Boyle Charles Avogadro Law

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Charles Law vs Boyle law

Amedeo Avogadro Law

Charles’ law and Boyle’s law are two very important laws concerned with gases. These two laws can describe many properties of the ideal gases. These laws are widely used in fields such as chemistry, thermodynamics, aviation and even military applications. It is vital to have a solid understanding in these two laws in order to excel in such fields. In this article, we are going to discuss what Charles’ law and Boyle’s law are, their definitions, applications of Charles’ law and Boyle’s law, their similarities, and finally the differences between Charles’ law and Boyle’s law.

The four laws are Boyle’s Law, Charles’s Law, Gay-Lussac’s Law and Avogadro’s Law. Avogadro’s Law Amadeo Avogadro was an Italian physicist who stated, in 1811, that the volume of any gas is proportional to the number of molecules of gas (measured in Moles – symbol mol). In other words if the amount of gas increases, then so does its volume. Nov 01, 2017 Avogadro law is sometime also called as Avogadro hypothesis or Avogadro’s principle. It is an experimental law which was given in 1811 by Amedeo Avogadro. According to Avogadro’s law, the final amount of air in the tyre (n 2) = (V 2 n 1)/V 1 = 5 moles. The deflated tyre would contain 5 moles of air. To learn more about Avogadro’s law and other important gas laws, such as Boyle’s law, register with BYJU’S and download the mobile application on your smartphone.

Boyle’s Law

Boyle’s law: The pressure exerted by a gas results from the impact of its molecules on the walls of the container. The collision rate, or the number of molecular collisions with the walls per second, is proportional to the number density of the gas.

Boyle’s law is a gas law. It is defined for an ideal gas. A proper understanding about ideal gas is necessary, to understand these ideal gas laws. Ideal gas is a gas for which the volume occupied by each molecule is zero; also the intermolecular attractions between the molecules are zero. Such ideal gases do not exist in real life conditions. The gases, which exist in real life, are known as real gasses. Real gases have molecular volumes and intermolecular forces. If the combined volume of all molecules of a real gas is negligible compared to the volume of the container, and the intermolecular forces are negligible compared to the velocities of the molecules, then the gas can be considered an ideal gas in that system. The Boyle’s law, which was proposed in 1662 by the chemist and physicist Robert Boyle, can be stated as follows. For a fixed amount of an ideal gas, kept at a fixed temperature, pressure and volume are inversely proportional.

A closed system is a system where no mass interchange between the surrounding and the system is possible, but energy exchange is possible. The Boyle’s law suggests that the product of the pressure and the volume of an ideal gas, in a constant temperature, to be constant. In other words, P V = K, where p is the pressure, V is the volume, and K is the constant. This means, if the pressure of such a system is doubled, the volume of that system becomes half of its original value.

Boyle charles avogadro lawrenceBoyle

Avogadro's Law Examples

Charles’ Law

Charles law is also a gas law, which is defined to an ideal gas in a closed system. This states that for a closed ideal gas system under constant pressure, the volume of the system is directly proportional to the temperature of the system. This law was first published by the French philosopher Joseph Louis Gay-Lussac, but he credited the discovery to Jacques Charles. This law suggests that for such a system, the ratio between the temperature and the volume must be a constant. In other words, V/T = K, where V is the volume of the gas and T is the temperature of the gas. It must be noted that mathematically, this proportionality will only work for Kelvin scale, which is an absolute temperature scale.

What is the difference between Charles’ law and Boyle’s law?

• Charles’ law is defined for a system with a constant pressure while Boyle’s law is defined for a system with constant temperature.

• The two terms involved in Charles’ law are directly proportional to each other while the terms involved in Boyle’s law are inversely proportional.

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Boyle's Law Charles Law Avogadro's Law Formula

