What is the density in grams per liter of nitrogen gas at STP?

The Ideal Gas Law is a fundamental principle that describes the relationship between the pressure, volume, temperature, and moles of a gas. It is expressed by the equation PV = nRT. In this equation, P stands for pressure, V represents volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

The value of R varies depending on the units being used; for instance, in this case, we use 0.08206 L atm K⁻¹ mol⁻¹ because pressure is in atmospheres (atm) and volume is in liters (L). The temperature, always in Kelvin, is part of the equation to ensure consistency across various conditions. When used properly, the Ideal Gas Law allows us to predict one of the variables if the other three are known, serving as an invaluable tool in calculating gas densities, like that of nitrogen gas at STP.

The molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. When we refer to the molar mass of nitrogen, we must consider that it naturally exists as a diatomic molecule (N₂).

To calculate the molar mass of N₂, we double the molar mass of a single nitrogen atom. Since the atomic mass of nitrogen is approximately 14.0067 grams per mole, the molar mass of N₂ is 28.0134 grams per mole. This value is crucial when converting between mass and moles, an essential step for finding density using the Ideal Gas Law.

The term 'STP' stands for Standard Temperature and Pressure. STP conditions are agreed upon standard sets of conditions for the measurement and documentation of chemical and physical processes: a temperature of 273.15 K (0°C) and a pressure of 1 atm. These reference conditions allow for consistency in experiments and calculations.

Under STP, gases have specific characteristics that can be reliably used for calculations such as density determination. One mole of an ideal gas occupies 22.4 liters at STP, which is known as the molar volume of a gas. Remember, this is an ideal approximation which works under the assumption that the gas perfectly follows the Ideal Gas Law.

Mole calculations involve determining the number of moles present in a given quantity of substance. Moles can be linked to the volume, mass, and number of particles of a substance through Avogadro's number (6.022 x 10²³ particles per mole).

In the context of determining the density of nitrogen gas, we first calculate the moles of nitrogen gas using the Ideal Gas Law rearranged to isolate n (n = PV/RT). With the moles known, we then calculate the mass by multiplying the moles by the molar mass of nitrogen (N₂). This step is crucial to determine the mass of the nitrogen gas present in a specific volume, which subsequently allows us to calculate the gas's density.