Question

The volume of a drop of water is \(0.0018 \mathrm{ml}\) then the number of water molecules present in two drop of water at room temperature is: (a) \(12.046 \times 10^{19}\) (b) \(1.084 \times 10^{18}\) (c) \(4.84 \times 10^{17}\) (d) \(6.023 \times 10^{23}\) jv

Short answer

The number of water molecules present in two drops of water at room temperature is approximately \(12.046 \times 10^{19}\).

Step-by-step solution

Determine the volume of water in two drops

First, calculate the total volume of two water drops by multiplying the volume of a single drop by 2. The volume of a single drop is 0.0018 ml, so for two drops it will be: \( 2 \times 0.0018 \, \mathrm{ml} \).

Convert volume from milliliters to liters

Since the volume is given in milliliters, convert it to liters because the molar volume at room temperature (which is approximately 22.4 liters) is used in liters. There are 1000 milliliters in 1 liter, so the conversion is: \( \frac{2 \times 0.0018 \, \mathrm{ml}}{1000} \, \mathrm{L} \).

Calculate number of moles of water

Using the molar volume at room temperature, which is 22.4 L for 1 mole of any gas, find out the number of moles of water in the converted volume. Note that water in liquid form is H2O with a molar mass of about 18 g/mol. Use the relationship \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \) to calculate the moles. First, find the mass of the water in two drops by using the density of water (1 g/ml), then calculate the number of moles.

Calculate the mass of the water in two drops

Using the density of water, which is approximately 1 g/ml, calculate the mass. The mass (in grams) will be equal to the volume (in milliliters) for water because of its density: \( \text{mass} = 2 \times 0.0018 \, \mathrm{grams} \).

Calculate the number of moles of water in the mass obtained

Now, find the number of moles using the mass calculated in the previous step and the molar mass of water: \( \text{moles of water} = \frac{\text{mass in grams}}{\text{molar mass of water}} \).

Calculate the number of water molecules in two drops

Since one mole of any substance contains Avogadro's number (\(6.023 \times 10^{23}\) entities) of molecules, multiply the number of moles of water by Avogadro's number to get the total number of water molecules.

Key concepts

Stoichiometry

Stoichiometry is the study of the quantitative relationships or ratios between reactants and products in chemical reactions. It is based on the laws of conservation of mass and fixed proportions, implying that matter is neither created nor destroyed in chemical reactions and that elements combine in fixed ratios to form compounds.

When solving stoichiometric problems, a balanced chemical equation is essential as it provides the ratio of moles of each reactant and product involved in the reaction. This allows chemists to predict the amounts of substances consumed and produced in a reaction, given the quantity of one of the substances. Take our water drop problem, for example. No chemical reaction is involved, but the concept of relating volume to moles and molecules still touches on the principles of stoichiometry—how many moles are contained within a given volume and, subsequently, how many molecules.

Avogadro's Number

Avogadro's number, approximately 6.022 × 10²³, represents the number of atoms, molecules, or ions in one mole of any substance. It's a fundamental constant in chemistry named after the Italian scientist Amedeo Avogadro. This number is used to convert between the microscopic scale of atoms and molecules and the macroscopic scale that we can measure in the laboratory.

For instance, when solving for the number of water molecules in two drops, we first determine the number of moles present in that volume of water and then use Avogadro's number to convert this amount to actual molecules. It bridges the gap between the tangible measurements we make and the untouchably tiny realms of atoms and molecules.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It corresponds to the sum of the atomic masses of the atoms in the molecule and provides an essential conversion factor in stoichiometry problems. In our scenario with water, the molar mass of H₂O is approximately 18 g/mol, because it contains two hydrogen atoms (1 g/mol each) and one oxygen atom (16 g/mol).

To calculate the molar mass, you simply list each element from the molecular formula of a substance, find each element's atomic mass on the periodic table, and multiply the atomic mass by the number of atoms of that element in the molecule, summing up the total weight. This helps us to convert grams to moles, an integral step in stoichiometric calculations.

Molar Volume

Molar volume is the volume that one mole of a substance occupies at a given temperature and pressure. For gases at standard temperature and pressure (STP, which is 0°C and 1 atm), the molar volume is 22.4 liters per mole. Molar volume allows you to relate a gas's volume to its amount in moles.

In the textbook exercise, molar volume is applied to find the number of moles from the volume of two water drops. Although water at room temperature is liquid and not a gas, if the question refers to a gas at room temperature the molar volume concept would still be useful. For liquids and solids, molar volume varies with the conditions and is not as straightforward as the ideal gas molar volume, but understanding the concept allows students to approach problems involving gas mixtures and reactions.