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We know that
1 gallon = 3.78541 L
1000 ml = 1.0 L
Density = mass / volume
Mass = volume *density
Therefore
(3.78541 L emulsion) x (500 mL oil / 1 L emulsion) x (0.87 g/mL oil) = 1647 g oil
Density = 0.87 g/ ml
Because the density of water = 1.0 g/ ml