The "effective" molar mass of air is 29 g / mol. Use this value to calculate the density of air

The "effective" molar mass of air is 29 g /...

Key Concepts

Unit Conversions

Unit conversions are essential when working with different systems of measurement in gas calculations. Converting pressures (such as torr to atm or pascals), temperatures (Celsius to Kelvin), and other quantities ensures that all variables in equations like the Ideal Gas Law are coherently expressed, thereby avoiding errors in the computation of properties like density.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) refers to a set of standard conditions, typically 0°C (273.15 K) and 1 atm pressure, that provide a common reference point for reporting gas properties. Using STP conditions simplifies calculations and comparisons related to gas volume and density, ensuring consistency in scientific communication.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, is a fundamental equation in thermodynamics that relates the pressure, volume, the number of moles, the gas constant, and temperature of an ideal gas. It allows one to derive expressions for various gas properties, including density, by relating mass, molar mass, and molar quantities under different thermodynamic conditions.

Molar Mass

Molar mass is the mass of one mole of a substance and serves as a crucial conversion factor linking the macroscopic gas measurements to microscopic particle counts. In gas density calculations, molar mass is used directly in formulas derived from the Ideal Gas Law to convert moles to mass.

Density Calculation of Gases

The density of a gas can be derived from the Ideal Gas Law by relating mass and volume. The formula ? = PM/RT is obtained by substituting the number of moles (n = mass/molar mass) into the Ideal Gas Law. This formula enables the calculation of gas density based on its pressure, molar mass, temperature, and the universal gas constant.

Transcript

00:01 Hi there.

00:02 In this problem, we are trying to calculate the density for a gas when we know it's molar mass.

00:09 And we actually have two problems here.

00:11 The first one, we are trying to find density at standard temperature and pressure, or stp.

00:18 And in the second problem, we are given a pressure and a temperature.

00:23 So let's get started.

00:25 First of all, we need an equation.

00:28 The equation i'm going to use from the unit is density is equal to molar mass.

00:33 Mass times pressure over the universal gas constant times temperature.

00:43 So for our first problem, for part a, let me plug in the values that are given to us in the problem.

00:53 We are given a molar mass of 29 grams per mole.

01:00 Pressure is standard pressure.

01:02 So i am going to select one atmosphere as my standard pressure.

01:07 Since i'm using one atmosphere as my pressure, i need to use the universal gas constant that has atmospheres as one of its units.

01:18 So that's 0 .0821 liters times atmospheres divided by mole times kelvin, and then all this is multiplied by standard temperature of 273 kelvin.

01:42 Checking out my units here, i see that moles will cancel with moles, atmospheres will cancel, and the unit kelvin will cancel.

01:54 That leaves me with the units grams per liter, which are the perfect units for the density of a gas...

Please give Ace some feedback