You are trying to determine the volume of the balloon needed to match the density of the air in the lab. you know that if you can get the balloon's density below this value, it will float. you measure both the temperature in the room as well as the mass of the balloon you will use and find they are 20.0°c and 0.577 grams, respectively. what volume of balloon will generate a density equal to that of the air around it?

The density of air surrounding the balloon may be calculated by assuming that air is an ideal gas and using the equation,
                                      PV = nRT
In terms of density, 
                                      density = PM/RT
Using the given data,
    density = (1 atm)(28.84 g/mol)/(0.0821 L.atm/molK)(20+273K) = 1.20 g/L

Using ratio and proportion,
         density of balloon = 0.577 g/ V = 1.20 g/L
 
The volume is equal to 0.48 L.