Ma The National Institute of Science and Technology (NIST) kinetics database lis

Question

Ma The National Institute of Science and Technology (NIST) kinetics database lists the rate constant, k, of a particular gaseous reaction as 6.17x1010 cm3 molecule-1 s-1at 298 K Convert the rate constant to units of M -1. s-1 Incorrect. The unit analysis will look like this Number cm mL L mole 3.71 x 1010 molec- s cm3ml 3 mL mol mol s M. s The necessary conversion factors are 1mL = 1 cm 1 L = 1000 mL 6.022x 1023 molecules 1 mol 1 mol/L-1 M (so 1L mol 1M- Convert the rate constant to units of Torr's Number k= 1.99 x 106 Torr S What is the order of this reaction? 0

Explanation / Answer

i)

Answer

k = 1.02×10-23M-1s-1

Explanation

Given rate constant unit = cm3/(molecule. s)

required rate constant unit = L/(mol.s)

conversion of cm3 to L

1cm3 = 1ml

1000ml = 1L

So, multiply the rate constant value with 1000

conversion of molecules to mol

1mole = 6.022×1023 molecules

So, divide the rate constant value by 6.022×1023

  Therefore

conversion factor = 1000/6.022×1023 = 1.66×10-24

   Converted value = 6.17×1.66×10-24 = 1.02×10-23

   Therefore, the rate constant is

k = 1.02×10-23 M-1 s-1

ii)

Answer

k = 5.50×10-28 torr-1 s-1

Explanation

Ideal gas equation is

PV = nRT

So,

P = (n/V) RT

1/P =( V/n) (1/RT)

Therefore,

(L/mol) (1/RT) = atm-1

  

k = 1.02×10-23 (L/mol)(1/RT) × s-1

k =1.02×10-23( L/mol) ×(1/(0.082057(Latm /mol K)×298K))×s-1

k = 4.17×10-25 atm-1 s-1

1atm = 760torr

atm-1 = 1.32×10-3torr-1

Therefore

k = 4.17×10-25 × 1.32×10-3torr-1 s-1

   k = 5.50×10-28 torr-1 s-1

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