A reaction has a rate constant of 0.0492 sec-1; how long will it take (in minutes) until 0.433 mol/L of the compound is left, if there was 0.656 mol/L at the start

λ(Decay constant) = 0.0492sec-¹

The relationship between Decay Constant and Half life (t½)

λ=0.693/t½

given the decay constant as 0.0492

We can get the Half life

t½ = 0.693/0.0492

t½= 14.09secs.

N = N°(½)ⁿ

Where N= Remaining Amount of the original Compound

N° = Original Amount of compound.

n is simply a tern used to represent the ratio of time taken/half life

In other words

n=t/t½

Given N°=0.656 mol/L

N=0.433mol/L

0.433 = 0.656(½)ⁿ

(½)ⁿ = 0.433/0.656

(½)ⁿ = 0.660

Taking the Natural Log(Ln) of both sides

Ln(½)ⁿ = Ln(0.66)

nLn(½) = -0.4155

n(-0.6931) = -0.4155

n= 0.4155/0.6931

n= 0.5995.

n = time/half life

t = half life x n

t = 14.09 x 0.5995

t = 8.45secs.

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