Quinck's method

To find the susceptibility arising due to water in the solution of MnCl2 , ionic molecular susceptibility ,magnetic moment of the Mn++ using quinche's Method

1. DETERMINATION OF MAGNETIC SUSCEPTIBILITY QUINCKE’S METHOD Dr. F. JEYAMANGALAM Associate Professor in Physics SARAH TUCKER COLLEGE [AUTONOMOUS ] TIRUNELVELI-627007 Georg Hermann Quincke

2. Aim: To determine i ) The susceptibility arising due to water in the solution of MnCl 2 ii) The ionic molecular susceptibility of the Mn ++ ion and iii) The magnetic moment of the Mn ++ in terms of Bohr Magneton using Quincke's method.   Apparatus Required: An electromagnet capable of producing field of the order of 5000 gauss , power supply unit including ammeter , travelling microscope , Mncl 2 , H 2 O, U – tube , water, funnel , 100 cc flask , digital balance , etc . DETERMINATION OF MAGNETIC SUSCEPTIBILITY

3. Formula:   1. Mass susceptibility χ s of the solution χ s = e.m.u/gm Where , g – acceleration due to gravity in cm s -2 h – the rise of liquid column in cm H – field strength in gauss   2. Mass susceptibility of anhydrous MnCl 2 χ c = e.m.u Where , χ c – mass susceptibility of anhydrous MnCl 2 in e.m.u / gm m – mass of anhydrous MnCl 2 for given concentration in gm χ w – susceptibility of water in e.m.u .  

4.   3. Molecular susceptibility of anhydrous MnCl 2 χ m = M χ c e.m.u   Where , M – molecular weight of anhydrous Mncl 2     4. Ionic molecular susceptibility of Mn ++ ion χ Mn ++ = χ m – 2 χ C l e.m.u   5. Magnetic moment of Mn ++ ion  B = Bohr M agneton   Where , - Bohr Magneton in e.m.u = 9.271 × 10 -21 e.m.u K - Boltzmann constant in erg/ deg K - 1.38 × 10 -16 erg/ deg N - Avagadro number per gm N - 6.023 × 10 23 / gm T - absolute temperature in kelvin .  

5. DETERMINATION OF MAGNETIC SUSCEPTIBILITY

6. I. Calibration of ammeter to measure the magnetic field Current (A) Magnetic field H ( Gauses ) 0.5 690 1.0 1280 1.5 1900 2.0 2550 2.5 3150 3.0 3760 3.5 4370 4.0 4970 Observation - Model Readings

7. PRINCIPLE When a solution of paramagnetic substance ( eg : MnCl 2 ) taken in a tube is placed between the poles of an electromagnet , there is a rise of the liquid level . A measurement of this rise enables us to determine the susceptibility of the solution.

8. The ammeter is calibrated to read the magnetic field directly. The U – tube is cleaned with warm chromic acid and filled with the solution of manganese chloride in water containing about 5 gm of hydrated salt MnCl 2 . 4H 2 O per 10 cc of solution. The narrow limb of the U – tube is inserted vertically between the pole pieces of the electromagnet. The wide limb (funnel) is then arranged so that when the magnet is energized, the meniscus is in the central region of uniform field. The meniscus is illuminated with an ordinary lamp and viewed with a travelling microscope. The horizontal crosswire of the eyepiece of the microscope is brought in line with the meniscus and its reading is noted. The value of magnetizing field is noted. The field is then switched off. The crosswire is again brought on the meniscus and its reading is noted. Thus the fall in height of the meniscus h for a particular field is measured. This is done over a range of magnetizing fields. The experiment is repeated by taking solution having different concentration of manganese salt. PROCEDURE

9. A graph can be drawn between molar concentration 'm' and ψ s (susceptibility). The graph is a straight line and from the graph the susceptibility of water ψ w is found . From the ψ s and ψ w , the mass susceptibility ψ m is calculated using the molecular weight . The ionic susceptibility of Mn ++ ion is found from ψ c and susceptibility of chlorine ψ cl . χ M n ++ = χ m - 2 χ C l -- From this, the magnetic moment μ B of Mn ++ ion is calculated using the formula  B =  

