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Ch 18: Thermal Properties of Matter
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 18: Thermal Properties of MatterProblem 21
Chapter 18, Problem 21

How many moles are in a 1.001.00-kg bottle of water? How many molecules? The molar mass of water is 18.018.0 g/mol.

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First, understand that the molar mass of water (H₂O) is given as 18.0 g/mol. This means that one mole of water weighs 18.0 grams.
Next, convert the mass of the water from kilograms to grams. Since 1 kilogram is equal to 1000 grams, a 1.00-kg bottle of water contains 1000 grams of water.
To find the number of moles of water, use the formula: \( \text{moles} = \frac{\text{mass in grams}}{\text{molar mass}} \). Substitute the values: \( \text{moles} = \frac{1000 \text{ g}}{18.0 \text{ g/mol}} \).
Once you have the number of moles, you can find the number of molecules using Avogadro's number, which is \( 6.022 \times 10^{23} \) molecules/mol. Multiply the number of moles by Avogadro's number to get the total number of molecules.
Finally, ensure that your units are consistent throughout the calculations and double-check your arithmetic to ensure accuracy.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It allows conversion between the mass of a substance and the amount in moles. For water, the molar mass is 18.0 g/mol, meaning one mole of water weighs 18 grams.
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Mole Concept

The mole is a fundamental unit in chemistry that represents a quantity of 6.022 x 10^23 entities, such as atoms or molecules. It provides a bridge between the atomic scale and macroscopic measurements, allowing chemists to count particles by weighing them.
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Avogadro's Number

Avogadro's Number, 6.022 x 10^23, is the number of atoms, ions, or molecules in one mole of a substance. It is a key constant for converting between moles and individual particles, enabling calculations of the number of molecules in a given mass of a substance.
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Related Practice
Textbook Question

At an altitude of 11,00011,000 m (a typical cruising altitude for a jet airliner), the air temperature is −56.5-56.5°C and the air density is 0.3640.364 kg/m3 . What is the pressure of the atmosphere at that altitude? (Note: The temperature at this altitude is not the same as at the surface of the earth, so the calculation of Example 18.418.4 in Section 18.118.1 doesn't apply.)

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Textbook Question

Modern vacuum pumps make it easy to attain pressures of the order of 10−1310^{-13} atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. At a pressure of 9.00×10−149.00\(\times\)10^{-14} atm and an ordinary temperature of 300.0300.0 K, how many molecules are present in a volume of 1.001.00 cm3?

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Textbook Question

Martian Climate. The atmosphere of Mars is mostly CO2 (molar mass 44.0 g/mol) under a pressure of 650 Pa, which we shall assume remains constant. In many places the temperature varies from 0.0°C in summer to -100°C in winter. Over the course of a Martian year, what are the ranges of (b) the density (in mol/m^3) of the atmosphere?

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Textbook Question

A large organic molecule has a mass of 1.41×10−211.41\(\times\)10^{-21} kg. What is the molar mass of this compound?

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Textbook Question

Modern vacuum pumps make it easy to attain pressures of the order of 10−1310^{-13} atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. How many molecules would be present at the same temperature but at 1.001.00 atm instead?

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Textbook Question

If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is 10031003°C and the pressure is 9292 atm?

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