One litre of $1 M$ solution of an acid $H A$ ( $K_{a} = 10^{- 4}$ at $25^{o} C$ ) has pH=2. It is diluted by water so that new pH becomes double. The solution was diluted to $5 \times 10^{a}$ ml. The value of $a$ is

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Solution

When $p H = 2$ , $[H^{+}] = 0.01 M$
When $p H = 4$ , $[H^{+}] = 0.0001 M$
$α c = 0.0001$
$K = α c \times \frac{α}{1 - α}$
$10^{- 4} = 0.0001 \times \frac{α}{1 - α}$
$α = 0.5$
$c = 2 \times 10^{- 4}$
$c_{1} V_{1} = c_{2} V_{2}$
$1 \times 1 = 2 \times 10^{- 4} \times V_{2}$
$V_{2} = 5000 L = 5 \times 10^{6} m l = 5 \times 10^{a} m l$
Thus, $a = 6$

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One litre of 1M solution of an acid HA (Ka=10−4 at 25oC) has pH=2. It is diluted by water so that new pH becomes double. The solution was diluted to 5×10a ml. The value of a is

When pH=2, [H+]=0.01MWhen pH=4, [H+]=0.0001Mαc=0.0001K=αc×α1−α10−4=0.0001×α1−αα=0.5c=2×10−4c1V1=c2V21×1=2×10−4×V2V2=5000 L=5×106ml=5×10amlThus, a=6

One litre of $1 M$ solution of an acid $H A$ ( $K_{a} = 10^{- 4}$ at $25^{o} C$ ) has pH=2. It is diluted by water so that new pH becomes double. The solution was diluted to $5 \times 10^{a}$ ml. The value of $a$ is