Question

How many molecules are in one drop of water if \(1.00 \mathrm{~g}\) of water contains \(3.34 \times 10^{22}\) molecules? (Given: \(1 \mathrm{~mL}=20\) drops)

Short answer

There are approximately \(1.67 \times 10^{21}\) molecules in one drop of water.

Step-by-step solution

Calculate the mass of a single drop

Since the problem states that 1 mL of water consists of 20 drops, and since the density of water is approximately 1 g/mL, 1 drop of water is 1/20th of a mL. Thus, the mass of a single drop of water is calculated as follows:\[ \text{Mass of one drop} = \frac{1.00\, \text{g}}{20} = 0.05\, \text{g} \]

Calculate the number of molecules in one drop

Given that 1.00 g of water contains \(3.34 \times 10^{22}\) molecules, we can calculate the number of molecules in one drop, which has a mass of 0.05 g. Using a direct proportion, the number of molecules in a drop is:\[ \text{Number of molecules in one drop} = \left(3.34 \times 10^{22} \right) \times \left(\frac{0.05}{1.00}\right) \]Solving this gives:\[ \text{Number of molecules in one drop} = 1.67 \times 10^{21} \]

Key concepts

Understanding the Mass of a Drop

When we talk about the mass of a drop, we're focusing on how much one tiny droplet of a substance weighs. In our exercise, we're looking at a drop of water. Since the exercise gives that 1 mL of water consists of 20 drops and water has a density close to 1 gram per milliliter, each drop represents 1/20th of that volume. This means, each drop of water weighs approximately 0.05 grams.

To gain a deeper understanding, remember that volume and mass are highly related in liquids, especially those with consistent density. Since water is a cornerstone example in many scientific calculations, knowing that 1 g corresponds to 1 mL helps to easily determine the mass of minute water volumes like individual drops.

The Density of Water

Density is a critical concept in understanding how much mass is contained in a given volume of a substance. For water, it is conveniently close to 1 gram per milliliter. This property makes calculations involving water simpler, especially when converting between volume and mass.

Knowing that water's density is roughly 1 g/mL allows us to confidently convert volume measurements into mass with ease. This characteristic plays a significant role in many practical scenarios, like when considering measurements for cooking or chemistry experiments. It simplifies direct conversions and provides a reliable framework for understanding how different amounts of water translate volumetrically and by weight.

Proportional Calculation Basics

Proportional calculations come in handy when comparing quantities that are directly related to each other. In the water drop exercise, we use proportions to calculate how many molecules are in a tiny amount of water based on known data.

Understanding proportions is about understanding equality between ratios. If we know a specific amount of water holds a certain number of molecules, then any smaller amount holds proportionally fewer molecules. In the example, the calculation \[ \text{Number of molecules in one drop} = \left(3.34 \times 10^{22} \right) \times \left(\frac{0.05}{1.00}\right) \] shows that we multiply the total number of molecules in 1 gram by the fraction of a gram that is in a single drop.

Molecular Quantity in Chemistry

The molecular quantity in chemistry helps us understand the absolute number of molecules in a given mass, which is crucial for grasping chemical reactions. The exercise states that 1 gram of water has approximately \(3.34 \times 10^{22}\) molecules. Remember, this number comes from Avogadro's number and the properties of water molecules.

In chemistry, knowing how many molecules are present enables precise control over reactions and compositions. It underscores the vast number of molecules even in small quantities and shows how molecular level observations are drawn from massive collections of molecules. By understanding molecular quantities, chemists can predict reactions' behaviors, structure larger compounds, and formulate solutions with exact concentrations.