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: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law

Problem 57

Chapter 17, Problem 57

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

Verified step by step guidance

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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

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.

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.

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.

Recommended video:

Guided course

17:04

Pressure and Atmospheric Pressure

Related Practice

Textbook Question

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

views

Textbook Question

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

views

Textbook Question

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.

views

Textbook Question

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?

views

Textbook Question

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?

views

Textbook Question

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.

views