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V adsorbed = ΔArea n ×F c SW
Includes the volume adsorbed per pulse and the cumulative volume adsorbed.
Pulse n area n Δarea n V adsorbed (cm 3 /g STP) Cumulative quantity (cm 3 /g STP)
1 0 0.0105809790 0.2800256 0.2800256
2 0.000471772 0.0105338018 0.2787771 0.5588027
3 0.00247767 0.0081033090 0.2144541 0.7732567
4 0.009846683 0.0007342960 0.0194331 0.7926899
5 0.010348201 0.0002327780 0.0061605 0.7988504
6 0.010030243 0.0005507360 0.0145752 0.8134256
7 0.009967717 0.0006132620 0.0162300 0.8296556
8 0.010580979 0 0.0000000 0.8296556

Gram molecular weight

Gram molecular weight is the weighted average of the number of moles of each active metal in the catalyst. Since this is a monometallic catalyst, the gram molecular weight is equal to the molecular weight of palladium (106.42 [g/mol]). The GMC Calc is calculated using [link] , where F is the fraction of sample weight for metal N and W atomicN is the gram molecular weight of metal N (g/g-mole). [link] shows the calculation for this experiment.

GMW Calc = 1 ( F 1 W atomic1 ) + ( F 2 W atomic2 ) + ... + ( F N W atomicN ) MathType@MTEF@5@5@+=faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8FesqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@5ADE@
GMW Calc = 1 ( F 1 W atomicPd ) = W atomicPd F 1 = 106 .42 g g-mole 1 =106 .42 g g-mole

Metal dispersion

The metal dispersion is calculated using [link] , where PD is the percent metal dispersion, V s is the volume adsorbed (cm 3 at STP), SF Calc is the calculated stoichiometry factor (equal to 2 for a palladium-hydrogen system), SW is the sample weight and GMW Calc is the calculated gram molecular weight of the sample [g/g-mole]. Therefore, in [link] we obtain a metal dispersion of 6.03%.

PD = 100 × ( V s × SF Calc SW × 22414 ) × GMW Calc MathType@MTEF@5@5@+=faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8FesqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9Gqpi0dc9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiuaiaabseadaWfqaqaaaWcbaaabeaakiabg2da9iaabgdacaqGWaGaaeimaiabgEna0oaabmaabaWaaSaaaeaacaqGwbWaaSbaaSqaaiaabohaaeqaaOGaey41aqRaae4uaiaabAeadaWgaaWcbaGaae4qaiaabggacaqGSbGaae4yaaqabaaakeaacaqGtbGaae4vaiabgEna0kaabkdacaqGYaGaaeinaiaabgdacaqG0aaaaaGaayjkaiaawMcaaiabgEna0kaabEeacaqGnbGaae4vamaaBaaaleaacaqGdbGaaeyyaiaabYgacaqGJbaabeaaaaa@4FBF@
PD=100× ( 0 .8296556 [ cm 3 ] ×2 0 .1289 [ g ] ×22414 [ cm 3 mol ] ) ×106 .42 [ g g-mol ] = 6.03 %

Metallic surface area per gram of metal

The metallic surface area per gram of metal is calculated using [link] , where SA Metallic is the metallic surface area (m 2 /g of metal), SW Metal is the active metal weight, SF Calc is the calculated stoichiometric factor and SA Pd is the cross sectional area of one palladium atom (nm 2 ). Thus, in [link] we obtain a metallic surface area of 2420.99 m 2 /g-metal.

SA Metallic = ( V S SW Metal ×22414 ) × ( SF Calc ) × ( 6 .022×10 23 ) ×SA Pd
SA Metallic = ( 0 .8296556 [ cm 3 ] 0 .001289 [ g metal ] ×22414 [ cm 3 mol ] ) × ( 2 ) × ( 6 .022×10 23 [ atoms mol ] ) ×0 .07 [ nm 2 atom ] =2420 .99 [ m 2 g-metal ]

Active particle size

The active particle size is estimated using [link] , where D Calc is palladium metal density (g/cm 3 ), SW Metal is the active metal weight, GMW Calc is the calculated gram molecular weight (g/g-mole), and SA Pd is the cross sectional area of one palladium atom (nm 2 ). As seen in [link] we obtain an optical particle size of 2.88 nm.

APS= 6 D Calc × ( W s GMW Calc ) × ( 6 .022×10 23 ) ×SA Metallic
APS= 600 ( 1 .202×10 -20 [ g Pd nm 3 ] ) × ( 0 .001289 [ g ] 106 .42 [ g Pd mol ] ) × ( 6 .022×10 23 [ atoms mol ] ) × ( 2420 .99 [ m 2 g Pd ] ) =2 .88nm

In a commercial instrument, a summary report will be provided which summarizes the properties of our catalytic material. All the equations used during this example were extracted from the AutoChem 2920-User's Manual.

Summary report provided by Micromeritics AuthoChem 2920.
Properties Value
Palladium atomic weight 106.4 g/mol
Atomic cross-sectional area 0.0787 nm²
Metal density 12.02 g/cm³
Palladium loading 1 wt%
Metal dispersion 6.03%
Metallic surface area 2420.99 m²/g-metal
Active particle diameter (hemisphere) 2.88 nm

References

  • A. J. Canty, Accounts Chem. Res. , 1992, 25 , 83.
  • H. S. Fogler, Elements of Chemical Reaction Engineering , Prentice-Hall, New York (1992).
  • Micromeritics Instrument Corporation, AutoChem 2920 – Automated catalyst characterization system – Operators Manual , V4.01 (2009).
  • M. O. Nutt, K. N. Heck, P. Alvarez, and M. S. Wong, Appl. Catal. B-Environ. , 2006, 69 , 115.
  • M. O. Nutt, J. B. Hughes, and M. S. Wong, Environ. Sci. Technol. , 2005, 39 , 1346.
  • P. A. Webb and C. Orr, Analytical Methods in Fine Particle Technology , Micromeritics Instrument Corp, 1997.
  • R. Zhang, J. A. Schwarz, A. Datye, and J. P. Baltrus, J. Catal. , 1992, 138 , 55.

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Source:  OpenStax, Physical methods in chemistry and nano science. OpenStax CNX. May 05, 2015 Download for free at http://legacy.cnx.org/content/col10699/1.21
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