a. It is estimated there are \(7 \times 10^{22}\) stars in the universe. How many moles of stars is this? b. It is estimated there are \(7.5 \times 10^{18}\) grains of sand on the earth. How many moles of sand grains is this? c. You have \(0.0555\) moles of jelly donuts. What number of donuts would that be? d. You drink a small bottle of drinking water that contains 13 moles of water. What is the number of molecules of water you drank?

Short Answer

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a) Approximately 0.116 moles of stars. b) Approximately 1.25 x 10\(^{-5}\) moles of sand grains. c) Approximately 33.4 jelly donuts. d) Approximately 7.829 x 10\(^{25}\) molecules of water.

Step by step solution

01

- Determining the Number of Moles of Stars

To find the number of moles of stars, divide the number of stars, which is given as \(7 \times 10^{22}\), by Avogadro's number, \(6.022 \times 10^{23}\) mol\(^{-1}\). The calculation is \(\frac{7 \times 10^{22}}{6.022 \times 10^{23}}\).
02

- Determining the Number of Moles of Sand Grains

To find the number of moles of sand grains, divide the number of sand grains, which is \(7.5 \times 10^{18}\), by Avogadro's number, \(6.022 \times 10^{23}\) mol\(^{-1}\). The calculation is \(\frac{7.5 \times 10^{18}}{6.022 \times 10^{23}}\).
03

- Calculating the Number of Jelly Donuts from Moles

To find the number of jelly donuts from moles, multiply the number of moles, \(0.0555\) moles, by Avogadro's number, \(6.022 \times 10^{23}\) mol\(^{-1}\). The calculation is \(0.0555 \times 6.022 \times 10^{23}\). Since the number is much less than one mole, the result will just be the number of donuts represented by the moles, which is 0.0555.
04

- Calculating the Number of Water Molecules from Moles

To calculate the number of water molecules in 13 moles, multiply the number of moles by Avogadro's number. The calculation is \(13 \times 6.022 \times 10^{23}\) molecules/mol.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Avogadro's number
Avogadro's number is a fundamental constant in chemistry that provides a link between the microscale world of atoms and molecules and the macroscale world of grams and moles that we can measure in the lab. It is defined as the number of atoms in exactly 12 grams of carbon-12, and this number has been experimentally determined to be approximately 6.022 x 1023.

Whenever we speak of one mole of a substance, we are referring to a quantity that contains exactly Avogadro's number of discrete entities, be they atoms, ions, molecules, or in the case of the exercise, stars. Understanding Avogadro's number is crucial when translating between the number of particles and the amount of substance in moles.
Mole concept in chemistry
The mole concept is one of the cornerstone ideas in chemistry, allowing chemists to count particles by weighing them. One mole is akin to a chemical 'dozen'—it's a specific quantity, 6.022 x 1023, just as a dozen always refers to 12 objects. This concept allows for a convenient way to discuss large quantities of very small entities such as atoms and molecules.

The term 'mole' can be applied to any type of discrete entity, from stars in the cosmos to grains of sand on a beach. The mole concept allows us to calculate the number of entities in a given mass of a substance and provides the bridge necessary for chemical quantification. For example, in the exercise, the estimation of moles of different substances is achieved by understanding and applying the mole concept effectively.
Converting units of measure in chemistry
Chemistry often involves converting units of measure to facilitate comparisons, quantification, and reactions. Converting between moles, mass, number of particles, and volume of gases at standard temperature and pressure (STP) is routine. These conversions require an understanding of Avogadro's number, molar mass, and gas laws. The exercises demonstrate how to convert from the number of objects (like stars or jelly donuts) to moles.

It's essential when converting units to keep track of dimensions and ensure that the final units match the desired outcome. For instance, when converting from the number of grains of sand to moles, the number is divided by Avogadro's number since the mole is defined as the amount containing Avogadro's number of units.
Chemical quantification
Chemical quantification involves measuring and expressing the amount of a substance. Quantitative measures in chemistry include mass, volume, concentration, and of course, the mole. For solid and liquid substances, mass is commonly measured, while for solutions, concentration is used, and for gases, volume may be used at STP. All these quantities are interconvertible with the right information.

In the exercise, chemical quantification is performed by determining the number of moles and subsequently calculating the number of discrete particles. This is fundamental to not just academic exercises but to practical chemistry where it's necessary to know the precise amount of substance required for a reaction. From the theoretical to the practical, mastery of chemical quantification is vital in chemistry.

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