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Consider two containers with the same volume and temperature.

 

The first container is labelled "Dry" and holds "dry" air = a ratio of nitrogen (N2) and oxygen (O2).

The second container is labelled "Humid" and holds "moist" air = the SAME ratio of nitrogen and oxygen, but also contains water (H2O) vapor.

According to the ideal gas law, if the pressures are equal, the weight of the gas inside the "Dry" container will be 

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