A 10 -cm-diameter cylinder of helium gas is 30 cm long and...

A 10 -cm-diameter cylinder of helium gas is 30 cm long and at $20^{\circ} \mathrm{C}$. The pressure gauge reads $120 \mathrm{psi}.$
a. How many helium atoms are in the cylinder?
b. What is the mass of the helium?
c. What is the helium number density?
d. What is the helium mass density?

Key Concepts

Mass Density

Mass density is defined as the mass per unit volume of a substance. In the context of gases, it can be found by multiplying the number density by the mass of an individual atom or molecule, and it gives insights into the distribution of mass within a gas under various conditions.

Number Density

Number density describes the number of atoms or molecules per unit volume. It provides a microscopic view of how particles are distributed within a gas by dividing the total number of particles by the volume of the container.

Unit Conversion

In problems involving gas laws, unit conversion is critical to ensure consistency in calculations. This includes converting pressure units (such as psi to pascals), length units (such as centimeters to meters), and volume units, so that all the quantities used in equations are in compatible units.

Mole and Avogadro's Number

The mole is a unit that measures the amount of substance, and Avogadro's number (approximately 6.022×10^23) represents the number of atoms or molecules in one mole. This concept is essential for converting between moles, which are used in macroscopic gas law calculations, and the actual count of atoms or molecules found in a substance.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates a gas's pressure, volume, number of moles, gas constant, and temperature. It is fundamental in calculating the amount of gas (in moles) in a container under known conditions and assumes no intermolecular forces and perfectly elastic collisions.

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