What is the total pressure exerted by a mixture of gases in a 20.0 L container at 29.7°C if the mixture contains 0.400 mol O2, 0.700 mol CH4, and 0.500 mol SO2, assuming ideal gas behavior?

First, understand that the problem involves calculating the total pressure exerted by a mixture of gases using the ideal gas law. The ideal gas law is given by the equation: $PV=nRT$, where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is the temperature in Kelvin.