The matter in interstellar space consists almost entirely of hydrogen atoms at a temperature of 100 K and a density of approximately 1 atom>cm3. What is the gas pressure in millimeters of mercury?

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Identify the given values: Temperature (T) = 100 K, Density (n) = 1 atom/cm³. Note that the density needs to be converted to atoms/m³ for use in the ideal gas law.

Convert the density from atoms/cm³ to atoms/m³ by multiplying by 10^6, because 1 cm³ = 10^-6 m³.

Use the ideal gas law in the form P = nRT, where P is the pressure, n is the number density of particles, R is the gas constant, and T is the temperature. The gas constant R for this calculation should be in units that match the other given values (Joules/(mol·K)).

Calculate the number of moles per cubic meter (n) by dividing the number of atoms/m³ by Avogadro's number (approximately 6.022 x 10^23 atoms/mol).

Convert the pressure from Pascals to millimeters of mercury (mmHg) by using the conversion factor 1 atm = 760 mmHg and 1 atm = 101325 Pa.

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Key Concepts

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this context, it allows us to calculate the pressure exerted by hydrogen atoms in interstellar space, given their low density and temperature.

Pressure Units

Pressure can be expressed in various units, including atmospheres (atm), pascals (Pa), and millimeters of mercury (mmHg). Understanding how to convert between these units is essential for accurately reporting the gas pressure in the context of the question.

Kinetic Molecular Theory

Kinetic Molecular Theory explains the behavior of gases in terms of particle motion. It posits that gas pressure results from collisions of gas particles with the walls of a container, which is relevant for understanding how the low density and temperature of hydrogen in interstellar space affect its pressure.

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Kinetic Molecular Theory

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