# 9.1 Catalyst characterization using thermal conductivity detector  (Page 4/4)

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${\text{V}}_{\text{adsorbed}}\text{=}\frac{{\text{ΔArea}}_{\text{n}}{\text{×F}}_{\text{c}}}{\text{SW}}$
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.

${\text{GMW}}_{\text{Calc}}=\frac{\text{1}}{\left(\frac{{\text{F}}_{\text{1}}}{{\text{W}}_{\text{atomic1}}}\right)+\left(\frac{{\text{F}}_{\text{2}}}{{\text{W}}_{\text{atomic2}}}\right)+\text{...}+\left(\frac{{\text{F}}_{\text{N}}}{{\text{W}}_{\text{atomicN}}}\right)}$
${\text{GMW}}_{\text{Calc}}\text{=}\frac{\text{1}}{\left(\frac{{\text{F}}_{\text{1}}}{{\text{W}}_{\text{atomicPd}}}\right)}\text{=}\frac{{\text{W}}_{\text{atomicPd}}}{{\text{F}}_{\text{1}}}\text{=}\frac{\text{106}\text{.42}\frac{\text{g}}{\text{g-mole}}}{\text{1}}\text{=106}\text{.42}\frac{\text{g}}{\text{g-mole}}$

## 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%.

$\text{PD}\underset{}{}=\text{100}×\left(\frac{{\text{V}}_{\text{s}}×{\text{SF}}_{\text{Calc}}}{\text{SW}×\text{22414}}\right)×{\text{GMW}}_{\text{Calc}}$
$\text{PD=100×}\left(\frac{\text{0}\text{.8296556}\left[{\text{cm}}^{\text{3}}\right]\text{×2}}{\text{0}\text{.1289}\left[\text{g}\right]\text{×22414}\left[\frac{{\text{cm}}^{\text{3}}}{\text{mol}}\right]}\right)\text{×106}\text{.42}\left[\frac{\text{g}}{\text{g-mol}}\right]=6.03%$

## 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.

${\text{SA}}_{\text{Metallic}}\text{=}\left(\frac{{\text{V}}_{\text{S}}}{{\text{SW}}_{\text{Metal}}\text{×22414}}\right)\text{×}\left({\text{SF}}_{\text{Calc}}\right)\text{×}\left(\text{6}{\text{.022×10}}^{\text{23}}\right){\text{×SA}}_{\text{Pd}}$
${\text{SA}}_{\text{Metallic}}\text{=}\left(\frac{\text{0}\text{.8296556}\left[{\text{cm}}^{\text{3}}\right]}{\text{0}\text{.001289}\left[{\text{g}}_{\text{metal}}\right]\text{×22414}\left[\frac{{\text{cm}}^{\text{3}}}{\text{mol}}\right]}\right)\text{×}\left(\text{2}\right)\text{×}\left(\text{6}{\text{.022×10}}^{\text{23}}\left[\frac{\text{atoms}}{\text{mol}}\right]\right)\text{×0}\text{.07}\left[\frac{{\text{nm}}^{\text{2}}}{\text{atom}}\right]\text{=2420}\text{.99}\left[\frac{{\text{m}}^{\text{2}}}{\text{g-metal}}\right]$

## 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.

$\text{APS=}\frac{\text{6}}{{\text{D}}_{\text{Calc}}\text{×}\left(\frac{{\text{W}}_{\text{s}}}{{\text{GMW}}_{\text{Calc}}}\right)\text{×}\left(\text{6}{\text{.022×10}}^{\text{23}}\right){\text{×SA}}_{\text{Metallic}}}$
$\text{APS=}\frac{\text{600}}{\left(\text{1}{\text{.202×10}}^{\text{-20}}\left[\frac{{\text{g}}_{\text{Pd}}}{{\text{nm}}^{\text{3}}}\right]\right)\text{×}\left(\frac{\text{0}\text{.001289}\left[\text{g}\right]}{\text{106}\text{.42}\left[\frac{{\text{g}}_{\text{Pd}}}{\text{mol}}\right]}\right)\text{×}\left(\text{6}{\text{.022×10}}^{\text{23}}\left[\frac{\text{atoms}}{\text{mol}}\right]\right)\text{×}\left(\text{2420}\text{.99}\left[\frac{{\text{m}}^{\text{2}}}{{\text{g}}_{\text{Pd}}}\right]\right)}\text{=2}\text{.88nm}$

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.

Properties Value
Atomic cross-sectional area 0.0787 nm²
Metal density 12.02 g/cm³
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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