Question

What are some first order half life practice problems?

Answer 1

Cobalt-60 has a half-life of 5.26 years.

a) Calculate the first-order rate constant.

b) If 20% decays, how much time did it take?

c) Write the rate law that describes this process.

d) Determine the initial rate of the process if one starts with `"1.00 M"` of cobalt-60.

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a) From the first-order half-life:

`t_"1/2" = ln2/k`

`=> color(blue)(k) = ln2/t_"1/2" = ln2/"5.26 yrs" = color(blue)("0.1318 yrs"^(-1))`

b) From the integrated rate law:

`ln(([A])/([A]_0)) = -kt`

`color(blue)(t) = -ln(([A])/([A]_0))/(k) = -ln((0.2cancel([A]_0))/(cancel([A]_0)))/(k)`

`= -ln(0.2)/("0.1318 yrs"^(-1)) = color(blue)("3.268 yrs")`

c) `color(blue)(r(t) = k[A])`

d) `color(blue)(r(t)) = "0.1318 yrs"^(-1)("1.00 M") = color(blue)("0.1318 M/yr")`