Afirst-order reaction has a half-life of 20.0 minutes. starting with 1.00 × 1020 molecules of reactant at time t = 0, how many molecules remain unreacted after 100.0 minutes?

Half-life time of a reaction is time at which reactant concentration becomes half of its initial value.

Half-life of the first order reaction is 20 min. Rate constant can be calculated as follows:

The rate expression for first order reaction is as follows:

initial number of molecules of reactant are , time is 100 min thus, putting the values to calculate number of reactant at time 100 min,

On rearranging,

Or,

Therefore, number of molecules unreacted will be

when the volume of gas is   changed from   717.73 ml   to 852 ml   the temperature will   change   from 315   c to 452   c

    calculation

this is calculated using the charles law formula

that is,   v1/t1 = v2/t2

          v1=?

        t1 = 315 c   into   kelvin = 315 +273 = 588 k

        v2 = 852   ml

        t2 = 425c + 273 =698 k

make v1   the subject of the formula ( by   multiplying both side by t1)

  v1=( v2 xt1) / t2

v1= (852 ml   x 588 k)/ 698 k= 717.73 ml

the answer to this question is 3.