Question

The rate law for the rearrangement of ch3nc to ch3cn at 800 k is rate = (1300 s-1)[ch3nc]. what is the half-life for this reaction?

Answer 1

The rate of reaction is always expressed in concentration per time like mol/L·s. The equation is:

r [mol/L·s] = kCⁿ, where n is the order of reaction. Since k is 1300/s, that means that Cⁿ = C such that (1/s)*(mol/L) = mol/L·s. Thus, n=1. For a first order reaction, the formula would be:

ln(A/A₀) = -kt
where
A is the amount of material after time t
A₀ is the amount of material at t=0

The half life is when A/A₀ = 1/2÷1 = 1/2. Thus, the half-life t is:

ln(1/2) = (-1300t)
t = 5.33×10⁻⁴ seconds