# For a first order reaction if the time for 50%, 75% and 87.5% changes are t1, t2 and t3 respectively then what would be the value of t1: t2: t3 ?

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Consider a first-order reaction

#"A →Products"#

The time required for the initial concentration

#1/2["A"]_0# is one half-life#1/4["A"]_0# is two half-lives#1/8["A"]_0# is three half-lives

Also,

The ratios are

Here is a typical plot for a first-order reaction.

The initial concentration is 1.7.

It takes

- 400 s for the concentration to drop by 50 % (to 0.85)
- 800 s for the concentration to drop by 75 % (0.42)
- 400 s for the concentration to drop by 87.5 % (to 0.21)

The times are in the ratio

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Describe your changes (optional) 200

Recall, for a first order elementary reaction,

Without more data, I couldn't give you a real value, but I could give you one as a factor of

We can conceptually assume that

Hence,

Moreover,

Describe your changes (optional) 200