Textbook Question
The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10-10 mm of Hg. At T=20°C, how many molecules are in a cylindrical chamber 40 cm in diameter and 30 cm tall?
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Ch 18: A Macroscopic Description of Matter
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 18, Problem 41
The molecular mass of water (H₂O) is 18 u. How many protons are there in 1.0 L of liquid water?
Verified step by step guidance1
Step 1: Determine the number of molecules in 1.0 L of water. Start by finding the mass of 1.0 L of water using its density, which is approximately 1 g/mL. Since 1.0 L is equivalent to 1000 mL, the mass of water is 1000 g.
Step 2: Calculate the number of moles of water in 1000 g. Use the molecular mass of water, which is 18 u (or 18 g/mol). The number of moles is given by dividing the mass of water by its molecular mass: \( \text{moles} = \frac{\text{mass}}{\text{molecular mass}} \).
Step 3: Find the number of molecules of water using Avogadro's number, \( 6.022 \times 10^{23} \) molecules/mol. Multiply the number of moles by Avogadro's number: \( \text{molecules} = \text{moles} \times 6.022 \times 10^{23} \).
Step 4: Determine the number of protons in a single water molecule. A water molecule (H₂O) consists of 2 hydrogen atoms and 1 oxygen atom. Each hydrogen atom has 1 proton, and the oxygen atom has 8 protons, so a single water molecule contains \( 2 + 8 = 10 \) protons.
Step 5: Calculate the total number of protons in 1.0 L of water by multiplying the number of water molecules by the number of protons per molecule: \( \text{total protons} = \text{molecules} \times 10 \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Molecular Mass
Molecular mass is the mass of a molecule calculated as the sum of the atomic masses of its constituent atoms. For water (H₂O), the molecular mass is approximately 18 atomic mass units (u), derived from 2 hydrogen atoms (1 u each) and 1 oxygen atom (16 u). This concept is essential for determining the number of molecules in a given mass of a substance.
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Avogadro's Number
Avogadro's number, approximately 6.022 x 10²³, is the number of atoms, ions, or molecules in one mole of a substance. This constant allows us to convert between the mass of a substance and the number of molecules it contains. Understanding this concept is crucial for calculating the number of molecules in 1.0 L of water based on its molecular mass.
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Protons in Water Molecules
Each water molecule (H₂O) contains 2 hydrogen atoms and 1 oxygen atom. Hydrogen has 1 proton per atom, and oxygen has 8 protons. Therefore, each water molecule contains a total of 10 protons. Knowing the number of protons in a molecule is important for understanding the composition of substances and their chemical properties.
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Related Practice
Textbook Question
The 828-m-tall Burj Khalifa in Dubai is the world's tallest building. It's essentially a steel building wrapped in exterior paneling and glass. During construction, when the beams were exposed to the elements, the building was 36 cm taller on the hottest afternoon of the year than on the coldest morning. By how much did the temperature vary throughout the year?
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Textbook Question
The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0×10-10 mm of Hg. What fraction is this of atmospheric pressure?
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Textbook Question
0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What is the volume V3?
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Textbook Question
0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are pressure p2?
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Textbook Question
A sealed container holds 3.2 g of oxygen at 1 atm pressure and 20°C. The gas first undergoes an isobaric process that doubles the absolute temperature, then an isothermal process that halves the pressure. What is the final volume of the gas in L?
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