Estimate the effective radius of a glycine molecule in water at 25 degree C give

Question

Estimate the effective radius of a glycine molecule in water at 25 degree C given that its diffusion coefficient is 1.055 times 10^-9 m^2/s and that the viscosity of water is 1.00 cP (1 centiPoise = 0.001 N.s/m^2). How much time is required for a glycine molecule under these conditions to travel a rms (root-mean-square) displacement of 1.0 cm? If the temperature were 37 degree C, estimate the time for a the same rms displacement. (a) The half-life of the first-order decay of radioactive^14 C is 5720 years. Calculate the rate constant for this reaction. (b) The natural abundance of^14 C in living matter is 1.1 times 10^-13 mol%. Radiochemical analysis of an object obtained in an archeological dig indicates that the^14 C content is 8.9 times 10^-15 mol%. Determine the age of the object State any assumptions that you make.

Explanation / Answer

a) Given that it is a first order decay.

Hence,

rate constant = 0.693/ half life

                     = 0.693 / 5720 yrs

                      = 0.00012 yr-1

b)   

Radio active decay is a first order reaction.

For first order recation,

half life t1/2 = 0.693 /k where k is rate constant

k = 0.693/ t1/2 --- Eq (1)

k = 1/t ln { [A]o/[A]t} -----Eq (2)

From Eqs (1) and (2),

0.693/ t1/2 = (1/t) ln {[A]o/ [A]t} ------Eq (3)

Given that

half life of 14C = 5720 yrs

age of the object, t = ?

Initial 14C, [A]o = 1.1 x 10-13 mol%

Final 14C, [A]t = 8.9 x 10-15 mol%

Substitute all the values in Eq (3),

0.693/ t1/2 = (1/t) ln {[A]o/ [A]t}

0.693/ 5720 = (1/t) ln { 1.1 x 10-13 mol%/8.9 x 10-15 mol% }

t = (5720/0.693) x ln { 1.1 x 10-13 mol%/8.9 x 10-15 mol% }

= 20754 yrs

t = 20754 yrs

Therefore,

age of the object = 20754 yrs

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