Question

The volume of one mole of water at \(277 \mathrm{~K}\) is \(18 \mathrm{ml}\). One \(\mathrm{ml}\) of water contains 20 drops. The number of molecules in one drop of water will be \(\left(N_{\mathrm{A}}=6 \times 10^{23}\right)\) (a) \(1.07 \times 10^{21}\) (b) \(1.67 \times 10^{21}\) (c) \(2.67 \times 10^{21}\) (d) \(1.67 \times 10^{20}\)

Short answer

The number of molecules in one drop of water is \(1.67 \times 10^{21}\) molecules.

Step-by-step solution

Calculate the number of molecules in one mole of water

Use Avogadro's number to find the total number of molecules in one mole of water, which is defined as the number of molecules present in 18 ml of water. Avogadro's number (\(N_A\)) tells us that there are \(6 \times 10^{23}\) molecules in one mole of any substance.

Determine the number of molecules per milliliter

Divide the total number of molecules in one mole by the volume of one mole to find the number of molecules per milliliter of water. So, divide \(6 \times 10^{23}\) by 18.

Calculate the number of molecules in one drop of water

Since 1 ml of water contains 20 drops, you need to divide the number of molecules per milliliter by 20 to find the number of molecules per drop.

Key concepts

Avogadro's Number

In the realm of chemistry, Avogadro's number is a fundamental constant denoting the exact number of atoms, ions, or molecules present in one mole of any substance. The value of Avogadro's number is approximately \(6.022 \times 10^{23}\) entities per mole. This number isn't arbitrary; it is based on the number of carbon atoms in 12 grams of carbon-12 isotope.

This constant creates a bridge between the micro world (atoms, molecules, ions) and the macro world (grams, liters, moles) we can measure. It's akin to converting individual items to boxes when each box contains the same number of items. When applying Avogadro's number, we're often dealing with massive quantities of tiny entities, making it an indispensable tool for chemists.

Mole Concept

The mole concept is a cornerstone of chemistry, acting as a conduit for translating between the atomic scale and a scale that we can physically measure. One mole is defined as the amount of any substance that contains as many entities (atoms, molecules, particles, etc.) as there are atoms in exactly 12 grams of pure carbon-12.

The beauty of the mole concept lies in its universality; it can be applied to every substance. For instance, one mole of iron contains the same number of atoms as one mole of gold, even though their masses are different. This is because a mole refers to quantity – not mass. This concept underpins countless calculations in chemistry, from the composition of compounds to chemical reactions.

Volume-to-Molecules Conversion

Converting volume to molecules is a practical application of Avogadro's number and the mole concept. Particularly in solutions and liquids, chemists often need to know how many molecules are present in a certain volume. To perform this conversion, one needs to understand the molar volume of a substance, which is the volume occupied by one mole of it under specified conditions of temperature and pressure.

For water, the molar volume at standard temperature and pressure is about 18 milliliters. By dividing Avogadro's number by this volume, we find the number of molecules per milliliter. This operation is crucial in many laboratory settings and forms the basis of exercises that students are likely to encounter in their studies.

Physical Chemistry Problems

Physical chemistry blends physics and chemistry, focusing on how matter behaves on a molecular and atomic level and how chemical reactions occur. Solving physical chemistry problems often involves calculations like the one in our exercise. Students must comprehend concepts like the mole, Avogadro's number, and conversion between mass, volume, and the number of particles.

Through practice, chemists can relate observable changes in a system, such as temperature rise or pressure increase, to the particulate nature of matter. These problems not only reinforce a deeper understanding of matter's microscopic properties but also demonstrate the principles that manifest in real-world phenomena and experimental data.