## 2 Materials and Methods
### Methodology  
Fatty acids of the _C. tinctoria_ seed oil were determined using Metcalfe procedure [44], and fatty acid composition were identified using a gas chromatography (Clarus580 GC) equipped with a FID detector. That equipment has been sourced from FARASOUT SANAT Eng CO, Tehran, Iran. One microliter of prepared sample was injected to the gas chromatography unit, which was equipped with a BP-30 column and FTIR detector that was kept isothermally standardized to encounter BS-EN 14103 standard. The total run time for each sample was 30 min. Fatty acid profile was determined by classifying and calculating relative peak areas.  
In order to perform the transesterification reaction, an ultrasonic reactor was used. In the first step, a catalyst (e.g., potassium hydroxide (KOH)) and methanol was mixed together by a magnetic stirrer. It is noteworthy that methoxide was prepared by mixing methanol that had a molar ratio of 1:7, with 1 wt% of KOH. The prepared methoxide was added to the _C. tinctoria_ seed oil. Then, the solution was transferred into the ultrasonic reactor. An ultrasonic device (Hielscher Model UP400S, USA) was applied to perform the transesterification reaction.That equipment has been sourced from FARASOUT SANAT Eng CO, Tehran, Iran, The ultrasonic device was controlled using a computer with the help of UPC software. An ultrasonic probe with a diameter of 10 mm and a height of 60 mm was used to transmit the ultrasound to the solution. The effective length of the probe that was placed inside the solution was 55 mm. The reaction time was adjusted every 5 min. The reaction temperature was adjusted to \(45\pm 0.45\)\({}^{\circ}\)C with the help of water circulating between the two reactor walls, and all experiments were performed at atmospheric pressure. After completing the reaction time, the biodiesel mixture was removed from the ultrasonic reactor. In order to stop the reaction, the biodiesel mixture was put into a cold ice bath. The mixture was stored in a separation plate and the mixture was completely separated into two phases. The lower phase was glycerin and the upper one was biodiesel. In Figure 3, the biodiesel production process is shown. After separation of the glycerin, the biodiesel should be purified. The separated part from the glycerin was washed by warm water to purify the biodiesel. In the next section, in order to remove the water from the biodiesel, the washed biodiesel was heated up for one hour in an oven (temperature was adjusted to 60 \({}^{\circ}\)C). Finally, a gas chromatography unit was used to identify the yield of the biodiesel. Equation (1) was used [34; 45] to determine the yield of the biodiesel.  
\[\textit{Biodiesel yield}=\frac{\sum A-\textit{AIS}}{\textit{AIS}}\times \frac{\textit{MIS}}{M} \tag{1}\]  
where \(\sum A\) is the total area under the peak of total fatty acids, _MIS_ is the weight of the internal standard, _AIS_ is the area under the peak for the internal standard (C19:0), and \(M\) is the weight of the sample.  
After purification of the biodiesel, the most important physicochemical properties of the biodiesel, including the kinematic viscosity at 40 \({}^{\circ}\)C (ASTM D445), density at 15 \({}^{\circ}\)C (ASTM D4052), pour point (ASTM D6751), cloud point (ASTM D6751), flash point (ASTM D93), oxidation stability at 110 \({}^{\circ}\)C (EN 14112), acid value (ASTM D664), and cetane number (ASTM D613), were determined, based on ASTM standard [46].