Modern vacuum pumps make it easy to attain pressures of the...

Modern vacuum pumps make it easy to attain pressures of the order of $10^{-13}$ atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of $9.05 \times 10^{-14}$ atm and an ordinary temperature of $295.0 \mathrm{~K}$, how many molecules are present in a volume of $1.05 \mathrm{~cm}^{3} ?$ (b) How many molecules would be present at the same temperature but at 1.10 atm instead?

Modern vacuum pumps make it easy to attain pressures of the order of $10^{-13}$ atm in the laboratory. Consider a volume of air and treat the air as an ideal gas.
(a) At a pressure of $9.05 \times 10^{-14}$ atm and an ordinary temperature of $295.0 \mathrm{~K}$, how many molecules are present in a volume of $1.05 \mathrm{~cm}^{3} ?$ (b) How many molecules would be present at the same temperature but at 1.10 atm instead?

Key Concepts

Unit Conversion

Converting units accurately is critical when applying the ideal gas law. This involves ensuring that pressure, volume, and temperature are expressed in compatible units—typically pressure in atmospheres or pascals, volume in liters or cubic meters, and temperature in Kelvin—to guarantee accurate and meaningful calculations in gas law problems.

Avogadro’s Number

Avogadro’s number is the constant that specifies the number of molecules or atoms in one mole of any substance. It serves as the bridge between the macroscopic measurements of substances (like moles) and the microscopic count of individual particles, making it essential for converting amounts of gas into the actual number of molecules.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental principle in thermodynamics that relates the pressure, volume, and temperature of a gas to the amount of substance present in moles. It assumes that the gas particles do not interact and occupy negligible space, enabling the calculation and comparison of gas behavior under various conditions.

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