Question

The rate constant for a first order reaction is 4.606 × 10⁻³ s⁻¹. The time required to reduce 2.0 g of the reactant to 0.2 g is ______.

Options

• 100 s

• 200 s

• 500 s

• 1000 s

Answer 1

The rate constant for a first order reaction is 4.606 × 10⁻³ s⁻¹. The time required to reduce 2.0 g of the reactant to 0.2 g is 500 s.

Explanation:

First-order rate law is given as:

`k = 2.303/t log ([R]_0/([R]))`    ...(i)

Where:

k = 4.606 × 10⁻³ s⁻¹,

[R]₀ = 2.0 g

[R] = 0.2 g

By putting these values in equation (i), we get

4.606 × 10⁻³ = `2.303/t log(2.0/0.2)`

4.606 × 10⁻³ = `2.303/t log (10)`

4.606 × 10⁻³ = `2.303/t (1)`

4.606 × 10⁻³ = `2.303/t`

`t = 2.303/(4.606 xx 10^-3)`

t = 500 s