PV=Nrt and Combined Gas

Total Page:16

File Type:pdf, Size:1020Kb

PV=Nrt and Combined Gas PV = nRT Ideal gasses are theoretical gasses that can be used to model the behavior of real gasses. In order for it to be considered ideal, individual gaseous particles must both not attract or repel one another, and also not have any volume. The breakdown of the formula is as follows: P - Pressure. Units typically consist of pascals, atmospheres, mmHg V - Volume. Units typically consist of Liters or m3 n - Number of moles of gas. Remember, a mol of a substance is a unitless amount of particles of the substance R - Ideal gas constant. It can vary based on the units you use. Remember to use the correct units so that they match the units of the other components of the equation! T - Temperature. Measured in Kelvin. If temperature is given in any other unit, remember to convert to Kelvin Pressure Conversions likely used in class 1 atm = 1.01325 Bar = 101.325 Kilopascal = 760.000002 Torr = 759.99995 mmHg If I have 4 moles of a gas at a pressure of 5.6 atm and a volume of 12 liters, what is the temperature? If I contain 3 moles of gas in a container with a volume of 60 liters and at a temperature of 400 K, what is the pressure inside the container? If I have an unknown quantity of gas held at a temperature of 1195 K in a container with a volume of 25 liters and a pressure of 560 atm, how many moles of gas do I have? What is the volume of 23g of neon gas at 1C and a pressure of 2 atm? Combined Gas Law = The combined gas law is effectively a restructuring of the ideal gas law, where both n (mols of gas) and R (already a constant) remain constant. It can be used to determine how changes in pressure, volume, or temperature can be used to calculate the conditions of the resulting system. If four moles of a gas at a pressure of 5.4 atmospheres have a volume of 120 liters, what is the temperature? If I initially have a gas with a pressure of 84 kPa and a temperature of 350 C and I heat it an additional 230 degrees, what will the new pressure be? Assume the volume of the container is constant. A sample of 25L of NH3 gas at 10C is heated at constant pressure until it fills a volume of 50L. What is the new temperature in C? .
Recommended publications
  • Solutes and Solution
    Solutes and Solution The first rule of solubility is “likes dissolve likes” Polar or ionic substances are soluble in polar solvents Non-polar substances are soluble in non- polar solvents Solutes and Solution There must be a reason why a substance is soluble in a solvent: either the solution process lowers the overall enthalpy of the system (Hrxn < 0) Or the solution process increases the overall entropy of the system (Srxn > 0) Entropy is a measure of the amount of disorder in a system—entropy must increase for any spontaneous change 1 Solutes and Solution The forces that drive the dissolution of a solute usually involve both enthalpy and entropy terms Hsoln < 0 for most species The creation of a solution takes a more ordered system (solid phase or pure liquid phase) and makes more disordered system (solute molecules are more randomly distributed throughout the solution) Saturation and Equilibrium If we have enough solute available, a solution can become saturated—the point when no more solute may be accepted into the solvent Saturation indicates an equilibrium between the pure solute and solvent and the solution solute + solvent solution KC 2 Saturation and Equilibrium solute + solvent solution KC The magnitude of KC indicates how soluble a solute is in that particular solvent If KC is large, the solute is very soluble If KC is small, the solute is only slightly soluble Saturation and Equilibrium Examples: + - NaCl(s) + H2O(l) Na (aq) + Cl (aq) KC = 37.3 A saturated solution of NaCl has a [Na+] = 6.11 M and [Cl-] =
    [Show full text]
  • THE SOLUBILITY of GASES in LIQUIDS Introductory Information C
    THE SOLUBILITY OF GASES IN LIQUIDS Introductory Information C. L. Young, R. Battino, and H. L. Clever INTRODUCTION The Solubility Data Project aims to make a comprehensive search of the literature for data on the solubility of gases, liquids and solids in liquids. Data of suitable accuracy are compiled into data sheets set out in a uniform format. The data for each system are evaluated and where data of sufficient accuracy are available values are recommended and in some cases a smoothing equation is given to represent the variation of solubility with pressure and/or temperature. A text giving an evaluation and recommended values and the compiled data sheets are published on consecutive pages. The following paper by E. Wilhelm gives a rigorous thermodynamic treatment on the solubility of gases in liquids. DEFINITION OF GAS SOLUBILITY The distinction between vapor-liquid equilibria and the solubility of gases in liquids is arbitrary. It is generally accepted that the equilibrium set up at 300K between a typical gas such as argon and a liquid such as water is gas-liquid solubility whereas the equilibrium set up between hexane and cyclohexane at 350K is an example of vapor-liquid equilibrium. However, the distinction between gas-liquid solubility and vapor-liquid equilibrium is often not so clear. The equilibria set up between methane and propane above the critical temperature of methane and below the criti­ cal temperature of propane may be classed as vapor-liquid equilibrium or as gas-liquid solubility depending on the particular range of pressure considered and the particular worker concerned.
