Liquid water has a density of 1.00 g / mL at 10.0^∘ C and 0.996 g / mL at 30.0^∘ C. Calculate

step 1 Hello, in this question we are given the density of water at this temperature. We are told that

Liquid water has a density of 1.00 g / mL at 10.0^∘ C and...

Liquid water has a density of $1.00 \mathrm{~g} / \mathrm{mL}$ at $10.0^{\circ} \mathrm{C}$ and $0.996 \mathrm{~g} / \mathrm{mL}$ at $30.0^{\circ} \mathrm{C}$. Calculate the change in volume that occurs when $500 . \mathrm{mL}$ of water is heated from $10.0^{\circ} \mathrm{C}$ to $30.0^{\circ} \mathrm{C}$.

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Key Concepts

Thermal Expansion

Thermal expansion refers to the tendency of a substance to change its dimensions, and consequently its volume, in response to a change in temperature. Generally, when a liquid is heated, it expands, leading to a decrease in density because the same mass occupies a larger volume.

Conservation of Mass

The principle of conservation of mass states that mass remains constant in an isolated system, regardless of any physical changes such as variations in temperature or volume. This principle is crucial when evaluating situations like the heating of water, where the mass stays the same while the density and volume change.

Density

Density is a measure of how much mass is contained within a given volume. It is typically expressed in units such as g/mL or kg/m³ and is used to characterize how compact the molecules in a substance are. Changes in temperature can alter a substance's density, as seen in the example where water's density decreases with a rise in temperature.

Mass-Volume Relationship

The mass-volume relationship is defined by the equation mass = density × volume. This relationship allows one to calculate either the mass or the volume of a substance if the other and the density are known. When a substance's density changes due to temperature variations, the volume must adjust accordingly if the mass remains constant.

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