The force constants for F2 and I2 are 470. and 172 Nm1, respectively. The atomic

Question

The force constants for F2 and I2 are 470. and 172 Nm1, respectively. The atomic masses in amu are as follows: 19 F - 18.9984, 127 I - 126.9045.

1) Calculate the ratio of the vibrational state populations n1/n0 for F2 at 310 K

2) Calculate the ratio of the vibrational state populations n1/n0 for F2 at 900 K

3) Calculate the ratio of the vibrational state populations n2/n0 for F2 at 310 K .

4) Calculate the ratio of the vibrational state populations n2/n0 for F2 at 900 K .

5) Calculate the ratio of the vibrational state populations n1/n0 for I2 at 310 K

6) Calculate the ratio of the vibrational state populations n1/n0 for I2 at 900 K

7) Calculate the ratio of the vibrational state populations n2/n0 for I2 at 310 K .

8) Calculate the ratio of the vibrational state populations n2/n0 for I2 at 900 K .

Explanation / Answer

For F2,

reduced mass for F2 (u1) = [(18.9984)^2/(18.9984 + 18.9984)]/6.023 x 10^26 = 1.58 x 10^-26 kg

vibrational frequency for F2 (v1) = [1/2pi.sq.rt.(k/u1)]

k = 470 N.m-1

v1 = (1/2 x 3.14) x sq.rt.(470/1.58 x 10^-26) = 2.746 x 10^13 s-1

Population analysis

1) n1/no = e^-(hv1/Kb.T)

T = 310 K

Kb = Bolzman constant

h = planck's constant

n1/no = e^-(6.626 x 10^-34 x 2.746 x 10^13/1.38 x 10^-23 x 310) = 0.0142

2) at T = 900 K

n1/no = e^-(6.626 x 10^-34 x 2.746 x 10^13/1.38 x 10^-23 x 900) = 0.2311

3) at T = 310 K

n2/no = e^-(2 x 6.626 x 10^-34 x 2.746 x 10^13/1.38 x 10^-23 x 310) = 0.0002

4) at T = 900 K

n2/no = e^-(2 x 6.626 x 10^-34 x 2.746 x 10^13/1.38 x 10^-23 x 900) = 0.0534

For I2

reduced mass for I2 (u2) = [(126.9045)^2/(126.9045 + 126.9045)]/6.023 x 10^26 = 1.05 x 10^-25 kg

vibrational frequency for F2 (v1) = [1/2pi.sq.rt.(k/u1)]

k = 172 N.m-1

v1 = (1/2 x 3.14) x sq.rt.(172/1.05 x 10^-25) = 6.445 x 10^12 s-1

Population analysis

5) n1/no = e^-(hv1/Kb.T)

T = 310 K

Kb = Bolzman constant

h = planck's constant

n1/no = e^-(6.626 x 10^-34 x 6.445 x 10^12/1.38 x 10^-23 x 310) = 0.3685

6) at T = 900 K

n1/no = e^-(6.626 x 10^-34 x 6.445 x 10^12/1.38 x 10^-23 x 900) = 0.7090

7) at T = 310 K

n2/no = e^-(2 x 6.626 x 10^-34 x 6.445 x 10^12/1.38 x 10^-23 x 310) = 0.1358

8) at T = 900 K

n2/no = e^-(2 x 6.626 x 10^-34 x 6.445 x 10^12/1.38 x 10^-23 x 900) = 0.5027

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