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In the given exercise, our goal is to compute the volume of both liquid water and steam. When determining volume, it's crucial to understand the relationship between density, mass, and volume. This is expressed in the formula:

• \( \text{density} = \frac{\text{mass}}{\text{volume}} \)
• Therefore, \( \text{volume} = \frac{\text{mass}}{\text{density}} \)

For the liquid water, knowing the mass in kilograms and the given density, you can plug these values into the formula to find the volume. Moreover, when dealing with gases (like steam), the Ideal Gas Law helps us calculate volume based on pressure, temperature, and amount of substance in moles. This law is given by:

• \( PV = nRT \)
• Solving for \( V \) gives \( V = \frac{nRT}{P} \)

When you apply these formulas correctly, you can compare how vastly different the volumes of liquids and gases are under similar conditions.

Density is a measure of how much mass fits into a given volume. For water at \(20^{\circ} \mathrm{C}\), this is \(998 \mathrm{~kg}/ \mathrm{m}^{3} \). Density plays a critical role in scuba diving, cooking, and various scientific calculations, like our exercise here.
To understand density, think about how tightly packed the molecules are within the substance. When calculating volume, you need the mass, which you often get from the molecular makeup of the compound. For water, knowing that the density is \(998 \mathrm{~kg}/ \mathrm{m}^{3} \) allows you to calculate the volume for any given mass by rearranging the formula, \( \text{density} = \frac{\text{mass}}{\text{volume}} \), to find volume.
This basic understanding of density is also applicable to other substances, each having its own unique density value which can change with temperature or pressure. This concept is fundamental for fields ranging from hydrology to material science.

The molar mass of a compound is the mass of one mole of its molecules. For water \( \text{H}_2\text{O} \), the molar mass is \(18.02 \text{g/mol}\). This value comes from the sum of the atomic masses of hydrogen and oxygen:

• Each hydrogen atom has a mass of about \(1.01 \text{g/mol}\), and there are two hydrogen atoms: \(2 \times 1.01 = 2.02 \text{g/mol} \).
• One oxygen atom has a mass of about \(16 \text{g/mol}\).
• Adding them together gives \(18.02 \text{g/mol}\).

In calculations, this molar mass helps convert between the number of moles and the mass in grams. For example, to find the mass of one mole of water, you multiply the molar mass \(18.02 \text{g/mol}\) by the number of moles. This is fundamental for stoichiometry in chemistry, helping you predict how substances will react and in what amounts.

Temperature conversion is essential in chemistry, particularly when applying the Ideal Gas Law, where temperatures must be in Kelvin. Kelvin is the standard unit of temperature in scientific calculations.
To convert from Celsius to Kelvin, you simply add \(273.15\). For instance, \(20^{\circ} \mathrm{C}\) becomes:

• \(20^{\circ} \text{C} + 273.15 = 293.15 \text{K} \)

And \(200^{\circ} \text{C}\) becomes:

• \(200^{\circ} \text{C} + 273.15 = 473.15 \text{K} \)

This conversion is necessary because the Ideal Gas Law, \( PV = nRT \), uses Kelvin to ensure that the temperature scale starts at absolute zero, making the mathematical relationships valid. Understanding this concept is important for consistency and accuracy in scientific experiments and calculations.