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Ideal Gas Constant R

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Understanding the Ideal Gas Constant (R)



The Ideal Gas Law is a fundamental equation in chemistry and physics, describing the behavior of ideal gases. An ideal gas is a theoretical gas composed of randomly moving point particles that do not interact except for perfectly elastic collisions. While no real gas perfectly behaves as an ideal gas, many gases approximate this behavior under certain conditions (low pressure and high temperature). Central to the Ideal Gas Law is the Ideal Gas Constant, denoted by 'R', which acts as a proportionality constant linking the pressure, volume, temperature, and amount of the gas. Understanding R is crucial for accurately predicting and interpreting the behavior of gases in various applications.

1. The Ideal Gas Law and the Derivation of R



The Ideal Gas Law is mathematically expressed as:

PV = nRT

Where:

P represents the pressure of the gas (typically in Pascals, Pa)
V represents the volume of the gas (typically in cubic meters, m³)
n represents the amount of substance (number of moles, mol)
T represents the absolute temperature of the gas (typically in Kelvin, K)
R is the Ideal Gas Constant

The value of R depends on the units used for pressure, volume, and temperature. It's derived from experimental observations and combines several fundamental physical constants. One common derivation involves combining Avogadro's Law, Boyle's Law, and Charles's Law, which individually describe the relationship between two of the variables (pressure, volume, temperature) while keeping the others constant. The combination of these laws yields the Ideal Gas Law and reveals the constant of proportionality, R.

2. Values and Units of the Ideal Gas Constant



The Ideal Gas Constant, R, has numerous values depending on the units employed. The most commonly used values include:

8.314 J/(mol·K): This value uses Joules (energy) for pressure-volume work, moles for amount of substance, and Kelvin for temperature. It's particularly useful in thermodynamic calculations.

0.0821 L·atm/(mol·K): This value uses Liters for volume, atmospheres for pressure, moles for amount of substance, and Kelvin for temperature. This is commonly used in chemistry calculations where volume is measured in liters and pressure in atmospheres.

62.36 L·torr/(mol·K): This value utilizes Torr (a unit of pressure) and Liters for volume.

The choice of which value to use depends entirely on the units used in the given problem. It's crucial to maintain consistency in units throughout the calculation. Using the wrong value of R will lead to an incorrect answer.

3. Applications of the Ideal Gas Constant



The Ideal Gas Constant plays a vital role in numerous scientific and engineering applications. These include:

Determining the molar mass of a gas: By knowing the pressure, volume, temperature, and mass of a gas sample, we can use the Ideal Gas Law to calculate the molar mass (grams per mole).

Calculating gas density: Gas density (mass per unit volume) can be calculated using the Ideal Gas Law and the molar mass of the gas.

Predicting the behavior of gases in chemical reactions: Stoichiometric calculations involving gases often rely on the Ideal Gas Law to relate the volume of gas produced or consumed to the number of moles.

Understanding atmospheric processes: Meteorology utilizes the Ideal Gas Law to model atmospheric pressure, temperature, and humidity.

Designing and analyzing industrial processes: Chemical engineers use the Ideal Gas Law in designing and optimizing various industrial processes involving gases, such as combustion engines, refrigeration systems, and gas pipelines.

Example: A 2.00 L container holds 0.500 moles of nitrogen gas at 25°C. What is the pressure of the gas in atmospheres?

We use the Ideal Gas Law and the appropriate value of R:

PV = nRT

P = nRT/V = (0.500 mol) (0.0821 L·atm/(mol·K)) (25 + 273 K) / (2.00 L) ≈ 5.64 atm


4. Limitations of the Ideal Gas Law and R



The Ideal Gas Law is an approximation. Real gases deviate from ideal behavior, particularly at high pressures and low temperatures. At high pressures, the gas molecules are closer together, and intermolecular forces become significant. At low temperatures, the kinetic energy of the molecules is reduced, making intermolecular attractions more influential. The van der Waals equation is an example of a more complex equation that accounts for these deviations. In such scenarios, using the Ideal Gas Law with R can lead to significant errors.


