The density of two liquids, A and B, are 1000. kg/m3 and 600. kg/m3, respectively. The two liquids are mixed in a certain proportion and the density of the resulting liquid is 850 kg/m3. How much of liquid B (in grams) does 1.0 kg of the mixture contain? Assume the volume of the two liquids is additive when mixed.

The mass of liquid B in the 1 Kg mixture is 300 g

Let the volume of liquid A be Va

Let the volume of liquid B be Vb

From the question given above, the following data were obtained:

Density of liquid A = 1000 kg/m³

Density of liquid B = 600 kg/m³

Density of mixture = 850 kg/m³

Mass of mixture = 1 kg

For Liquid A:

Density of liquid A = 1000 kg/m³

Volume of liquid A = Va

Mass of Liquid A =?

Mass = Density × Volume

Mass of Liquid A = 1000 × Va

For Liquid B:

Density of liquid B = 600 kg/m³

Volume of liquid B= Va

Mass = Density × Volume

Mass of Liquid B = 600 × Va

Density of mixture = 850 kg/m³

Mass of mixture = 1 kg

Volume = mass /density

Volume of mixture = 1 / 850

Mass of mixture = 1 Kg

Mass of mixture = Mass of liquid A + Mass of liquid B

Volume of mixture = Va + Vb

Volume of mixture = 0.0012 m³

Thus,

0.0012 = Va + Vb

Substitute Vb in equation 2 into equation (1)

1 = 1000(Va) + 600[0.0012 – Va]

1 = 1000Va + 0.72 – 600Va

Collect like terms

1 – 0.72 = 1000Va – 600Va

0.28 = 400Va

Divide both side by 400

Va = 0.28 / 400

Volume of mixture = 0.0012 m³

Volume of liquid A (Va) = 0.0007 m³

Vb = 0.0012 – Va

Vb = 0.0012 – 0.0007

Volume of liquid B (Vb) = 0.0005 m³

Mass of liquid B = 600(Vb)

Mass of liquid B = 600(0.0005)

Mass of liquid B = 0.3 Kg

Multiply by 1000 to express in grams

Mass of liquid B = 0.3 × 1000

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Mass of liquid B = 271.2 gram

Explanation:

Given:

Density of liquid A = 1000 kg/m³

Density of liquid B = 600 kg/m³

Density of mixture = 850 kg/m³

Mass of mixture = 1 kg

Assume:

Volume of liquid A = Va

Volume of liquid B = Vb

So,

Volume of mixture = Va + Vb

Mass of liquid A = 1000(Va)

Mass of liquid B = 600(Vb)

Mass of mixture = Mass of liquid A + Mass of liquid B

1 = 1000(Va) + 600(Vb)

Volume of mixture = 1 / 850

So,

(1/850) = Va + Vb

Vb = (1/850) - Va

1 = 1000(Va) + 600[(1/850) - Va]

Va = 7.25 × 10⁻⁴

Vb = (1/850) - Va

Vb = (1/850) - [7.25 × 10⁻⁴]

Vb = 4.25 × 10⁻⁴

Mass of liquid B = 600(Vb)

Mass of liquid B = 600(4.25 × 10⁻⁴)

Mass of liquid B = 271.2 gram

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