Question

For a diatomic molecule with a rotational constant B=1.656x10¹¹ s^-1 and a reduced mass µ=4.00x10^-27 kg, the equilibrium bond length, R_e, can be calculated to be (in Å or 10^-10 m):

1.28

2.26

3.39

1.13

2.56

If two molecules A-B and C-D have the same force constant and the reduced mass of A-B is 4 times that of C-D, the vibrational frequency of C-D should be __X__time that of A-B:

1/2

1

1/4

2

4

For a chemical reaction starting with only one reactant A producing product P , the half-life t_1/2 is found to be 0.10 s and the rate constant k was found to be 5.0 M/s for an initial concentration [A]₀=1.0 M. This means that the reaction is:

not possible to determine

second order

first order

zeroth order

Answer 1

B = h²/8π²I is rotational constant

h=6.626 ×10^-34 ( Planck's constant )

I = moment of inertia

here ,B =1.656× 10¹¹ s^-1 and = 4.00 × 10^-27 kg

Also, I = R_e²

So, I = h²/B 8π²

=(6.626 × 10^-34 )^2 /1.656×10^ 11×8 × (3.14 )^2

= 3.3912 × 10^ -80 kg / m²

So, R_e² =I /

R_e = I/

=3.3912 ×10^ -80 /4.00×10 ^ -27

= 2.8987 ×10 ^ -27 m²

= 2.8987 × 10^-7 ° A ²

^{= 28.987 × 10 ^-6 °A}

Here, K = 5.0 M/s

The general equation for unit of rate constant for n^th order reaction, k= Mol ^{(1- n)} L^{(n -1 )} s ^-1

Also, mol L^-1 = M

Here, unit of k is mol L^-1s^-1

Putting n = 0 in the general equation we get,

k = mol L^-1s^-1

= M / s

Hence, the given reaction is zeroth order .