Question

After 65.0 min, 34.0% of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics?

Answer 1

first order rate equations are linear- (time x rate = % decay) a half life is defined as the time it takes to decay 50% of the substance. We know it takes 65 minutes to decay 66% (100%-34%) of the substance

eq: time * rate = %decay
eq1: 65 * rate = .66 (66%)
eq2: X * rate = .5 (50%)

since rate is the same in both equations you can divide them (or plug in rate= .66/66)

X/65= .5/.66
X= (65*.5)/(.66)
X= 49.242min OR 49min15sec

which makes sense since you would expect to decay 50% sooner then 34%.

I bet there was a shortcut that I missed