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nika2105 [10]
3 years ago
11

A first-order reaction has a half-life of 20.0 minutes. Starting with 1.00 × 1020 molecules of reactant at time t = 0, how many

molecules remain unreacted after 100.0 minutes?
Chemistry
1 answer:
zalisa [80]3 years ago
7 0

Half-life time of a reaction is time at which reactant concentration becomes half of its initial value.

Half-life of the first order reaction is 20 min. Rate constant can be calculated as follows:

K=\frac{0.6932}{t_{1/2}}=\frac{0.6932}{20 min}=0.03466 min^{-1}

The rate expression for first order reaction is as follows:

k=\frac{2.303}{t}log\frac{A_{0}}{A_{t}}

initial number of molecules of reactant are 10^{20}, time is 100 min thus, putting the values to calculate number of reactant at time 100 min,

0.03466 min^{-1}=\frac{2.303}{100 min}log\frac{[10^{20}]}{A_{t}}

On rearranging,

\frac{10^{20}}{A_{t}}=31.988

Or,

A_{t}=3.13\times 10^{18}

Therefore, number of molecules unreacted will be 3.13\times 10^{18}

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