Final answer:
The question seeks to calculate the multiple of the root mean square speed of water molecules at 20°C using the given vapor pressure, molecular mass, and ideal gas law relations. Additional context would be required to provide a precise multiple of the speed.
Step-by-step explanation:
The question pertains to the root mean square speed (vrms) of water molecules at a temperature of 20°C, which can be estimated using the ideal gas law and assuming that water vapor behaves like an ideal gas under these conditions. Considering that the vapor pressure of water at this temperature is given (2.33 × 103 Pa) and the molecular mass of water is 18.0 g/mol, we can calculate the density of water vapor and use the ideal gas equation (PV = nRT) to solve for n/V, the molar density. Once n/V is known, we can relate it to the molecular speed using kinetic molecular theory.
The vapor pressure of water at 20 °C also sets the conditions for 100% relative humidity and indicates that a maximum of 17.2 g of water vapor per cubic meter is the saturation vapor density at that temperature. To find out what multiple of vrms is being asked about, we would need additional context from the student, such as the specific condition or speed they are referring to.