Skip to main content
Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 17 - Temperature, Thermal Expansion, and the Ideal Gas LawProblema 57
Capitolo 17, Problema 57

How many moles of water are there in 1.00 L at STP? How many molecules?

Guida verificata passo dopo passo
1
Determine the density of water at standard temperature and pressure (STP). The density of water is approximately 1.00 g/mL, which means 1.00 L of water has a mass of 1000 g.
Calculate the molar mass of water (H₂O). The molar mass is the sum of the atomic masses of its elements: hydrogen (H) has an atomic mass of approximately 1.01 g/mol, and oxygen (O) has an atomic mass of approximately 16.00 g/mol. Therefore, the molar mass of water is \( 2(1.01) + 16.00 = 18.02 \) g/mol.
Use the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \) to calculate the number of moles of water. Substitute the mass of water (1000 g) and the molar mass of water (18.02 g/mol) into the formula.
To find the number of molecules, use Avogadro's number, which is \( 6.022 \times 10^{23} \) molecules/mol. Multiply the number of moles of water by Avogadro's number to determine the total number of water molecules.
Express the final answers in terms of moles and molecules, ensuring the units are consistent and properly labeled.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
5m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Molarity and Moles

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. In this context, to find the number of moles of water in 1.00 L, we use the molar mass of water (approximately 18.02 g/mol) and the density of water (about 1 g/mL) to determine that 1 L of water contains roughly 55.5 moles.
Video consigliato:
Percorso guidato
07:19
Moles & Avogadro's Number

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of particles (atoms, molecules, etc.) in one mole of a substance. This constant allows us to convert between moles and the number of molecules. For example, to find the number of molecules in the calculated moles of water, we multiply the number of moles by Avogadro's number.
Video consigliato:
Percorso guidato
07:19
Moles & Avogadro's Number

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a reference point used in chemistry, defined as 0 degrees Celsius (273.15 K) and 1 atmosphere of pressure. At STP, gases behave ideally, and it provides a consistent basis for calculations involving gases and solutions. While the question focuses on water, understanding STP is crucial for contextualizing the conditions under which the calculations are made.
Video consigliato:
Percorso guidato
17:04
Pressure and Atmospheric Pressure
Pratica correlata
Domanda del libro di testo

Show that the bulk modulus (Section 12–5) for an ideal gas held at constant temperature is B = P, where P is the pressure.

1297
views
Domanda del libro di testo

A precise steel tape measure has been calibrated at 14°C. At 37°C, what will be the percentage error?

1053
views
Domanda del libro di testo

A helium balloon rises because of a buoyant force. By what percentage does the buoyant force on a helium balloon change if the temperature of the helium is increased from 15°C to 25°C while the temperature of the surrounding air is unchanged? Assume that the pressure of the helium remains constant.

975
views
Domanda del libro di testo

An air bubble at the bottom of a lake 32.0 m deep has a volume of 1.00 cm³ . If the temperature at the bottom is 5.5°C and at the top 18.5°C, what is the radius of the bubble just before it reaches the surface?

977
views
Domanda del libro di testo

You buy an “airtight” potato chip bag packaged at sea level, and take the chips on an airplane flight. When you take the potato chip bag out of your “carry-on” bag, you notice it has noticeably “puffed up.” Airplane cabins are typically pressurized at 0.75 atm, and assuming the temperature inside an airplane is about the same as inside a potato chip processing plant, by what percentage has the bag “puffed up” in comparison to when it was packaged?

908
views
Domanda del libro di testo

Use the ideal gas law to show that, for an ideal gas at constant pressure, the coefficient of volume expansion is equal to β = 1/ T, where T is the kelvin temperature. Compare to Table 17–1 for gases at T = 293 K.

99
views