(a) Calculate the mass of nitrogen present in a volume of 3000 cm^3 if the temperature of the ga

step 1 Hello, so in this problem we have nitrogen gas and we want to find the mass of the nitrogen gas

(a) Calculate the mass of nitrogen present in a volume of...

(a) Calculate the mass of nitrogen present in a volume of 3000 $\mathrm{cm}^{3}$ if the temperature of the gas is $22.0^{\circ} \mathrm{C}$ and the absolute pressure of $2.00 \times 10^{-13} \mathrm{atm}$ is a partial vacuum easily obtained in laboratories. (b) What is the density (in $\mathrm{kg} / \mathrm{m}^{3} )$ of the $\mathrm{N}_{2}$ ?

Key Concepts

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, is a fundamental relation in physical chemistry and thermodynamics that connects the pressure, volume, temperature, and number of moles of a gas. It allows for the prediction and calculation of one state variable if the others are known, making it a key tool in understanding and calculating the behavior of gases under different conditions.

Temperature Conversion

For accurate gas law calculations, temperature must be measured in an absolute scale, such as Kelvin. This involves converting from Celsius to Kelvin by adding 273.15, which ensures that the temperature is suitable for use in the Ideal Gas Law and other thermodynamic equations.

Molar Mass

Molar mass is the mass of one mole of a substance and serves as a bridge between the number of molecules (or moles) and the mass of a material. In the context of gases, it is used to convert the amount of substance obtained from the Ideal Gas Law into a measurable mass.

Density

Density is defined as the mass per unit volume of a substance. In gases, density can be determined by using the calculated mass from the Ideal Gas Law and the given volume, providing insights into how packed the gas molecules are in a given space.

Unit Conversion

Consistent unit usage is critical in any physical calculation. This involves converting measurements (for example, from cubic centimeters to cubic meters or from grams to kilograms) to ensure that all quantities are expressed in compatible units, which is essential for the correct application of formulas like the Ideal Gas Law.

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