Question

How many water molecules are there in one drop of water (volume \(0.0018 \mathrm{ml}\) ) at room temperature? a. \(4.86 \times 10^{17}\) b. \(6.023 \times 10^{24}\) c. \(2.584 \times 10^{19}\) d. \(6.023 \times 10^{19}\)

Short answer

The correct answer is d. \(6.023 \times 10^{19}\).

Step-by-step solution

Convert Volume to Liters

First, we need to convert the volume of the drop of water from milliliters (ml) to liters (L) because the density of water is typically given in grams per liter. Since 1 ml equals 0.001 L, the volume of 0.0018 ml is equivalent to 0.0018 ml * 0.001 L/ml = 0.0000018 L.

Calculate the Mass of Water

Next, use the density of water, which is approximately 1 g/L, to convert the volume to mass. Since the volume of the drop of water is 0.0000018 L, the mass of the water is 0.0000018 L * 1 g/L = 0.0000018 g.

Convert Mass to Moles

We use the molar mass of water to convert the mass to moles. The molar mass of water (H2O) is 18 g/mol. Hence, the number of moles of water is 0.0000018 g / 18 g/mol = 0.0000001 mol.

Calculate the Number of Molecules

To find the number of molecules, multiply the number of moles by Avogadro's number ( 6.022 × 10^{23}). So, 0.0000001 mol * 6.022 × 10^{23} molecules/mol = 6.022 × 10^{19} molecules.

Key concepts

Volume Conversion

When working with volumes in chemistry, especially when dealing with very small quantities, like a drop of water, it's important to convert measurements into appropriate units. This often requires converting from milliliters (ml) to liters (L). This conversion simplifies calculations, especially when dealing with water density. To convert from ml to L, remember that 1 ml is equivalent to 0.001 L. This means you multiply the milliliter value by 0.001 to get the volume in liters.

For example, a drop of water with a volume of 0.0018 ml is converted by calculating:

• 0.0018 ml × 0.001 L/ml = 0.0000018 L

This conversion helps keep calculations neat and prevents errors when you move on to related steps like mass and mole calculations.

Mass Calculation

In chemistry, mass plays a crucial role when working with substances like water. To calculate mass, you typically use the density of the substance. In the case of water, the density is conveniently 1 gram per milliliter (1 g/ml). This means that 1 ml of water weighs 1 gram.

Once you've converted your volume to liters, as in our example with 0.0000018 L for a drop of water, you can find its mass by multiplying the volume by the density. Using water's density in grams per liter:

• Mass of water = Volume (L) × Density (g/L)
• Mass = 0.0000018 L × 1 g/L = 0.0000018 g

Understanding this calculation helps bridge the data from volumetric measurements to the concept of moles, as you determine how much matter is present.

Mole Concept

The mole is a fundamental concept in chemistry that connects the macroscopic world we observe with the microscopic world of atoms and molecules. One mole of any substance contains the same number of entities, such as atoms or molecules, which is Avogadro's number. This is crucial for quantifying substances and their reactions.

In our water example, we need to convert mass into moles using the molar mass. The molar mass of water, or H₂O, is approximately 18 g/mol. This means 18 grams of water is equal to 1 mole of water molecules. For our drop of water:

• Number of moles = Mass (g) / Molar Mass (g/mol)
• Number of moles = 0.0000018 g / 18 g/mol = 0.0000001 mol

This step is key to transitioning from a quantity of mass to the number of molecules, thanks to Avogadro's number.

Avogadro's Number

Avogadro's number is a defining constant in chemistry, representing the number of atoms or molecules in one mole of a substance. It is approximately 6.022 × 10²³ entities per mole. This large number bridges the gap between the atomic scale and the human scale, making it possible to calculate specific quantities in chemical reactions.

When you have the number of moles, multiplying by Avogadro's number gives the number of molecules. For our tiny droplet of water, which contains 0.0000001 mol:

• Number of molecules = Number of moles × Avogadro's number
• Number of molecules = 0.0000001 mol × 6.022 × 10²³ molecules/mol = 6.022 × 10¹⁹ molecules

This calculation highlights Avogadro's number's incredible utility, allowing us to transition from macroscopic masses and volumes to the actual count of molecules in any sample.