    [Show full text]
  • Pressure Diffusion Waves in Porous Media
    Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory Title Pressure diffusion waves in porous media Permalink https://escholarship.org/uc/item/5bh9f6c4 Authors Silin, Dmitry Korneev, Valeri Goloshubin, Gennady Publication Date 2003-04-08 eScholarship.org Powered by the California Digital Library University of California Pressure diffusion waves in porous media Dmitry Silin* and Valeri Korneev, Lawrence Berkeley National Laboratory, Gennady Goloshubin, University of Houston Summary elastic porous medium. Such a model results in a parabolic pressure diffusion equation. Its validity has been Pressure diffusion wave in porous rocks are under confirmed and “canonized”, for instance, in transient consideration. The pressure diffusion mechanism can pressure well test analysis, where it is used as the main tool provide an explanation of the high attenuation of low- since 1930th, see e.g. Earlougher (1977) and Barenblatt et. frequency signals in fluid-saturated rocks. Both single and al., (1990). The basic assumptions of this model make it dual porosity models are considered. In either case, the applicable specifically in the low-frequency range of attenuation coefficient is a function of the frequency. pressure fluctuations. Introduction Theories describing wave propagation in fluid-bearing porous media are usually derived from Biot’s theory of poroelasticity (Biot 1956ab, 1962). However, the observed high attenuation of low-frequency waves (Goloshubin and Korneev, 2000) is not well predicted by this theory. One of possible reasons for difficulties in detecting Biot waves in real rocks is in the limitations imposed by the assumptions underlying Biot’s equations. Biot (1956ab, 1962) derived his main equations characterizing the mechanical motion of elastic porous fluid-saturated rock from the Hamiltonian Principle of Least Action.
    [Show full text]
  • What Is High Blood Pressure?
    ANSWERS Lifestyle + Risk Reduction by heart High Blood Pressure BLOOD PRESSURE SYSTOLIC mm Hg DIASTOLIC mm Hg What is CATEGORY (upper number) (lower number) High Blood NORMAL LESS THAN 120 and LESS THAN 80 ELEVATED 120-129 and LESS THAN 80 Pressure? HIGH BLOOD PRESSURE 130-139 or 80-89 (HYPERTENSION) Blood pressure is the force of blood STAGE 1 pushing against blood vessel walls. It’s measured in millimeters of HIGH BLOOD PRESSURE 140 OR HIGHER or 90 OR HIGHER mercury (mm Hg). (HYPERTENSION) STAGE 2 High blood pressure (HBP) means HYPERTENSIVE the pressure in your arteries is higher CRISIS HIGHER THAN 180 and/ HIGHER THAN 120 than it should be. Another name for (consult your doctor or immediately) high blood pressure is hypertension. Blood pressure is written as two numbers, such as 112/78 mm Hg. The top, or larger, number (called Am I at higher risk of developing HBP? systolic pressure) is the pressure when the heart There are risk factors that increase your chances of developing HBP. Some you can control, and some you can’t. beats. The bottom, or smaller, number (called diastolic pressure) is the pressure when the heart Those that can be controlled are: rests between beats. • Cigarette smoking and exposure to secondhand smoke • Diabetes Normal blood pressure is below 120/80 mm Hg. • Being obese or overweight If you’re an adult and your systolic pressure is 120 to • High cholesterol 129, and your diastolic pressure is less than 80, you have elevated blood pressure. High blood pressure • Unhealthy diet (high in sodium, low in potassium, and drinking too much alcohol) is a systolic pressure of 130 or higher,or a diastolic pressure of 80 or higher, that stays high over time.
