Question

PLEASE MAKE SURE YOUR ANSWERS ARE CORRECT

Part A

What is the half-life of a first-order reaction with a rate constant of 7.60×10⁻⁴  s−1?

Express your answer with the appropriate units.

Part B

A certain first-order reaction has a rate constant of 1.50×10⁻³ s−1. How long will it take for the reactant concentration to drop to 18 of its initial value?

Express your answer with the appropriate units.

Answer 1

A)

if 1st order, then we can relate the half life with the rate constant

HL = ln(2) / k

this is always true, for any concentrations

now, express HL :

HL = ln(2) / (7.6*10^-4) = 912.035 seconds (as we u sed K in secondws)

change to minutes --> 912.035/60 = 15.2 minutes approx

B)

Assuume 18% of initial amount

from first law kinetics:

ln(Cf) = ln(Ci) - kt

Cf = 18/100*Ci = (18 fractional)

ln(0.18*Ci) = ln(Ci) - (1.5*10^-3) * t

solve for t

ln(0.18Ci/Ci) = - (1.5*10^-3) * t

t = -ln(0.18)/(1.5*10^-3)

t = 1143.198 seconds

t = 1143.198/60 = 19.05 mins