Question

Suppose a chemical reaction is first order and has a half-life of 2.5 hr at 100 ºC.  Which of the following statements is false regarding this reaction if the temperature is changed?  

Question 5 options:

	A) The half-life at 125 ºC is 1.8 hr.
	B) The half-life at 275 ºC is 3.5 hr.
	C) The half-life at 75 ºC is 4.7 hr.
	D) Not enough information has been provided in order to make a conclusion.

Answer 1

Sol.

For a first order reaction ,

Rate constant = k = 0.693 / t1/2 ( equation 1 )

where t1/2 is half - life

Also , Arrhenius equation is :

ln ( k2 / k1 ) = ( Ea / R ) × ( T2 - T1 ) / ( T2 × T1 )

( equation 2 )

where k2 and k1 are rate constants at temperatures T2 and T1 respectively  

Ea is activation energy and R is gas constant

So , with the help of equations 1 and 2 , we can calculate half - lifes at different temperatures

But the value of activation energy , Ea is not provided in the question . So , it is impossible to calculate half - lifes at different temperatures without Ea value .

Therefore , answer is   (D) , Not enough information has been provided in order to make a conclusion