10. EXPERIMENTAL SETUP FOR QUINCKE’S METHOD

11. II. Measurement of fall in height of the liquid meniscus using travelling microscope Least count = pitch / No. of HSD = 0.001 cm Concen tration gm /cc Magnetic field ( Gauses ) Microscopic readings X 10 -2 (m) Rise in height h X 10 -2 (m) Susceptibility χ s x 10 -5 emu/ gm M.S.R V.S.R T.R 5 Without field 4.60 31 4.631 --- --- 1.886 2550 4.65 45 4.695 0.064 1.929 3760 4.75 14 4.764 0.133 1.844 4970 4.90 13 4.913 0.282 2.237 7 Without field 5.05 04 5.054 --- --- 2.075 2550 5.10 13 5.113 0.059 1.778 3760 5.20 08 5.280 0.226 3.133 4970 5.35 03 5.353 0.299 2.373 9 Without field 4.80 48 4.848 --- --- 2.531 2550 4.90 12 4.912 0.064 1.929 3760 5.00 38 5.038 0.190 2.634 4970 5.15 04 5.154 0.306 2.428 Mean

12. Molar concentration in gm χ s x 10 -5 emu/ gm (0,0)

13. CALCULATION Atomic Weight of Mn =54.94gm Atomic Weight of Cl =35.45 gm Atomic Weight of O=16.00gm Atomic Weight of H = 1.00997gm Molecular Weight of MnCl 2 .4H 2 O= 54.99+2(35.45)+4[(2x1.00997)+16] = 197.9038gm Molecular Weight of anhydrous MnCl 2 = 197.9038 - 4[(2x1.00997)+16] = 125.9 gm Mass of anhydrous MnCl 2 for concentration 5/10 gm of MnCl 2 contain m = =0.3180 gm ; similarly m = = 0.4453 gm ; m = = 0.5725gm  

14. To find χ c , χ m and χ Mn ++ Let χ w = -0.5x10 -5 ; for 5/10gm , χ s = 1.8864 x 10 -5 emu/ gm χ c = = 7.0044x10 -5 emu/ gm ; for 7/10gm χ c = 5.2826 x 10 -5 emu/ gm ; for 9/10gm, χ c = 4.7945 x 10 -5 emu/ gm ; Mean χ c = 5.6937 x 10 -5 emu/ gm Molar susceptibility of anhydrous MnCl2, χ m = m χ c emu/ gm χ m = 125.9 x 5.6937 x 10 -5 emu = 716.836 x 10 -5 emu   χ M n ++ = χ m - 2 χ C l -- χ C l = 25.1x10 -5 emu χ M n ++ =716.836-2x(-25.1x 10 -5 )emu =767.036x 10 -5 emu

15. To find  B Magnetic moment of mn ++ion,  B = Bohr M agneton  B = B M =1.0786x10 20 x3.997x10 -20  B = 4.3110 Bohr M agneton  

16. RESULT Mass susceptibility of the solution of anhydrous MnCl 2 χ c = 5.6937 x 10 -5 emu/ gm Molecular susceptibility of anhydrous MnCl 2 χ m = 716.836 x 10 -5 emu Ionic molecular susceptibility of Mn ++ ion χ M n ++ =767.036x 10 -5 emu Magnetic moment of Mn ++ ion  B = 4.3110 Bohr M agneton

17. II MSc Non Electronics Lab Manuel – Department of Physics Sarah Tucker College ( Autonomous) , Tirunelveli -7 Google Images YouTube Links https:// www.youtube.com/watch?v=yzgdq8uUfO4&t=193s https ://www.youtube.com/watch?v=3PgAhleLqAI&t=2064s https://www.youtube.com/watch?v=jwo7AmtV2bs https://www.youtube.com/watch?v=831EI3r2QSY