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JEE MainChemistryModeratePhysical Chemistry

For a reaction, X(g)→Y(g)+Z(g)X(g) \rightarrow Y(g) + Z(g) the half life
period is 10 min. In What period of time would the concentration of X be
reduced to 10 of original concentration.

Show answer and solution
X(g)→Y(g)+Z(g)X(g) \rightarrow Y(g) + Z(g)
The reaction is a first order reaction hence,
K=0.693t1/2=2.303tlogaa−x=0.69310min⁡K = \frac{0.693}{t_{1/2}} = \frac{2.303}{t}log\frac{a}{a - x} = \frac{0.693}{10\min}
=2.303tlogaa/10=0.69310=2.303tlog10= \frac{2.303}{t}log\frac{a}{a/10} = \frac{0.693}{10} = \frac{2.303}{t}log10
∴t=2.303×10.693=33min\therefore t = \frac{2.303 \times 10}{.693} = 33min

Source: Grass-G / CH-20 Chemistry Paper 12 Dec..docx

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