the solution after mixing
                        = 150 + 150 = 300 mL
Now comma space space space space space straight N subscript 1 straight V subscript 1 space equals space straight N subscript 2 straight V subscript 2
or space space space space space space space space space 1 cross times 15 space equals space straight N subscript 2 space cross times space 300
therefore space space space space space straight N subscript 2 space equals space 15 over 300 space equals space 1 over 20
Since HCl is a strong electrolyte, it is completely dissociated. 
   HCl space plus space straight H subscript 2 straight O space space rightwards harpoon over leftwards harpoon space space straight H subscript 3 straight O to the power of plus left parenthesis aq right parenthesis space plus space Cl to the power of minus left parenthesis aq right parenthesis
space space space space open square brackets straight H to the power of plus close square brackets space equals space open square brackets HCl close square brackets space equals space 1 over 20 straight N space equals space 1 over 20 straight M
We space know comma space
space space space space space space pH space equals space minus log space open square brackets straight H subscript 3 straight O to the power of plus close square brackets space equals space minus log space open square brackets 1 over 20 close square brackets
space space or space pH space equals space log space 20 space equals space 1.3010