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liquid A has a density of 0.7g/cm^3

liquid B has a density of 1.6g/cm^3


140g of liquid A is and 128g of liquid B are mixed to make liquid C


work out the density of liquid C

Verified Answer :

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\(\rho = \frac{m}{V} \Rightarrow V=\frac{m}{\rho}\)
ρ - density, m - mass, V - volume

Liquid A:
\(\rho=0.7 \ \frac{g}{cm^3} \\ m=140 \ g \\ \\ V=\frac{140 \ g}{0.7 \ \frac{g}{cm^3}}=200 \ cm^3\)

Liquid B:
\(\rho=1.6 \ \frac{g}{cm^3} \\ m=128 \ g \\ \\ V=\frac{128 \ g}{1.6 \ \frac{g}{cm^3}}=80 \ cm^3\)

Liquid C:
\(m=140 \ g + 128 \ g=268 \ g \\ V=200 \ cm^3 + 80 \ cm^3=280 \ cm^3 \\ \\ \rho=\frac{268 \ g}{280 \ cm^3} \approx 0.96 \ \frac{g}{cm^3}\)

The density of liquid C is approximately 0.96 g/cm³.

density is defined as mass per unit volume

in this case liquids A and B with 2 different densities are mixed and we are asked to find the density of the liquid C


liquid A has a density of 0.7 g/cm³

mass of liquid A added is 140 g

therefore volume of liquid A added is - 140 g / 0.7 g/cm³ = 200 cm³


liquid B has a density of 1.6 g/cm³

mass of liquid B added is 128 g

volume of liquid B added is - 128 g / 1.6 g/cm³ = 80 cm³


the total mass of liquid C after adding liquid A and B = 140 g + 128 g = 268 g

total volume in liquid C - 200 cm³ + 80 cm³ = 280 cm³

density of liquid C = mass / volume

= 268 g / 280 cm³ = 0.957 g/cm³

density of liquid C - 0.957 g/cm³

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