I have a question regarding gas volume; please advise

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The pressure at the top of the tower is 1 kPa, and the temperature is 45 degrees. The stream exiting from the top of the tower is a mixture of water (in gaseous form) and air; the flow rate of water is 3.125 kg/hr, while the flow rate of air is 6 kg/hr. I would like to calculate the volumetric flow rate at the top of the tower. Currently, there are two methods. The first involves using Dalton’s law of partial pressures to calculate the partial pressure of each substance, and then using PV=nRT to determine the total volume by adding up these values. The second method is to treat water and air as a mixture, determine the total number of moles, and then use PV=nRT to calculate the total volume V. I ran a simulation using Aspen, and the results were pretty much the same as those from the second method. But why is the first method much larger than the second one? Seeking your advice