An expensive vacuum system can achieve a pressure as low as 1.00 ×10^-7 N / m^2 at 20^∘ C. How m

step 1 So we want to find out the number of atoms in a cubic centimeter at a pressure of 1 .00 into 10

An expensive vacuum system can achieve a pressure as low as...

An expensive vacuum system can achieve a pressure as low as $1.00 \times 10^{-7} \mathrm{N} / \mathrm{m}^{2}$ at $20^{\circ} \mathrm{C}$. How many atoms are there in a cubic centimeter at this pressure and temperature?

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) relates pressure, volume, temperature, and the number of moles of a gas. This equation is fundamental in thermodynamics and provides a way to connect measurable macroscopic properties of a gas to the amount of substance present, allowing us to calculate one quantity if the others are known.

Mole Concept and Avogadro's Number

The mole concept links the macroscopic scale of material amounts to the microscopic scale of atoms or molecules through Avogadro's number (approximately 6.022×10^23 particles per mole). This relationship is essential for converting between the amount in moles and the actual number of atoms or molecules present in a sample.

Unit Conversions

Accurate application of physical laws like the ideal gas law requires consistent units, making it necessary to convert temperatures to the Kelvin scale, pressures to standard SI units, and volumes as needed. Proper unit conversion ensures that the calculations accurately reflect the underlying relationships between physical quantities.

Number Density

Number density refers to the number of particles (atoms or molecules) per unit volume. It is often derived from the ideal gas law by determining the number of moles per given volume and then using Avogadro's number to convert to the actual number of particles. This concept is crucial for understanding the distribution of particles in a gas, especially under conditions of low pressure or high vacuum.

Transcript

Please give Ace some feedback