## 3 Results and Discussion
### C\({}_{2}\)H\({}_{2}\) Gas Sensing Properties
The response of sensor increased steeply from 0.5 ppm to 10 ppm and then increased slowly from 10 ppm to 500 ppm. Sensitivity is one of the most important parameters, which measures the variation of the response as a function of the variation of the concentration (\(c\)). The figure of the sensitivity as shown in Figure 7a can be calculated as the derivative of the response curve of SnO\({}_{2}\)-rGO. Moreover, Figure 7b shows that response versus concentration maintained good linearity when the gas concentration was below 10 ppm, with \(R^{2}\) = 0.994, and the equation for the response \(y\) and concentration \(x\) can be depicted as:  
\[y=0.447x+1.421 \tag{2}\]  
In this case, we defined that the limit of detection is the lowest concentration when the response reached 2. Thus, it can be calculated that when sensing response (\(y\)) goes to 2 the concentration (\(x\)) goes to 1.3 ppm. Figure 7: (**a**) Corresponding response variations of the SnO\({}_{2}\)-rGO sensor as a function of C\({}_{2}\)H\({}_{2}\) gas concentrations at 180 \({}^{\circ}\)C; (**b**) The limit of detection and the linear relationship between response and concentration; (**c**) Response of SnO\({}_{2}\)-rGO gas sensors to 50 ppm different gases (hydrogen, carbon monoxide, carbon dioxide, methane and acetylene) and (**d**) The stability of SnO\({}_{2}\)–rGO sensor with respect to 10, 50 and 200 ppm C\({}_{2}\)H\({}_{2}\), respectively. Generally, a chemical sensor may be sensitive not only to its intended chemical for measurement, but also to a number of chemicals that can equally be present in the environment, so selectivity is another important property of gas sensors. The figure of the selectivity can be calculated using Equation (13) presented in [33]. The response of SnO\({}_{2}\)-rGO gas sensors to 50 ppm different gases (hydrogen, carbon monoxide, carbon dioxide, methane and acetylene) at 180 \({}^{\circ}\)C are described in Figure 7c. The highest response is observed for C\({}_{2}\)H\({}_{2}\) sensing performance, which is almost 2.7, 4.5, 9.6 and 1.5 times higher than for H\({}_{2}\), CO, CO\({}_{2}\) and CH\({}_{4}\), respectively. All those results reveal that the SnO\({}_{2}\)-rGO sensor can be used for C\({}_{2}\)H\({}_{2}\) detection. Better response to C\({}_{2}\)H\({}_{2}\) might be attributed to higher reactivity and smaller bond energy of H-C\(\equiv\)C-H (490 kJ/mol) compared with other test gases. Although the bond energy of CH\({}_{4}\) (431 kJ/mol) and H\({}_{2}\) (436 kJ/mol) is close to C\({}_{2}\)H\({}_{2}\), interaction strength between the sensing layer and target gas is an effective factor on the sensor response [34]. In the case of the SnO\({}_{2}\)-rGO gas sensor, H\({}_{2}\) and CO may decompose easily at about 200 \({}^{\circ}\)C, where the exothermic reactions become impulsive, hence showing higher response [35]. The fabricated sensor did not show a remarkable response toward CO\({}_{2}\) due to insufficient interaction strength between sensing layer and exposed gas [36]. Moreover, based on the molecular frontier orbital theory, we calculated the highest occupied molecular (HOMO) and lowest unoccupied molecular (LUMO) values of hydrocarbon gases and conducted response testing of SnO\({}_{2}\). The results showed that the ability of losing electron weakens in the following order: C\({}_{2}\)H\({}_{4}\), C\({}_{2}\)H\({}_{2}\), C\({}_{2}\)H\({}_{6}\) and CH\({}_{4}\), which is in strong agreement with our experimental data [32]. Generally, sensor selectivity is a complicated problems associated with the intricate film nanostructure and complicated sensing mechanisms. Sensor selectivity may need further investigation with respect to critical applications [37]. Furthermore, the stability of SnO\({}_{2}\)-rGO sensor upon exposure to 10 ppm, 50 ppm and 200 ppm C\({}_{2}\)H\({}_{2}\) gas was investigated. The measurements lasted for 30 days and responses were tested every 5 days. As shown in Figure 7d, the responses to 10 ppm, 50 ppm and 100 ppm C\({}_{2}\)H\({}_{2}\) gas were kept at an almost constant level.