What would be the stall speed of Solar Impulse?
Solar Impulse has no flaps and a high aspect ratio wing. Therefore, the c$_{l_{max}}$ of the wing should be no higher than 1.8, most likely 1.6. While a rigid airfoil can be designed with a higher c$_{l_{max}}$, it will not have an attractive L/D and a shorter wing would have a c$_{l_{max}}$ below that of the airfoil. Since no fuel is consumed, mass is constant, which makes it very easy to give a lower bound for the minimum speed.

Solar Impulse 2 has 269.5 m² wing area to carry its 2.3 tons of mass. This is a wing loading of just 8.53 kg/m². If we assume standard day conditions at sea level (density $\rho$ = 1.225 kg/m³), we find vor v$_{min}$:

$$v_{min} = \sqrt{\frac{2\cdot m\cdot g}{c_{l_{max}}\cdot S\cdot \rho}} = 9.24 \;\small{\frac{m}{s}} \;\text{or}\; 33.27\; \small{\frac{km}{h}}$$

For those of you from metrically challenged cultures: This is 18 knots or 20.67 mph.