Using evans method: m= ( 477x delta V)/ Qx Vref x c delta v (in Hz) = frequency

Question

Using evans method: m= ( 477x delta V)/ Qx Vref x c

delta v (in Hz) = frequency shift of a solvent peak

Q=2

Vref= frequency of the pure solvent reference peak (Hz)

c= concentration

through bonds and through space. The frequency shift Av (in Hz) of a solvent peak due to a paramagnetic complex can be related to the magnetic susceptibility, (cm' mol 1) by the following equation: 477AV Km where Q for a spectrometer with an electromagnet or 2 for a superconducting magnet, c is the concentration of the paramagnetic complex and is the frequency of the pure solvent reference peak (Hz).

Explanation / Answer

Molar mass of the sample = 330 g mol-1.

We took 7.4 mg = (7.4 mg)*(1 g/1000 mg) = 7.4*10-3 g sample.

Moles of sample taken = (7.4*10-3 g)/(330 g mol-1) = 2.242*10-5 mole; volume of sample taken = 1 mL = 1 cm3 (since 1 mL = 1 cm3).

Concentration of the sample = (2.242*10-5 mole)/(1 cm3) = 2.242*10-5 mol/cm3.

We have = 17.6 ppm = (17.6 ppm)*(frequency of the machine)/(106) (assuming frequency of the machine = 0 ppm) = (17.6 ppm)*(500*106 Hz)/(106 Hz) = 8800 Hz (since 1 MHz = 106 Hz)

Again, ref = (2.5 ppm)*(500*106 Hz)/(106) = 1250 Hz

Plug in values.

M = (477*8800 Hz)/(2*1250 Hz).(2.242*10-5 mol/cm3) = 7.48*107 cm3/mol 7.5*107 mol/cm3 (ans).

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