Phosphorus-32 has a half-life of 14.0 days. starting with 6.00 g of 32p, how many grams will remain after 112 days ?

The radioactive decay follows first order kinetics

For first order reaction the relation between rate constant half life is

K = 0.693 / t1/2

K = 0.693 / 14 = 0.0495 day^-1

The first order rate equation is

ln (A / At) = Kt

Where

A = initial amount

At = amount left at time t

t = time

K = rate constant

Putting values

ln (6 / At) = 0.0495 X 112

ln (6 /At) = 5.544

taking antilog

6 / At = 255.7

At = 0.0235 g

1. for the first question, we must find the mass of the anhydrous salt, mgso₄. the molar mass for mgso₄·7h₂o is 246.47 g/mol, while that of mgso₄ is 120.37 g/mol.7.834 g mgso₄·7h₂o * 1 mol mgso₄·7h₂o/246.47 g * 1 mol mgso₄/1 mol mgso₄·7h₂o * 20.37 g mgso₄/mol = 0.647 g mgso₄

2. mass of water = mass of sample - mass of anhydrous salemass of water = 7.834 - 0.647 = 7.19 gpercent water in hydrate = 7.19/7.834 * 100 = 91.74%