Suppose you find a rock originally made of potassium-40, half of which decays into argon-40 every 1.25 billion years. you open the rock and find 31 atoms of argon-40 for every atom of potassium-40. how long ago did the rock form?

We see that in 1 rock, there are 31 atoms of Argon and 1 atom of Potassium so the relative concentration of Potassium is:

1 / 32

or can be written as:

1 / 2^5

So this means that 5 half-lives have passed.

So the years are:

years passed = 5 * 1.25 billion years = 6.25 billion years

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