A polycondensation reaction takes place between 1.2 moles of a dicarboxylic acid, 0.4 moles of glycerol (a triol) and 0.6 moles
of ethylene glycol (a diol). A.Calculate the critical extents of reaction for gelation using (i) the statistical theory of Flory and (ii) the Carothers theory.B.Comment on the observation that the measured value of the critical extent of reaction is 0.866.
B) To Obtain the measured value of critical extent of reaction ( 0.866) 1 mol of Glycerol will react with 1 mol of dicarboxylic acid, but the same can not be applied to our obtained value because our stoichiometry is different
Explanation:
Given data :
Polycondensation reaction takes place between : 1.2 moles of dicarboxylic acid , 0.4 moles of glycerol and 0.6 moles of ethylene glycol
A) Calculate the critical extents of reaction for gelation
i) using statistical theory of floxy
(Pa)c = 0.816
(Pb)c = 0.816
ii) using Carothers theory
( Pc ) = 0.917
attached below is the detailed solution
B) To Obtain the measured value of critical extent of reaction ( 0.866) 1 mol of Glycerol will react with 1 mol of dicarboxylic acid, but the same can not be applied to our obtained value because our stoichiometry is different
Minimizing the initial velocity of the soccer ball would minimize the amount of mechanical energy it has. It shall maintain a minimal gravitational potential possible at all time. It should therefore stay to the ground as close as possible. An elliptical trajectory would thus be unfavorable; the ball shall maintain a uniform circular motion as it orbits the planet.
<em>Equation 1</em> (see below) relates net force the object experiences, to its orbit velocity and its mass required for it to stay in orbit :
<em>(equation 1)</em>
The soccer ball shall experiences a combination of gravitational pull and air resistance (if any) as it orbits the planet. Assuming negligible air resistance, the net force acting on the soccer ball shall equal to its weight, where the gravitational acceleration constant. Thus
<em>(equation 2)</em>
Substitute equation 2 to the left hand side of <em>equation 1</em> and solve for ; note how the mass of the soccer ball, , cancels out:
<em>(equation 3)</em>
<em>Equation 4 </em> gives the value of gravitational acceleration, , a point of negligible mass experiences at a distance from a planet of mass (assuming no other stellar object were present)