The half-life of sodium-25 is 1.0 minute. Starting with 1 kg of this isotope, how
much will remain after half an hour?

First order rate depicts that the variation of rate is dependent only one of the reactant's concentration. The population of the reactant can be find out with the help of integrated rate law at any time after the beginning of the reaction.

Explanation:

Relation between half-life and rate constant for first order is given as:

k

=

0.693

t

1

2

On putting the value of half-life, we get:

k

=

0.693

1

=

0.693

(

min

)

−

1

First order rate law can be written as:

k

=

1

t

ln

a

0

a

t

Where,

k is rate constant

t is time required for decay

a

0

is the initial amount

a

t

is the amount left at time t.

On putting the values, we get:

0.693

=

1

30

ln

1

a

t

Therefore,

ln

1

a

t

=

0.693

×

30

a

t

=

9.35

×

10

−

10

k

g

Therefore, amount left after 0.5 hour is

9.35

×

10

−

10

k

g

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