A 47.0-cm^3 sample of ocean water has a density of 1025 kg / m^3. Assuming all of the solids st

step 1 Let's calculate the density of the water sample after 4 .1 milliliters has evaporated. We'll fir

A 47.0-cm^3 sample of ocean water has a density of 1025 kg...

A $47.0-\mathrm{cm}^{3}$ sample of ocean water has a density of $1025 \mathrm{~kg} / \mathrm{m}^{3}$. Assuming all of the solids stay in solution, what will be the density of this water sample in units of $\mathrm{g} / \mathrm{cm}^{3}$ after $4.1 \mathrm{~mL}$ of water has evaporated?

Key Concepts

Conservation of Mass

The conservation of mass principle states that mass cannot be created or destroyed in a closed system. When water evaporates from a solution, the mass of the solute remains constant, even though the overall mass of the solution decreases. This principle is key to calculating the new density after evaporation since the mass of dissolved solids remains unchanged.

Density

Density is a measure of how much mass is contained in a given volume. It is defined as mass per unit volume and plays a crucial role in understanding the physical properties of materials, especially fluids. In problems like this, density helps determine how the mass of a solution is distributed in a given volume and how it changes if the volume is altered, such as by evaporation.

Unit Conversion

Unit conversion involves translating quantities from one set of units to another to maintain consistency, particularly when performing calculations. Here, converting between kg/m³ and g/cm³ is essential because the problem presents the density in one system (SI units) and asks for the answer in another system (cgs units).

Evaporation and Concentration Change

Evaporation is the process by which a liquid changes into vapor, thereby reducing the volume of the liquid. When water evaporates from a solution, the concentration of any dissolved solids increases because their mass stays constant while the volume decreases. In the context of density calculations, understanding this effect is critical, as the new density is based on the reduced volume and the unaltered mass of the solutes.

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