A first reaction takes 40 minutes for 30% decomposition, Calculate its half life period.

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Solution

Let $A_{o} = 100, A_{30} = 100 - 30 = 70, t_{30} = 40 m i n s$

$∴ t_{30} = \frac{2.303}{K} l o g \frac{A_{o}}{A_{30}}$

$K = \frac{2.303}{40} l o g \frac{100}{70}$

$K = 8.9 \times 10^{- 3} m i n^{- 1}$

$t_{1 / 2} = \frac{0.693}{K} = \frac{0.693}{8.9 \times 10^{- 3}}$

$= 77.7 m i n$

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A first reaction takes 40 minutes for 30% decomposition, Calculate its half life period.

Let Ao=100, A30=100−30=70, t30=40 mins ∴ t30=2.303K logAoA30 K=2.30340 log10070 K=8.9×10−3 min−1 t1/2=0.693K=0.6938.9×10−3 =77.7 min

Let $A_{o} = 100, A_{30} = 100 - 30 = 70, t_{30} = 40 m i n s$

$∴ t_{30} = \frac{2.303}{K} l o g \frac{A_{o}}{A_{30}}$

$K = \frac{2.303}{40} l o g \frac{100}{70}$

$K = 8.9 \times 10^{- 3} m i n^{- 1}$

$t_{1 / 2} = \frac{0.693}{K} = \frac{0.693}{8.9 \times 10^{- 3}}$

$= 77.7 m i n$