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
