Chem 2 - Rate law

Question

The rate constant for this first-order reaction is 0.0152 s−1 at 300 °C. A⟶products If the initial mass of A is 17.92 g, calculate the mass of A remaining after 1.91 min.

mass of A: ? g

Answer 1

For a 1st order reaction, half life (t1/2) = 0.693/k = 0.693 / 0.0152 s^-1 = 45.6 seconds

Since this is a first order decay, we can use FR = 0.5ⁿ

FR = fraction remaining = ?

n = number of half lives that have elapsed = 1.91 min x 60 sec / min =114.6 sec / 45.6 sec = 2.51 half lives

FR = 0.5^2.51 = 0.176 remaining

mass remaining = 0.176 x 17.92 g = 3.15 g

You can also solve this problem using the more conventional integrated rate law for a first order reaction:

ln[A] = -kt + ln[A]_o

ln[A] = -0.0152 s^-1 x 114.6 s + ln (17.92)

ln [A] = -1.742 + 2.886 = 1.144

[A] = 3.14 g