chem hw question

Question

The rate constant for this first-order reaction is 0.0292 s−1 at 300 °C.

A⟶products

If the initial mass of A is 18.06 g, calculate the mass of A remaining after 1.20 min.

Answer 1

For first order reactions, a relatively simple equation to learn and memorize is...

FR = 0.5ⁿ where FR = fraction remaining and n = number of half lives that have elapsed

In this problem, they don't give us the half life but we can get it from t1/2 = 0.693/k which is the equation for half life of a first order reaction.

t1/2 = 0.693/0.0292 = 23.7 sec

Now, how many half lives is 1.20 min?

1.20 min x 60 sec / min = 72 sec and 72 sec / 23.7 sec = 3.04 half lives

FR = 0.5^3.04

FR = 0.122

Amount remaining = 0.122 x 18.06 g = 2.196 g = 2.20 g

Answer 2

ln (conc)_time = ln (conc) _initial - kt

ln(grams) = ln(18.06 ) - 0.0292 X 1.20 ( 60 seconds)

I multiplied with 60 because the rate constant is given in 1/sec while the time is given in minutes both must be in same units.

ln(grams) = 0.791

Grams after 1.2 minutes = e ^0.791 = 2.20 grams