91Ó°ÊÓ

To find the volume of a cylinder, we rely on a simple mathematical formula:

• Volume (\( V \)) of a cylinder = \( \pi r^2 h \).

Here, \( \pi \) is a mathematical constant approximately equal to 3.14159, \( r \) represents the radius of the cylindrical base, and \( h \) is the height of the cylinder.

In the case of a cylindrical glass of water, given the radius (\( r \)) is 4.50 cm, and the height (\( h \)) is 12.0 cm, we substitute these values into the formula.
Doing this calculation, \( V \) becomes:\[ V = \pi \times (4.50)^2 \times 12.0 \]After calculation, \( V \approx 763.82 \, \text{cm}^3 \).

This formula finds the space inside a cylinder, aiding in various science and engineering applications, ensuring that computations involving cylindrical containers are accurate and efficient.

Density is a physical property representing how much mass is contained in a specific volume of a substance. For water, this is typically 1.00 \( \text{g/cm}^3 \) at standard conditions. Understanding density helps us to determine mass if volume is known.

• Formula for mass: Mass = Volume \( \times \) Density.

In our scenario, to calculate the mass of water inside the cylindrical glass, we multiply the calculated volume of the cylinder (763.82 \( \text{cm}^3 \)) by the density of water (1.00 \( \text{g/cm}^3 \)).

This calculation becomes simple:\[ \text{Mass} = 763.82 \, \text{cm}^3 \times 1.00 \, \text{g/cm}^3 \]and thus, \( \text{Mass} = 763.82 \, \text{g} \). The density of water is a fundamental constant in science and engineering, ensuring accurate calculations in a wide range of applications.

The molar mass of a substance is the mass of one mole of its molecules or atoms. For water (\( \text{H}_{2} \text{O} \)), the molar mass is approximately 18.02 \( \text{g/mol} \). This can be calculated by summing the atomic masses of the constituent atoms (2 hydrogen and 1 oxygen).

Converting from grams to moles involves dividing the mass of the sample by its molar mass:

• Formula: Moles = \( \frac{\text{Mass}}{\text{Molar Mass}} \).

In this context, we have the mass of water as 763.82 g, hence, \( \text{Moles} \) becomes:\[ \text{Moles} = \frac{763.82 \, \text{g}}{18.02 \, \text{g/mol}} \]Through calculation, \( \text{Moles} \approx 42.41 \).

This concept is core in chemistry, enabling the translation between mass and the number of molecules or atoms in a sample, which is essential for qualitative analysis and stoichiometric calculations.