Question

By how much (in picograms) does the mass of 1 mol of ice at \(0^{\circ} \mathrm{C}\) differ from that of \(1 \mathrm{~mol}\) of water at \(0^{\circ} \mathrm{C} ?\)

Short answer

The mass of 1 mol of ice at 0 degrees Celsius and that of 1 mol of water at 0 degrees Celsius is virtually identical, so the difference would be zero picograms.

Step-by-step solution

Understanding the question

The question is mainly about the molar mass of a substance, which is the mass in grams of 1 mole (6.022 x 10^23 molecules or atoms) of that substance. Here we are asked to find the difference in mass of 1 mole of ice and 1 mol of water at 0 degrees Celsius. Since both ice and water have the same molecular formula, H2O, the molar mass for both will be the same, which is roughly 18 grams per mol.

Calculate the molar mass of water

Firstly, to obtain the molar mass of water, add the atomic masses of the elements in water. Each water molecule, H2O, contains two hydrogen atoms and one oxygen atom. The atomic mass of hydrogen is approximately 1 g/mol, and that of oxygen is approximately 16 g/mol. Therefore, the molar mass of water is: (2 x atomic mass of hydrogen) + atomic mass of oxygen = (2 x 1 g/mol) + 16 g/mol = 18 g/mol.

Finding the difference

In this final step, you will see the mass difference between 1 mol of ice and 1 mol of water at 0 degrees Celsius. Since both ice and water are H2O, the molar mass for both will be the same at roughly 18 g/mol. Consequently, the difference in mass between one mole of ice and one mole of water at 0 degrees Celsius is zero.

Key concepts

Molar Mass Calculation

Understanding how to calculate the molar mass of a compound is a foundational skill in chemistry. Molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol). A mole is a standard unit of measurement in chemistry that represents a very large number of particles, specifically Avogadro's number which is approximately 6.022 x 10^23 particles.

To calculate the molar mass of water (H₂O), you need to sum the atomic masses of its constituting atoms from the periodic table. Each hydrogen (H) atom has an approximate atomic mass of 1 gram per mole, and oxygen (O) has an approximate atomic mass of 16 grams per mole. With two hydrogens and one oxygen in each water molecule, the calculation becomes:
\[ (2 \times 1 \text{ g/mol}) + (16 \text{ g/mol}) = 18 \text{ g/mol} \]
By using this method, you can determine the molar mass of any chemical compound by adding up the atomic masses of the elements present in the formula.

Mass Conversion

Mass conversion is crucial when working with chemical quantities since chemists often need to convert between units of mass to describe amounts on both the macroscopic and atomic scales. In the case of the exercise, we were looking at a mass in picograms (pg), a much smaller unit than grams.

To illustrate, if we had a difference in mass for a chemical substance, converting from grams to picograms involves multiplying by 10^12, since one gram equals one trillion picograms. In pure numerical terms, the conversion looks like this:
\[ 1 \text{ g} \times 10^{12} = 1 \text{ pg} \]
Conversely, to convert from picograms to grams, you divide by 10^12. Being proficient in unit conversions is a vital skill for accurately measuring and describing chemical quantities in different units.

Thermodynamic Properties of Water

The thermodynamic properties of water are fascinating due to water's unique behavior under different temperatures and pressures. For instance, water has a high heat capacity, meaning it can absorb a lot of heat before its temperature rises. This characteristic is essential for the regulation of the Earth's climate and for sustaining life.

At 0 degrees Celsius, water can exist as both ice (solid) and liquid water, a phenomenon that occurs due to the thermodynamic principle known as the phase equilibrium. When considering thermodynamic properties, it's also essential to look at the physical state of water; ice has a more extensive and fixed structure, leading to a lower density compared to liquid water, which allows ice to float on liquid water.

Despite their physical differences, ice and liquid water at 0 degrees Celsius have the same molecular structure (H₂O), leading to identical molar masses, as seen in the original exercise. This outcome illustrates how, despite a change in physical state, the chemical composition and molar mass remain constant.