Question

What is the rate constant of a first-order reaction that takes 5.50 minutes for the reactant concentration to drop to half of its initial value?

Answer 1

For a first order reaction, the half life is inversely proportional to the rate constant. 
The formula is
half life = ln(2)/k = 0.693/k
where k is the rate constant

t = 5.50 minutes

k = ln(2)/5.50 = 0.126 min^-1

Your rate constant is 0.126 min^-1.