Why do Helium Balloons Float in the Air? Have you ever wondered why helium fille

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Why do Helium Balloons Float in the Air?

Have you ever wondered why helium filled balloons sold in stores float in the air, but the ones you blow air into do not, even though they are the same size? The reason is that the same volume of helium weighs less than air. According to Avogadro’s Law, balloons of similar volume contain similar number of moles of substance. However, helium is lighter than air because its molar mass is lower than oxygen’s and nitrogen’s, the two major components of air.Gases are different from liquids and solids in that they have neither a fixed volume nor a fixed shape. The behavior of gases depends on four variables: pressure (P), volume (V), temperature (T), and amount (number of moles, n). There are three key laws that express the relationship between these variables: Boyle’s, Charles’s, and Avogadro’s Law. These laws express the effect of one variable on another, while the other two variables remain constant.

Avogadro’s Law

The Italian chemist and physicist, Amedeo Avogadro (1776 – 1856), established Avogadro's Law in 1811. This gas law states that equal volumes of gases at fixed temperature and pressure contain the same number of particles. This means that a sample of one gas under specific conditions of pressure and temperature will have the same number of moles as another gas, as long as the pressure and temperature are kept constant.

In addition, the volume occupied by a gas is proportional to the number of gas particles in the sample, regardless of the chemical composition of the molecules. Therefore, the volume, pressure, and temperature of a gas sample can provide a direct measurement of the number of particles in the sample, even if the chemical formula is not known. Mathematically, Avogadro’s Law is expressed as shown below

where V is the volume of gas and n is the number of moles of gas.

Here the unit is the mole, which is 6.022×1023 objects. For instance, a mole of marbles is 6.022×1023 marbles, and a mole of hydrogen atoms is 6.022×1023 hydrogen atoms. This number is Avogadro’s number, and it is the number of atoms in 12 g of isotopically pure carbon-12. You can use this number to convert from moles to molecules. Multiply the number of moles by Avogadro’s number to find the number of molecules.  

A molecule is made up of more than one atom. To find the number of atoms in a mole of molecules, such as CH4, first multiply the number of moles by Avogadro’s number. Then multiply by the number of atoms in the molecule. In the case of CH4, there are 4 hydrogen atoms and 1 carbon atom. An example of calculating the number of atoms in 7 mols of CH4 is shown below.   

Molar Volume

The molar volume is the volume of one mole of gas at a given temperature and pressure. By definition, the molar volume of a substance can be obtained from the ratio between the volume of a gas and the number of moles

where Vm is the molar volume, V is the volume, and n is the number of moles of gas. At a given temperature and pressure, all gases will have the same molar volume. For example, at standard temperature and pressure (273.15 K, 1.00 atm), the molar volume is 22.4 L/mol.

This value is obtained directly from the ideal gas equation as shown below.

where Vm is the molar volume, n is 1 mol, R is the gas constant of 0.082 L atm mol–1 K–1, T is the standard temperature of 273 K, and P is the standard pressure of 1.00 atm.

To test Avogadro’s Law, either keep the volume constant and determine the number of moles or vice versa. In this experiment, volume, temperature, and pressure will be constant. Given the constant volume, the number of moles in the flask will be constant for all the gases. However, the mass of the gases will vary in accordance with their molar masses. The mathematical relationship between the number of moles and mass is shown below

where n is the number of moles, m is the mass in g, and MM is the molar mass in g/mol.

Using this equation, the following equation for constant volume, V0, can be derived from the Ideal Gas La

where m is the mass of gas, P is the pressure, V0 is the constant volume, R is the gas constant, T is the temperature, and MM is the molar mass.

About This Lab

In this lab, you will test Avogadro's Law. To do this, you will determine the number of moles in 150 mL samples of different gases by measuring the mass of the sample and using the molar mass of each gas. Each sample will be at room temperature and pressure.  

You will be working with the gases listed in Figure 2.  

Formula

MM (g/mol)

propane

C3H8

44.10

butane

C4H10

58.12

methane

CH4

16.04

flask=88.000

flask with methane=88.100

How many moles of methane were in the Erlenmeyer flask? A.1.72 × 10-3 mol B.6.23 × 10-3 mol C.6.23 × 10-2 mol D.2.26 × 10-3 mol

Formula

MM (g/mol)

propane

C3H8

44.10

butane

C4H10

58.12

methane

CH4

16.04

Explanation / Answer

Mass of CH4 = Mass of flask+CH4-Mass of flask = 88.10-88.00 = 0.1 g

Number of moles of methane = mass/molar mass = 0.1/16 = 0.00625 = 6.25*10^-3

Answerm: B.6.23 × 10-3

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