The following is a crude but effective method for estimating...

The following is a crude but effective method for estimating the order of magnitude of Avogadro's number using stearic acid $\left(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\right)$ shown here. When stearic acid is added to water, its molecules collect at the surface and form a monolayer; that is, the layer is only one molecule thick. The crosssectional area of each stearic acid molecule has been measured to be $0.21 \mathrm{nm}^{2}$. In one experiment it is found that $1.4 \times 10^{-4} \mathrm{~g}$ of stearic acid is needed to form a monolayer over water in a dish of diameter $20 \mathrm{~cm} .$ Based on these measurements, what is A vogadro's number?

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental constant denoting the number of constituent particles (usually atoms or molecules) in one mole of a substance. It serves as the bridge between the microscopic world of individual molecules and the macroscopic amounts encountered in laboratory measurements, allowing chemists to correlate mass with count of particles.

Monolayer Coverage

Monolayer coverage refers to a single, one-molecule-thick layer formed over a surface. This concept is used to estimate the number of molecules present based on their known cross-sectional area, making it a valuable tool for approximating quantities like Avogadro's number in experimental setups.

Molecular Cross-Sectional Area

The molecular cross-sectional area is the effective area that a molecule occupies when arranged in a layer. By knowing this area, one can calculate the total number of molecules needed to cover a given surface area by dividing the total area by the area occupied by each molecule.

Mole Concept

The mole concept is a central idea in chemistry that relates the measurable mass of a material to a specific number of particles. It provides a way to convert between masses of substances and the number of atoms or molecules present, utilizing Avogadro's number as the conversion factor.

Order-of-Magnitude Estimation

Order-of-magnitude estimation is a technique used to approximate values by focusing on the scale or power of ten rather than precise figures. This approach is especially useful in physics and chemistry when dealing with complex systems, offering a rough estimate that captures the essential size of a quantity such as Avogadro's number.

Unit Conversion and Dimensional Analysis

Unit conversion and dimensional analysis involve converting measurements from one set of units to another to ensure consistency in calculations. This process is critical in experimental estimations like determining Avogadro’s number as it requires accurate conversion of mass, area, and other units into a coherent framework for calculation.

Transcript

00:04 Step 1, avogados number is the number of molecules present in one mole.

00:12 So to determine the avogados number in this assignment, we should calculate the number of molecules and the number of moles of scleric acid.

01:01 And step to the surface of a dish is equal to pi x r square and r is equal to radius is equal to r divided by two is equal to 20 cm divided by 2 is equal to radius is 10 cm the surface of a dish is equal to pi this is equal to 3 .14x into 10 centimeter square the surface of a dish is equal to 3 .14x hundred centimeter cube square.

02:58 The surface of a dish is equal to 314 square square centimeter is equal to 314 square square centimeter is equal to 3, 1, 4, multiply 10, raise to the power 14 square nanometer.

03:36 Sorry, here is nometer square.

03:45 So one molecule of cedaric acid has a cross -sectional area of cross -sectional area.

04:09 Area of 0 .21 nanometer square, nanometer square, which means that it will cover 0 .21 nanometer square of this surface.

04:50 To find out the number of molecules needed to cover the whole surface, we must divide it by 0 .21 and we have n is equal to 314 x 10 raise to the power 14 nanometer square divided by 0 .211 nanometer square n is equal to 1 .5 x 10.

05:53 To the power 17.

06:03 In step 3, molar mass is equal to mass divided by moles and moles is equal to mass divided by molar mass.

06:46 Molar mass of carbon is equal to 12 .0 .1 gram per mole and molar mass of hydrogen is equal to 1 gram per mole...

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