    [Show full text]
  • THE SOLUBILITY of GASES in LIQUIDS INTRODUCTION the Solubility Data Project Aims to Make a Comprehensive Search of the Lit- Erat
    THE SOLUBILITY OF GASES IN LIQUIDS R. Battino, H. L. Clever and C. L. Young INTRODUCTION The Solubility Data Project aims to make a comprehensive search of the lit­ erature for data on the solubility of gases, liquids and solids in liquids. Data of suitable accuracy are compiled into data sheets set out in a uni­ form format. The data for each system are evaluated and where data of suf­ ficient accuracy are available values recommended and in some cases a smoothing equation suggested to represent the variation of solubility with pressure and/or temperature. A text giving an evaluation and recommended values and the compiled data sheets are pUblished on consecutive pages. DEFINITION OF GAS SOLUBILITY The distinction between vapor-liquid equilibria and the solUbility of gases in liquids is arbitrary. It is generally accepted that the equilibrium set up at 300K between a typical gas such as argon and a liquid such as water is gas liquid solubility whereas the equilibrium set up between hexane and cyclohexane at 350K is an example of vapor-liquid equilibrium. However, the distinction between gas-liquid solUbility and vapor-liquid equilibrium is often not so clear. The equilibria set up between methane and propane above the critical temperature of methane and below the critical temperature of propane may be classed as vapor-liquid equilibrium or as gas-liquid solu­ bility depending on the particular range of pressure considered and the par­ ticular worker concerned. The difficulty partly stems from our inability to rigorously distinguish between a gas, a vapor, and a liquid, which has been discussed in numerous textbooks.
    [Show full text]
  • Ideal Gas Law PV = Nrt R = Universal Gas Constant R = 0.08206 L-Atm R = 8.314 J Mol-K Mol-K Example
    Ideal gas law PV = nRT R = universal gas constant R = 0.08206 L-atm R = 8.314 J mol-K mol-K Example: In the reaction of oxygen with carbon to produce carbon dioxide, how many liters of oxygen at 747 mm Hg and 21.0 °C are needed to react with 24.022 g of carbon? CHEM 102 Winter 2011 Practice: In the reaction of oxygen and hydrogen to make water, how many liters of hydrogen at exactly 0 °C and 1 atm are needed to react with 10.0 g of oxygen? 2 CHEM 102 Winter 2011 Combined gas law V decreases with pressure (V α 1/P). V increases with temperature (V α T). V increases with particles (V α n). Combining these ideas: V α n x T P For a given amount of gas (constant number of particles, ninitial = nafter) that changes in volume, temperature, or pressure: Vinitial α ninitial x Tinitial Pinitial Vafter α nafter x Tafter Pafter ninitial = n after Vinitial x Pinitial = Vafter x Pafter Tinitial Tafter 3 CHEM 102 Winter 2011 Example: A sample of gas is pressurized to 1.80 atm and volume of 90.0 cm3. What volume would the gas have if it were pressurized to 4.00 atm without a change in temperature? 4 CHEM 102 Winter 2011 Example: A 2547-mL sample of gas is at 421 °C. What is the new gas temperature if the gas is cooled at constant pressure until it has a volume of 1616 mL? 5 CHEM 102 Winter 2011 Practice: A balloon is filled with helium.