  • Slide 1

Boyle Charles Avogadro Laws

Chapter 8 Gases The Gas Laws of Boyle, Charles and Avogadro The Ideal Gas Law Gas Stoichiometry Daltons Laws of Partial Pressure The Kinetic Molecular Theory of Gases Effusion and Diffusion Collisions of Gas Particles with the Container Walls Intermolecular Collisions Real Gases Chemistry in the Atmosphere Slide 2 6/8/20142 States of Matter Solid Liquid Gas We start with gases because they are simpler than the others. Slide 3 Pressure (force/area, Pa=N/m 2 ): A pressure of 101.325 kPa is need to raise the column of Hg 76 cm (760 mm). standard pressure 760 mm Hg = 760 torr = 1 atm = 101.325 kPa Slide 4 V 1 / V 2 = T 1 / T 2 (fixed P,n) P 1 V 1 = P 2 V 2 (fixed T,n) Boyles Law Charles Law V x P = const V / T = const V / n = const (fixed P,T) Avogadro 1662 1787 1811 n = number of moles Slide 5 Boyles Law: Pressure and Volume The product of the pressure and volume, PV, of a sample of gas is a constant at a constant temperature: PV = k = Constant (fixed T,n) Slide 6 Boyles Law: The Effect of Pressure on Gas Volume Example The cylinder of a bicycle pump has a volume of 1131 cm 3 and is filled with air at a pressure of 1.02 atm. The outlet valve is sealed shut, and the pump handle is pushed down until the volume of the air is 517 cm 3. The temperature of the air trapped inside does not change. Compute the pressure inside the pump. Slide 7 Charles Law: T vs V At constant pressure, the volume of a sample of gas is a linear function of its temperature. V = bT T(C) =273C[(V/V o )] When V=0, T=-273C Slide 8 Charles Law: T vs V The Absolute Temperature Scale Kelvin temperature scale T (Kelvin) = 273.15 + t (Celsius) Gas volume is proportional to Temp V = V o ( 1 + ) t 273.15 o C Slide 9 Charles Law: The Effect of Temperature on Gas Volume V 1 / V 2 = T 1 / T 2 (at a fixed pressure and for a fixed amount of gas) V vs T Slide 10 Avogadros law (1811) V = an n= number of moles of gas a = proportionality constant For a gas at constant temperature and pressure the volume is directly proportional to the number of moles of gas. Slide 11 V 1 / V 2 = T 1 / T 2 (at a fixed pressure) P 1 V 1 = P 2 V 2 (at a fixed temperature) Boyles Law Charles Law V = kP -1 V = bT V = an (at a fixed pressure and temperature) Avogadro V = nRTP -1 n = number of moles PV = nRT ideal gas law an empirical law Slide 12 Example At some point during its ascent, a sealed weather balloon initially filled with helium at a fixed volume of 1.0 x 10 4 L at 1.00 atm and 30 o C reaches an altitude at which the temperature is -10 o C yet the volume is unchanged. Calculate the pressure at that altitude. n 1 = n 2 V 1 = V 2 P 2 = P 1 T 2 /T 1 = (1 atm)(263K)/(303K) Slide 13 STP (Standard Temperature and Pressure) For 1 mole of a perfect gas at OC (273K) (i.e., 32.0 g of O 2 ; 28.0 g N 2 ; 2.02 g H 2 ) nRT = 22.4 L atm = PV At 1 atm, V = 22.4 L STP = standard temperature and pressure = 273 K (0 o C) and 1 atm Slide 14 The Ideal Gas Law What is R, universal gas constant? the R is independent of the particular gas studied PV = nRT Slide 15 ideal gas law constants Slide 16 Example What mass of Hydrogen gas is needed to fill a weather balloon to a volume of 10,000 L, 1.00 atm and 30 C? 1) Use PV = nRT; n=PV/RT. 2) Find the number of moles. 3) Use the atomic weight to find the mass. Slide 17 n = PV/RT = (1 atm) (10,000 L) (293 K) -1 (0.082 L atm mol -1 K -1 ) -1 = 416 mol (416 mol)(1.0 g mol -1 ) = 416 g Example What mass of Hydrogen gas is needed to fill a weather balloon to a volume of 10,000 L, 1.00 atm and 30 C? Slide 18 Use volumes to determine stoichiometry. Gas Stoichiometry The volume of a gas is easier to measure than the mass. Slide 19 Gas Density and Molar Mass Slide 20 Example Calculate the density of gaseous hydrogen at a pressure of 1.32 atm and a temperature of -45 o C. Slide 21 Example Fluorocarbons are compounds containing fluorine and carbon. A 45.6 g sample of a gaseous fluorocarbon contains 7.94 g of carbon and 37.7 g of fluorine and occupies 7.40 L at STP (P = 1.00 atm and T = 273 K). Determine the molecular weight of the fluorocarbon and give its molecular formula. Slide 22 Example Fluorocarbons are compounds of fluorine and carbon. A 45.60 g sample of a gaseous fluorocarbon contains 7.94 g of carbon and 37.66 g of fluorine and occupies 7.40 L at STP (P = 1.00 atm and T = 273.15 K). Determine the approximate molar mass of the fluorocarbon and give its molecular formula. Slide 23 Mixtures of Gases Daltons Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. Slide 24 Mole Fractions and Partial Pressures The mole fraction of a component in a mixture is define as the number of moles of the components that are in the mixture divided by the total number of moles present. Slide 25 Example A solid hydrocarbon is burned in air in a closed