The ratio of the densities of three liquids is 1 : 2 : 3. If they are mixed in (i) equal volume, (ii) equal mass, then what will be the densities of their mixtures?
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(i) Let the densities of the liquids be d, 2d and 3d. Let volume V of each of the three liquids be mixed. `therefore` Total volume of the mixture = V + V + V = 3V and total mass of the mixture = `V*d+V*2d+V*3d=6Vd.` `therefore` Density of the mixture = `(6Vd)/(3V)=2d` So, the density of the mixture will be twice the density of the first liquid. (ii) If the mixture is prepared by mixing m mass of each of the three liquids, then the total mass of the mixture = m + m + m = 3m. Total volume of the mixture = `m/d+m/(2d)+m/(3d)=11/6*m/d` `therefore` Density of the mixture = `(3m)/(11/6*m/d)=18/11d` So, the density of the mixture will be `18/11` times the density of the first liquid.
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