Question

The total no. of neutrons present in \(54 \mathrm{~mL} \mathrm{H}_{2} \mathrm{O}(l)\) are: (a) \(3 N_{A}\) (b) \(30 \mathrm{~N}_{\mathrm{A}}\) (c) \(24 \mathrm{~N}_{\mathrm{A}}\) (d) none of these

Short answer

The total number of neutrons in 54 mL of water is (b) 30NA.

Step-by-step solution

Find the number of moles of water

Use the density of water (1 g/mL at room temperature) to find the mass of 54 mL of water. Since the density of water is 1 g/mL, 54 mL of water has a mass of 54 grams. Use the molar mass of water (approximately 18.015 g/mol) to calculate the number of moles: Number of moles (n) = mass (m) / molar mass (M).

Calculate the number of water molecules

Multiply the number of moles of water by Avogadro's number (\(N_{A}\)) to find the number of water molecules. Avogadro's number (\(N_{A}\)) is approximately \(6.022 \times 10^{23}\) molecules/mol.

Determine the total number of neutrons in water molecules

Each water molecule (\(H_{2}O\)) has 10 neutrons (8 from the oxygen atom and 1 from each of the two hydrogen atoms). Multiply the total number of water molecules by 10 to find the total number of neutrons.

Match the result with the given options

Compare the calculated total number of neutrons with the given options to find the correct answer.

Key concepts

Molar Mass of Water

Understanding the molar mass of water is a fundamental concept in chemistry that serves as a stepping stone to more complex calculations in stoichiometry. The molar mass is essentially the weight of one mole of a substance and is measured in grams per mole (g/mol). Water, with its chemical formula being \( H_2O \), consists of two hydrogen atoms and one oxygen atom. Since the atomic mass of hydrogen is roughly 1.008 g/mol and that of oxygen is about 16.00 g/mol, the molar mass of a water molecule can be estimated by adding the masses of its constituent atoms: \( 2(1.008 \text{ g/mol}) + 16.00 \text{ g/mol} = 18.016 \text{ g/mol} \). This value is crucial when converting between the mass of water and the number of moles, thus enabling the calculation of the number of water molecules in a given sample.

Avogadro's Number

Avogadro's number, denoted as \(N_A\), is another cornerstone of chemistry embodying the microscopic scale of atoms and molecules. This voluminous constant, \(6.022 \times 10^{23}\), represents the number of units, usually atoms or molecules, in one mole of any substance. This number is derived from the number of atoms found in 12 grams of pure carbon-12. Avogadro's number transforms a countable quantity of atoms or molecules into a measurable mass on a human scale and inversely so. Thus, whenever a problem in chemistry involves counting individual atoms or molecules, such as in the determination of the number of neutrons in water molecules, Avogadro's number becomes indispensable.

Stoichiometry in Chemistry

Stoichiometry is the calculation of reactants and products in chemical reactions. It is a quantitative relationship that allows chemists to predict the outcomes of chemical reactions, making it a powerful tool in both lab and industrial settings. In stoichiometric calculations, the molar mass of substances and Avogadro's number often come into play, providing the basis for converting grams to moles, moles to molecules, or atoms and vice versa. Stoichiometry hinges on the law of conservation of mass, ensuring that atoms are not lost or gained in chemical reactions but simply rearranged. It is critical to understand this principle when solving chemistry problems, like calculating the total number of neutrons in a certain volume of water, as it grounds the logic for the proportional relationships between elements and compounds.

Moles to Molecules Conversion

Linking moles to molecules is an essential skill in chemistry, allowing scientists to jump from the macroscopic world we can measure to the microscopic world we cannot see. This conversion makes use of Avogadro's number to translate moles, a unit of measurement representative of a chemical substance's amount, into actual numbers of molecules. The formula to convert moles to molecules is relatively straightforward: number of molecules = number of moles \(\times\) Avogadro's number (\(N_A\)). For example, when calculating how many neutrons there are in a certain quantity of water, we first determine the number of moles of water from its mass and molar mass and then convert these moles into molecules by multiplying by Avogadro's number. Each molecule of water contributes a set number of neutrons, and by accounting for every molecule, we can arrive at a total neutron count.