Question

The fundamental vibrational frequency of HBr
molecule is 2650 cm-?. Calculate its force constant.
[H = 1 ; Br = 81]​

Answer 1

Answer:

2439cm -1 is Frequectyy of HBr ...is it crct

Answer 2

The force constant of the molecule HBr is 411.2 N/m.

Given:

The fundamental vibrational frequency of HBr = 2650 $cm^{-1}$

To Find:

Force constant, k =?

Solution:

The fundamental frequency is given by the formula -

$v = \frac{1}{2\pi c}\sqrt{\frac{k}{µ} }$     where,

ν = vibrational frequency = 2650 $cm^{-1}$

c = speed of light = 3 × 10⁸ m/s = 3 × 10¹⁰ cm/s

μ = Reduced mass of the molecule HBr = $\frac{m_{1} m_{2}}{m_{1}+ m_{2}}$ = $\frac{(1) (81)}{1+ 81}$ × $10^{-3} kg/mol$

To convert this into kg, this value needs to be divided by Avogadro's number,

μ = $\frac{81}{82}$ × 1.67 × 10⁻⁷ kg

Now,

$v = \frac{1}{2\pi c}\sqrt{\frac{k}{µ} }$

Squaring on both sides,

$v^{2} = \frac{1}{4\\\pi ^{2} c^{2} }\frac{k}{µ} \\ v^{2} (4\pi ^{2} c^{2}) (µ) = k$

∴ k = 2650² × [4 × 3.14² × (3 × 10¹⁰)² ] × $\frac{81}{82}$ × 1.67 × 10⁻⁷

≅ 411.2 N/m

Hence the force constant of the molecule is 411.2 N/m.