    [Show full text]
  • Chapter 3 3.4-2 the Compressibility Factor Equation of State
    Chapter 3 3.4-2 The Compressibility Factor Equation of State The dimensionless compressibility factor, Z, for a gaseous species is defined as the ratio pv Z = (3.4-1) RT If the gas behaves ideally Z = 1. The extent to which Z differs from 1 is a measure of the extent to which the gas is behaving nonideally. The compressibility can be determined from experimental data where Z is plotted versus a dimensionless reduced pressure pR and reduced temperature TR, defined as pR = p/pc and TR = T/Tc In these expressions, pc and Tc denote the critical pressure and temperature, respectively. A generalized compressibility chart of the form Z = f(pR, TR) is shown in Figure 3.4-1 for 10 different gases. The solid lines represent the best curves fitted to the data. Figure 3.4-1 Generalized compressibility chart for various gases10. It can be seen from Figure 3.4-1 that the value of Z tends to unity for all temperatures as pressure approach zero and Z also approaches unity for all pressure at very high temperature. If the p, v, and T data are available in table format or computer software then you should not use the generalized compressibility chart to evaluate p, v, and T since using Z is just another approximation to the real data. 10 Moran, M. J. and Shapiro H. N., Fundamentals of Engineering Thermodynamics, Wiley, 2008, pg. 112 3-19 Example 3.4-2 ---------------------------------------------------------------------------------- A closed, rigid tank filled with water vapor, initially at 20 MPa, 520oC, is cooled until its temperature reaches 400oC.
    [Show full text]
  • Ideal Gasses Is Known As the Ideal Gas Law
    ESCI 341 – Atmospheric Thermodynamics Lesson 4 –Ideal Gases References: An Introduction to Atmospheric Thermodynamics, Tsonis Introduction to Theoretical Meteorology, Hess Physical Chemistry (4th edition), Levine Thermodynamics and an Introduction to Thermostatistics, Callen IDEAL GASES An ideal gas is a gas with the following properties: There are no intermolecular forces, except during collisions. All collisions are elastic. The individual gas molecules have no volume (they behave like point masses). The equation of state for ideal gasses is known as the ideal gas law. The ideal gas law was discovered empirically, but can also be derived theoretically. The form we are most familiar with, pV nRT . Ideal Gas Law (1) R has a value of 8.3145 J-mol1-K1, and n is the number of moles (not molecules). A true ideal gas would be monatomic, meaning each molecule is comprised of a single atom. Real gasses in the atmosphere, such as O2 and N2, are diatomic, and some gasses such as CO2 and O3 are triatomic. Real atmospheric gasses have rotational and vibrational kinetic energy, in addition to translational kinetic energy. Even though the gasses that make up the atmosphere aren’t monatomic, they still closely obey the ideal gas law at the pressures and temperatures encountered in the atmosphere, so we can still use the ideal gas law. FORM OF IDEAL GAS LAW MOST USED BY METEOROLOGISTS In meteorology we use a modified form of the ideal gas law. We first divide (1) by volume to get n p RT . V we then multiply the RHS top and bottom by the molecular weight of the gas, M, to get Mn R p T .
    [Show full text]
  • Pressure Vs. Volume and Boyle's
    Pressure vs. Volume and Boyle’s Law SCIENTIFIC Boyle’s Law Introduction In 1642 Evangelista Torricelli, who had worked as an assistant to Galileo, conducted a famous experiment demonstrating that the weight of air would support a column of mercury about 30 inches high in an inverted tube. Torricelli’s experiment provided the first measurement of the invisible pressure of air. Robert Boyle, a “skeptical chemist” working in England, was inspired by Torricelli’s experiment to measure the pressure of air when it was compressed or expanded. The results of Boyle’s experiments were published in 1662 and became essentially the first gas law—a mathematical equation describing the relationship between the volume and pressure of air. What is Boyle’s law and how can it be demonstrated? Concepts • Gas properties • Pressure • Boyle’s law • Kinetic-molecular theory Background Open end Robert Boyle built a simple apparatus to measure the relationship between the pressure and volume of air. The apparatus ∆h ∆h = 29.9 in. Hg consisted of a J-shaped glass tube that was Sealed end 1 sealed at one end and open to the atmosphere V2 = /2V1 Trapped air (V1) at the other end. A sample of air was trapped in the sealed end by pouring mercury into Mercury the tube (see Figure 1). In the beginning of (Hg) the experiment, the height of the mercury Figure 1. Figure 2. column was equal in the two sides of the tube. The pressure of the air trapped in the sealed end was equal to that of the surrounding air and equivalent to 29.9 inches (760 mm) of mercury.
