The infrared spectrum of a putative metal hydride complex exhibited an intense f

Question

The infrared spectrum of a putative metal hydride complex exhibited an intense feature at 1910 cm-1 that was thought to be due to iridium-hydrogen stretching (Ir-1H). An isotopic substitution experiment aimed at confirming the origin of this spectral feature was conducted in which deuterium gas was used in place of hydrogen gas to synthesize the iridium complex. What is the expected wavenumber of the corresponding iridium-deuterium (Ir-2H) stretching vibration?  _______ cm-1

The infrared spectrum of a putative metal hydride complex exhibited an intense feature at 1910 cm-1 that was thought to be due to iridium-hydrogen stretching (Ir-1H). An isotopic substitution experiment aimed at confirming the origin of this spectral feature was conducted in which deuterium gas was used in place of hydrogen gas to synthesize the iridium complex. What is the expected wavenumber of the corresponding iridium-deuterium (Ir-2H) stretching vibration? _______ cm-1

Explanation / Answer

streching frequency v = const sqrt ( K/u) where u = reduced mass

u for Ir-H = mIr x mH/( mIr + mH) = ( 192.17 x 1.008)/( 192.17+1.008) = 1.002584

u for Ir-2H = ( 192.17 x2.014)/(192.17+2.014) = 1.993

now Ir-de strching /Ir-H strech = sqrt ( u Ir-H)/u Ir-D)

Ir-deut strech /1910 = sqrt( 1.002584/1.993)

Ir-deut strech = 1354.7 = 1355 cm-1

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