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
Answer : The percent abundance of the heaviest isotope is, 78 %
Explanation :
Average atomic mass of an element is defined as the sum of masses of each isotope each multiplied by their natural fractional abundance.
Formula used to calculate average atomic mass follows:
As we are given that,
Average atomic mass = 48.68 amu
Mass of heaviest-weight isotope = 49.00 amu
Let the percentage abundance of heaviest-weight isotope = x %
Fractional abundance of heaviest-weight isotope =
Mass of lightest-weight isotope = 47.00 amu
Percentage abundance of lightest-weight isotope = 10 %
Fractional abundance of lightest-weight isotope =
Mass of middle-weight isotope = 48.00 amu
Percentage abundance of middle-weight isotope = [100 - (x + 10)] % = (90 - x) %
Fractional abundance of middle-weight isotope =
Now put all the given values in above formula, we get:
Therefore, the percent abundance of the heaviest isotope is, 78 %