Question

Equal volumes of water and a liquid of relative density 2 are mixed together. What is the density of the mixture??

Answer 1

Let the volume mixed be V and density of water be d.

Relative density of liquid = 2

➝ density of liquid / density of water =2

⠀➝ density of liquid / d =2

⠀➝ density of liquid = 2d ...(i)

Mass of water present in volume V,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ mw = d × V ....(ii)

Mass of liquid present in volume V,

⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀m1 = 2d × V ...(iii)

total mass of the mixture = mw + m1

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀ ⠀= dV + 2dV

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀⠀ = 3dV

total volume of the mixture = V+ V

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀⠀⠀ = 2V

Hence ,

Density of the mixture = 3dV / 2V

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀ = 3d / 2

Density of water in cgs units = 1g / cm³

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ i.e., d = 1g / cm³

∴ ⠀Density of mixture = 3/2 × 1g /cm³

⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 3/2 g / cm³ = 1.5 g / cm ³

Answer 2

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Let the volume mixed be V and density of water be d.

Relative density of liquid = 2

➝ density of liquid / density of water =2

⠀➝ density of liquid / d =2

⠀➝ density of liquid = 2d ...(i)

Mass of water present in volume V,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ mw = d × V ....(ii)

Mass of liquid present in volume V,

⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀m1 = 2d × V ...(iii)

total mass of the mixture = mw + m1

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀ ⠀= dV + 2dV

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀⠀ = 3dV

total volume of the mixture = V+ V

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀⠀⠀ = 2V

Hence ,

Density of the mixture = 3dV / 2V

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀ = 3d / 2

Density of water in cgs units = 1g / cm³

⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ i.e., d = 1g / cm³

∴ ⠀Density of mixture = 3/2 × 1g /cm³

⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 3/2 g / cm³ = 1.5 g / cm ³