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Let's start by understanding the ideal gas law, a fundamental principle in chemistry. The ideal gas law is represented by the equation: \[ PV = nRT \]where: - **P** is the pressure in pascals (Pa) - **V** is the volume in cubic meters (m³) - **n** is the number of moles - **R** is the universal gas constant (8.314 J/(mol·K)) - **T** is the temperature in kelvin (K) This equation helps us relate the pressure, volume, temperature, and amount (moles) of an ideal gas. An ideal gas perfectly follows this law without any deviations. Although real gases exhibit slight deviations, they are minimal under many conditions.

Pressure conversion is crucial when working with the ideal gas law. In our exercise, the pressure is given in millimeters of mercury (mmHg), which needs converting to pascals (Pa) to use in the ideal gas law.To convert mmHg to Pa:\[ 1 \text{ mmHg} = 133.322 \text{ Pa} \]Given pressure:\[ P = 10^{-8} \text{ mmHg} \]Thus, converting to pascals:\[ P = 10^{-8} \text{ mmHg} \times 133.322 \text{ Pa/mmHg} = 1.33322 \times 10^{-6} \text{ Pa} \]This conversion is necessary because pascals are the SI unit for pressure and are compatible with the gas constant R in our calculations.

Volume conversion is also essential. Here, the volume is given in milliliters (mL), which must be converted to cubic meters (m³). This ensures consistency with the gas constant R in the ideal gas law.To convert mL to m³: \[ 1 \text{ mL} = 1 \times 10^{-6} \text{ m}^3 \]In our problem, the volume was given as 1 milliliter, so:\[ V = 1 \times 10^{-6} \text{ m}^3 \]Using cubic meters aligns with the ideal gas law equation, making calculations straightforward and accurate.

Avogadro's number (6.022 \times 10^{23} \text{ molecules/mol}) is a key concept in chemistry that helps convert moles of a substance to the number of molecules. In our exercise, we first find the number of moles of gas and then convert it to molecules.The number of moles ( n ) is calculated using the rearranged ideal gas law:\[ n = \frac{PV}{RT} \]After calculating the moles, we convert them to molecules using Avogadro's number:\[ \text{Number of molecules} = n \times 6.022 \times 10^{23} \text{ molecules/mol} \]For instance, if we have 3.20 \times 10^{-16} \text{ mol}, then:\[ \text{Number of molecules} = 3.20 \times 10^{-16} \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \ \text{Number of molecules} = 1.93 \times 10^8 \text{ molecules/mL} \]By using Avogadro's number, we can see the microscopic world of molecules and their interactions through calculations.