    [Show full text]
  • High Blood Pressure: Weight Control
    Sacramento Heart & Vascular Medical Associates February 18, 2012 500 University Ave. Sacramento, CA 95825 Page 1 916-830-2000 Fax: 916-830-2001 Patient Information For: Only A Test High Blood Pressure: Weight Control What is high blood pressure? Blood pressure is the force of blood against artery walls as the heart pumps blood through the body. High blood pressure (hypertension) is blood pressure that keeps being higher than normal. How is high blood pressure affected by weight? One of the most important causes of high blood pressure is overweight. An unhealthy weight puts stress on the heart and lungs, forcing them to work harder. Losing weight reduces the stress on your heart. It can also lower your blood pressure. What can I do to control my weight? Change your eating habits so that you lose 1 to 2 pounds a week until you reach a healthy weight. Even a modest weight loss of 5 to 10 pounds can help. Your diet needs to be low in fat, cholesterol, and salt. Be careful about serving sizes. Don't drink a lot of juice or soda. Also limit the amount of alcohol you drink. A regular, moderate exercise program can help you lose weight or keep a normal weight because it increases your metabolism and burns up calories. It reduces stress and promotes good health. Exercise also lowers your cholesterol and blood sugar levels. Ask your healthcare provider to recommend a diet and exercise program that is right for you. How long will the effects last? If you are overweight and have high blood pressure, you will need to control your blood pressure all of your life.
    [Show full text]
  • The Application of Temperature And/Or Pressure Correction Factors in Gas Measurement COMBINED BOYLE’S – CHARLES’ GAS LAWS
    The Application of Temperature and/or Pressure Correction Factors in Gas Measurement COMBINED BOYLE’S – CHARLES’ GAS LAWS To convert measured volume at metered pressure and temperature to selling volume at agreed base P1 V1 P2 V2 pressure and temperature = T1 T2 Temperatures & Pressures vary at Meter Readings must be converted to Standard conditions for billing Application of Correction Factors for Pressure and/or Temperature Introduction: Most gas meters measure the volume of gas at existing line conditions of pressure and temperature. This volume is usually referred to as displaced volume or actual volume (VA). The value of the gas (i.e., heat content) is referred to in gas measurement as the standard volume (VS) or volume at standard conditions of pressure and temperature. Since gases are compressible fluids, a meter that is measuring gas at two (2) atmospheres will have twice the capacity that it would have if the gas is being measured at one (1) atmosphere. (Note: One atmosphere is the pressure exerted by the air around us. This value is normally 14.696 psi absolute pressure at sea level, or 29.92 inches of mercury.) This fact is referred to as Boyle’s Law which states, “Under constant tempera- ture conditions, the volume of gas is inversely proportional to the ratio of the change in absolute pressures”. This can be expressed mathematically as: * P1 V1 = P2 V2 or P1 = V2 P2 V1 Charles’ Law states that, “Under constant pressure conditions, the volume of gas is directly proportional to the ratio of the change in absolute temperature”. Or mathematically, * V1 = V2 or V1 T2 = V2 T1 T1 T2 Gas meters are normally rated in terms of displaced cubic feet per hour.
    [Show full text]
  • Lecture 6: Entropy
    Matthew Schwartz Statistical Mechanics, Spring 2019 Lecture 6: Entropy 1 Introduction In this lecture, we discuss many ways to think about entropy. The most important and most famous property of entropy is that it never decreases Stot > 0 (1) Here, Stot means the change in entropy of a system plus the change in entropy of the surroundings. This is the second law of thermodynamics that we met in the previous lecture. There's a great quote from Sir Arthur Eddington from 1927 summarizing the importance of the second law: If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equationsthen so much the worse for Maxwell's equations. If it is found to be contradicted by observationwell these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of ther- modynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. Another possibly relevant quote, from the introduction to the statistical mechanics book by David Goodstein: Ludwig Boltzmann who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. There are many ways to dene entropy. All of them are equivalent, although it can be hard to see. In this lecture we will compare and contrast dierent denitions, building up intuition for how to think about entropy in dierent contexts. The original denition of entropy, due to Clausius, was thermodynamic.
    [Show full text]