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The Amazing World of Solutes, Solvents, and Solutions - What Is Density?

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Density is a physical property of matter that describes the amount of mass contained in a given volume. It is represented by the formula ρ=mV\rho = \frac{m}{V}.

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In the context of solutions, a Solute is the substance that is dissolved, and a Solvent is the substance that does the dissolving. The combination of both forms a Solution.

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When a solute like salt is added to a solvent like water, the mass of the solution increases while the volume remains relatively similar. This results in an increase in the Density of the solution.

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The S.I. unit of density is kg/m3kg/m^3, but it is also commonly expressed in g/cm3g/cm^3 or g/mLg/mL.

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Whether an object floats or sinks in a liquid depends on its density relative to the liquid. If the object's density is less than the liquid's density (Dobject<DliquidD_{object} < D_{liquid}), it floats; otherwise, it sinks.

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Relative Density is the ratio of the density of a substance to the density of water at 4∘C4^\circ C. It has no units because it is a ratio of identical quantities.

📐Formulae

Density(ρ)=Mass(m)Volume(V)Density (\rho) = \frac{Mass (m)}{Volume (V)}

Mass of Solution=Mass of Solute+Mass of Solvent\text{Mass of Solution} = \text{Mass of Solute} + \text{Mass of Solvent}

Relative Density=Density of SubstanceDensity of Water\text{Relative Density} = \frac{\text{Density of Substance}}{\text{Density of Water}}

1 g/cm3=1000 kg/m31 \text{ g/cm}^3 = 1000 \text{ kg/m}^3

💡Examples

Problem 1:

A glass contains 250 cm3250 \text{ cm}^3 of a sugar solution with a total mass of 300 g300 \text{ g}. Calculate the density of the solution.

Solution:

Density=MassVolumeDensity = \frac{\text{Mass}}{\text{Volume}} Density=300 g250 cm3=1.2 g/cm3Density = \frac{300 \text{ g}}{250 \text{ cm}^3} = 1.2 \text{ g/cm}^3

Explanation:

The density is found by dividing the total mass of the solution by its total volume. The result 1.2 g/cm31.2 \text{ g/cm}^3 indicates the solution is denser than pure water (1 g/cm31 \text{ g/cm}^3).

Problem 2:

You have a solution with a total mass of 550 g550 \text{ g}. If the mass of the solvent used was 475 g475 \text{ g}, calculate the mass of the solute added using vertical subtraction.

Solution:

550−47575\begin{array}{r} 550 \\ - 475 \\ \hline 75 \end{array}

Explanation:

To find the mass of the solute, we subtract the mass of the solvent from the total mass of the solution. The mass of the solute is 75 g75 \text{ g}.

Problem 3:

An iron nail has a mass of 15.6 g15.6 \text{ g} and a volume of 2 cm32 \text{ cm}^3. Find its density and determine if it will sink in water (Density of water =1 g/cm3= 1 \text{ g/cm}^3).

Solution:

Density=15.6 g2 cm3=7.8 g/cm3\text{Density} = \frac{15.6 \text{ g}}{2 \text{ cm}^3} = 7.8 \text{ g/cm}^3

Explanation:

Since 7.8 g/cm37.8 \text{ g/cm}^3 is much greater than 1 g/cm31 \text{ g/cm}^3, the iron nail will sink in water.