container, producing a mixture of gases having a total pressure of 3.34 atm. Analysis of the mixture shows it to contain 0.340 g of water vapor, 0.792 g of carbon dioxide, 0.288 g of oxygen, 3.790 g of nitrogen, and no other gases. Calculate the mole fraction and partial pressure of carbon dioxide in this mixture. Slide 26 2NH 4 ClO 4 (s) N 2 (g) + Cl 2 (g) + 2O 2 (g) + 4 H 2 (g) Slide 27 The Ideal Gas Law is an empirical relationship based on experimental observations. Boyle, Charles and Avogadro. Kinetic Molecular Theory is a simple model that attempts to explain the behavior of gases. The Kinetic Molecular Theory of Gases Slide 28 1. A pure gas consists of a large number of identical molecules separated by distances that are large compared with their size. The volumes of the individual particles can be assumed to be negligible (zero). 2. The molecules of a gas are constantly moving in random directions with a distribution of speeds. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. 3. The molecules of a gas exert no forces on one another except during collisions, so that between collisions they move in straight lines with constant velocities. The gases are assumed to neither attract or repel each other. The collisions of the molecules with each other and with the walls of the container are elastic; no energy is lost during a collision. 4. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. Slide 29 Pressure (impulse per collision) x (frequency of collisions with the walls) impulse per collision momentum (m u) frequency of collisions number of molecules per unit volume (N/V) frequency of collisions speed of molecules (u) P (m u) [(N/V) u] Pressure and Molecular Motion Slide 30 P (m u) [(N/V) u] PV Nmu 2 Correction: The molecules have a distribution of speeds. Mean-square speed of all molecules = u2u2 Pressure and Molecular Motion Slide 31 PV Nmu 2 1. 1/2m = kinetic energy (KE ave ) of one molecule. 2. KE is proportional to T (KE ave = RT) 3. Divide by 3 (3 dimensions) 4. N = nN a (molecules = moles x molecules/mole) u2u2 Make some substitutions Slide 32 The Kinetic Molecular Theory of Gases Slide 33 Speed Distribution Temperature is a measure of the average kinetic energy of gas molecules. Slide 34 Velocity Distributions Distribution of Molecular Speeds u mp : u avg : u rms = 1.000 : 1.128: 1.225 Slide 35 At a certain speed, the root-mean-square-speed of the molecules of hydrogen in a sample of gas is 1055 ms -1. Compute the root-mean square speed of molecules of oxygen at the same temperature. Strategy 1.Find T for the H 2 gas with a u rms = 1055 ms -1 2. Find u rms of O 2 at the same temperature H 2 about 4 times velocity of O 2 Example Slide 36 Gaseous Diffusion and Effusion Diffusion: mixing of Gases Effusion: rate of passage of a gas through a tiny orifice in a chamber. e.g., NH 3 and HCl Slide 37 Example A gas mixture contains equal numbers of molecules of N 2 and SF 6. A small portion of it is passed through a gaseous diffusion apparatus. Calculate how many molecules of N 2 are present in the product of gas for every 100 molecules of SF 6. Slide 38 Real Gases Ideal Gas behavior is generally conditions of low pressure and high temperature Slide 39 Real Gases Kinetic Molecular Theory model assumed no interactions between gas particles and no volume for the gas particles 1873 Johannes van der Waals Correction for attractive forces in gases (and liquids) Correction for volume of the molecules P corrected V corrected = nRT Slide 40 The Person Behind the Science Johannes van der Waals (1837-1923) Highlights 1873 first to realize the necessity of taking into account the volumes of molecules and intermolecular forces (now generally called 'van der Waals forces') in establishing the relationship between the pressure, volume and temperature of gases and liquids. Moments in a Life 1910 awarded Nobel Prize in Physics Slide 41 Significant Figures Zeros that follow the last non-zero digit sometimes are counted. E.g., for 700 g, the zeros may or not be significant. They may present solely to position the decimal point But also may be intended to convey the precision of the measurement. The uncertainty in the measurement is on the order of +/- 1 g or +/- 10g or perhaps +/- 100 g It is impossible to tell which without further information. If you need 2 sig figs and want to write 40 use either Four zero decimal point 40. or 4.0 x 10 +1 Slide 42 When you can measure what you are speaking about and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, you knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge but you have scarcely, in your thoughts advanced to the stage of science, whatever the matter may be. Lecture to the Institution of Civil Engineers, 3 May 1883 The Person Behind the Science Lord Kelvin (William Thomson) 1824-1907