*3.7. Equations*

The partitioning coe fficient (P) was calculated using the following formula:

$$P = \text{[furfural]} \text{\_{\text{or}}\%\text{[furfural]}} \text{\_{\text{alg}\_{\prime}}} \tag{1}$$

where [furfural]org is the concentration (g/l) of furfural in the organic layer and [furfural]aq is the concentration of furfural in the water layer.

The total amount of acid sites according to Boehm titration was calculated as follows:

n total acids = [(CNaOH\*VNaOH added - (CHCl\*VHCl added - CNaOH\*VNaOH titration)/ 1 5 )-n total acids in reference]/m, (2)

where c (NaOH and HCl) are concentrations in mol/L, V (NaOH and HCl) are added volumes in mL, V (NaOH titration) is the volume of NaOH in ml needed to achieve equilibrium in titration, m is the mass of carbon weighed and n (total acids in reference) represents a blank solution without carbon. The factor 1 5 is due to the measurement of the 10 mL aliquots representing 1 5 of the reaction base.

The yield of furfural was calculated as follows:

$$\text{Y}\_{\text{furfurnal}}\,\text{(\%)} = \text{[c}\_{\text{furnf measas}}\,\text{org/c}\_{\text{furnf max}}\text{]} \times 100\text{\%} \,\text{(}\tag{3}$$

where c furf. meas. org is the measured furfural concentration in the organic phase of the sample and c furf max is the theoretical maximum concentration of furfural in the sample.

The conversion of xylose was calculated as follows:

$$\mathbf{C\_{xyzlose}}\text{ (\%)}=\mathbf{[n\\_xyl\\_trivial]}\text{ }\mathbf{n\\_xyl\\_final}\text{ }\mathbf{l}\times\mathbf{100}\text{\%}\text{ }\tag{4}$$

where n xyl initial is the initial amount of xylose (in moles) fed to the reaction and n xyl final is the amount of xylose left in the reaction mixture after the reaction.

The selectivity of the xylose to furfural conversion was calculated as follows:

$$\mathcal{S}\left(\%\right) = \left[ \left( \text{c\\_furf\,max\, total} / \text{c\\_furf\,max} \right) \left( \text{conv}\,\text{version} \right) \times 100\%\right] \tag{5}$$

where c furf. meas total. is the measured total furfural concentration in the organic and aqueous phases of the sample and c furf max is the theoretical maximum concentration of furfural in the sample.
