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I get some disturbing results when I try to hydrogenate on the H-cube.
First: When I have the flow at 1ml/min I get 63% product, when I have 2 ml/min I get full conversion of Starting material to product.
I expected to have less conversion of starting material to product when I increased the flow, because I thought that the product will have less time to interact with the catalyst on the cartridge.
Is my reasoning wrong?
Second: We get higher conversion to product when we have lower hydrogenation pressure, why is that?

You are right that the higher flow rate generates lower residence time on the catalyst, which may decrease the conversion. However the H-Cube always regulates the gas/liquid ratio to have approximately 7% of gas in the line, which means that if the flow rate is higher, then the amount of the Hydrogen will be also higher. This is the reason of the higher conversion. The actual amount of the Hydrogen in your system can be calculated:
p = set pressure (bar)
c(reag) = reagent concentration (mol/L)
v(reag) = reagens flow rate (mL/min)
H2 equiv. = equivalent hydrogen needed for the reaction
Bub% = Bubble detector % (in the H-Cube: 7)
n(reag) = c(reag)*v(reag) = mol reagent consumed
n(H2-needed) = n(reag)*H2 equiv = mol hydrogen needed
n(H2-calc) = (v(reag)+Bub%/100*v(reag))*Bub%/100/24.5*p = mol hydrogen in the system, calculated
Compare the calculated amount of hydrogen with the needed one. Hydrogen excess of at least 40% should be used, but higher is better if you don't have selectivity issues.

Regarding the second question, there is no exact technical explanation for the results. The simplest answer may be that your specific reaction is working better at low pressures. For example if you have a Cbz deprotection reaction, than it always works better at low pressures. If the answer is not in the chemistry, than a technical option may be that the gas introduction is smoother on lower pressures, and because of the improved gas/liquid homogeneity the yield of your reaction is increased (You may check the gas introduction homogeneity on the service screen in the bubdet window).
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