Question

A first order reaction has rate constant 1 × 10⁻² s⁻¹. What time will, it take for 20 g or reactant to reduce to 5 g?

Options

• 693.0 s

• 138.6 s

• 238.6 s

• 346.5 s

Answer 1

138.6 s

Explanation:

Given,

Rate constant (k) = 1 × 10⁻² s⁻¹

Initial concentration (a) = 20 g

Final concentration (a − x) = 5 g

For a first order reaction,

Rate constant (k) = `2.303/"t" log ("a"/("a" - "x"))`

In terms of time,

t = `2.303/"k" log ("a"/("a" - "x"))`

Putting the values,

t = `2.303/(1 xx 10^-2) log (20/5)` = 138.6 s

As a result, the time necessary will be 138.6 seconds.