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In: Chemistry

The fundamental vibrational frequencies for 1H2and 14N2 are 4401 and 2359 cm−1, respectively, and De for...

The fundamental vibrational frequencies for 1H2and 14N2 are 4401 and 2359 cm−1, respectively, and De for this molecules is 7.677×10−19 and 1.593×10−18 J respectively.

Part A

Using this information, calculate the bond energy of 1H2.

Express your answer to four significant figures and include the appropriate units.

EH2 =

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Part B

Calculate the bond energy of 14N2.

Express your answer to four significant figures and include the appropriate units.

EN2 =

Expert Solution

The expression for Energy, E_n=hν(n+1/2)- [(hν)²(n+1/2)²]/4D_e

For, fundamental vibration, n=0

Therefore, E₀=hν/2- (hν)²/16D_e

Where, h=Planck’s constant =6.626x10^-34Js

and ν=fundamental frequency

Bond Energy =D₀= D_e-E₀

Part A: For H₂: 1/λ=4401cm^-1 ; D_e=7.677x10^-19J

ν=c/ λ=1.32x10¹⁴s^-1

E₀= (6.626x10^-34) (1.32x10¹⁴) /2- [(6.626x10^-34) (1.32x10¹⁴)]²/16(7.677x10^-19)

E₀= 4.3108x10^-20J

Therefore, Bond Energy =D₀= D_e-E₀ =7.677x10^-19 - 4.3108x10^-20 J =7.246 x10^-19 J

Part B: For N₂: 1/λ=2359cm^-1 ; D_e=1.593 x10^-18J

ν=c/ λ=7.07x10¹³s^-1

E₀= (6.626x10^-34) (7.07x10¹³) /2- [(6.626x10^-34) (7.07x10¹³)]²/16(1.593x10^-18)

E₀= 2.333x10^-20J

Therefore, Bond Energy =D₀= D_e-E₀ =1.593 x10^-18 - 2.333x10^-20 J =1.569 x10^-18 J

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