## 2 Materials and Methods
### Modelling Methodology  
The decomposition of formic acid reaction was modelled using the software Aspen Plus V11. The model selected to accurately predict the behaviour of the vapour-liquid equilibrium of the reaction system was the non-random two-liquid (NRTL) model [44]. The process-modelling studies were performed in a batch reactor with a 100 mL volume and a temperature range of 30-60 \({}^{\circ}\)C. Characteristically, 10 mL of the required concentration of formic acid was deposited into the batch reactor. The catalyst used was 2%Pd\({}_{6}\)Zn\({}_{4}\), the formic acid/metal molar ratio was 2000:1, and the stirring rate was 1400 rpm.  
The most significant feature of the NRTL method [45] is its applicability to multicomponent systems, presuming that the local compositions can be depicted by a relationship similar to that acquired for binary systems [46]:  
\[\frac{x_{ji}}{x_{ki}}=\left(\frac{x_{j}}{x_{k}}\right)e^{[-\frac{(x_{ij}g_{ji}- \alpha_{ik}g_{ki})}{RT}]} \tag{1}\]  
where \(x_{ji}\) and \(x_{ki}\) are the mole fractions of components \(j\) and \(k\), respectively, in the neighbourhood of molecule \(i\); \(g_{ji}\) and \(g_{ki}\) are the Gibbs energies of interaction for the \(j+i\) and \(k+i\) pairs; and \(\alpha_{ij}\) and \(\alpha_{ik}\) are characteristic constants of the corresponding binary mixtures.  
The activity coefficients can be expressed as follows:  
\[ln\gamma_{j}=\left(\frac{\sum_{i}\tau_{ij}G_{ji}x_{j}}{\sum_{k}G_{ki}x_{k}} \right)+\sum_{j}\left\{\left(\frac{x_{j}G_{ij}}{\sum_{k}x_{k}G_{kj}}\right) \cdot\left[\tau_{ij}-\left(\frac{\sum_{i}x_{i}\tau_{ij}G_{ij}}{\sum_{k}x_{k}G _{kj}}\right)\right]\right\} \tag{2}\]  
where  
\[\tau_{ij}=\frac{\left(g_{ij}-g_{jj}\right)}{RT} \tag{3}\]  
and  
\[G_{ij}=e^{(-\alpha_{ij}\tau_{ij})} \tag{4}\]  
The reactor energy balance, coupled with the material balance, can determine the heating or cooling requirements. The energy balance given for the batch stirred reactor can be expressed as follows:  
\[\frac{dT}{dt}=\frac{(r_{A}V)(\Delta\mathrm{H}_{RX})-UA(T-T_{a})}{\sum N_{i}C_ {pi}} \tag{5}\]  
where \(T\) is the reaction temperature, \(r_{A}\) is the rate of reaction, \(V\) is the volume, \(\Delta\mathrm{H}_{RX}\) is the constant heat of reaction, \(U\) is the overall heat transfer coefficient, \(A\) is the batch reactor heat exchange area, \(T_{a}\) is the ambient temperature, \(N_{i}\) is the number of moles, and \(C_{pi}\) is the average heat capacity of species \(i\).  
The decomposition of formic acid can take place via two possible pathways dependent upon the catalyst, reaction temperature, and reactant concentrations. The dehydrogenation of formic acid is shown in Equation (1), and the dehydration reaction is shown by Equation (2). The former reaction is slightly exothermic, while the latter reaction is slightly endothermic. The type of catalyst used can determine which pathway is favoured for the decomposition of formic acid [47; 48].  
\[HCOOH\to CO_{2}+H_{2}\ \Delta_{r}H^{0}=31.2\ \mathrm{kJ}/\mathrm{mol}\ \Delta_{r}G^{0}=-33.0\ \mathrm{kJ}/\mathrm{mol} \tag{6}\]  
\[HCOOH\to CO+H_{2}O\ \Delta_{r}H^{0}=28.4\ \mathrm{kJ}/\mathrm{mol}\ \Delta_{r}G^{0}=-13.0\ \mathrm{kJ}/\mathrm{mol} \tag{7}\]  
The rate of reaction based on the dehydrogenation of formic acid can be expressed using the Power-Law method:  
\[r=k\times C^{n} \tag{8}\]  
where \(r\) is the rate of reaction, \(k\) is the kinetic rate constant, \(C\) is the concentration of formic acid, and \(n\) is the order of reaction [5]. The estimated activation value of 22 kJ/mol was obtained for the catalyst used in this study (Pd/Zn catalyst), and the estimation was based on the experimental data of this study. The order of the reaction was accepted to be 0.2, the same as for Pd/C [5], which reproduced the experimental results satisfactorily.