5. Summary



The Ideal Gas Constant (R) is a fundamental constant that links the pressure, volume, temperature, and amount of an ideal gas. Its value depends on the units used, and selecting the correct value is essential for accurate calculations. The Ideal Gas Law, using R, has widespread applications in various fields, from predicting the behavior of gases in chemical reactions to understanding atmospheric phenomena and designing industrial processes. However, it's crucial to remember that the Ideal Gas Law is an approximation, and deviations from ideal behavior occur, especially at extreme conditions.


FAQs



1. What happens to the value of R if I change the units of pressure or volume? The value of R changes proportionally to reflect the new units. Different units require a different numerical value for R to maintain the consistency of the Ideal Gas Law.

2. Can I use the Ideal Gas Law for all gases under all conditions? No. The Ideal Gas Law is an approximation, and it works best for gases at low pressures and high temperatures where intermolecular forces are negligible. Real gases deviate significantly from ideal behavior at high pressures and low temperatures.

3. How is the Ideal Gas Constant related to Avogadro's number? Avogadro's number (6.022 x 10²³ particles/mol) is implicitly incorporated into the derivation of R. R essentially represents the average kinetic energy of a single molecule times Avogadro's number.

4. Why is the temperature always in Kelvin in the Ideal Gas Law? The Kelvin scale is an absolute temperature scale, meaning it starts at absolute zero (0 K), the theoretical point at which all molecular motion ceases. Using Kelvin ensures the direct proportionality between temperature and kinetic energy in the Ideal Gas Law.

5. What are some real-world examples where the Ideal Gas Law is used? The Ideal Gas Law is used in weather forecasting, designing internal combustion engines, analyzing the behavior of gases in chemical plants, and determining the molar mass of unknown gases in laboratory settings.

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IDEAL AND REAL GAS LAWS - University of Colorado Colorado … The ideal gas law constant, R, dictates the units of pressure, volume and temperature. The most common used value for R when dealing with gases is 0.0821 L . atm/mol K.

Experiment 14 - Calculation of the Ideal Gas Constant - Alameda This constant, R, is called the ideal gas constant. The resulting equation is the familiar ideal gas law: PV = nRT Eq 1 The object of the present experiment is to measure R using a sample of hydrogen gas, H2. To do this, we must simultaneously measure P, V, T, and n. The value of R can then be calculated and compared with the accepted value of ...

Universal Gas Constant: R - Active Learner Universal Gas Constant: R Units R atm.cc / g-mole, K 82.06 BTU / lb-mole. R 1.987 psia.cu ft / lb-mole. R 10.73 ... mm Hg, liters / g-mole. K 62.37 in. Hg.cu ft /lb-mole. R 21.85 cal / g-mole. K 1.987 kPa.m3 / kg-mole. K 8.314 J / kg-mole. K 8314. Title: Microsoft PowerPoint - Geol and Res Prop_part 5 hydrocarbon.pptx Author: kvalverde ...

The Ideal Gas Constant - Pennsylvania State University The ideal gas law in terms of R is PmRTV , where P is the absolute pressure of the gas, V is the volume occupied by the gas, m is the mass of the gas, and T is the absolute temperature of the gas.

The Ideal Gas Constant - Anasayfa Universal gas constant and ideal gas law • The universal gas constant (R u) is, as its name implies, universal, i.e. the same regardless of the gas being considered. • The ideal gas law in terms of R u is where P is the absolute pressure of the gas, V is the volume occupied by the gas, n is the number of mols of the gas, and T is the ...

Eight Methods for Determining R in the Ideal Gas Law - arXiv.org Sections 1 through 4 of this essay discuss the ideal gas law of physics and chemistry and how researchers have determined the numerical value of the “parameter” of the law—the parameter known formally as the molar gas con-stant (also called the “universal” gas constant, or simply the “gas constant”) and generally represented as R.

Ideal Gas Laws - phys.ufl.edu 2 gas at 20 C has a pressure of 100 atmos. What is the mass of N 2 in the cylinder? m=M (PV/RT) M is the molecular weight =28kg/kmole . R = 83100 J/kmole K . Calculate m = 12 grams. You can determine how much gas is in cylinder by weighing it. (Need to know empty weight of cylinder.)

Gas Laws: Determination of Gas Constant R - interchemnet.com Gas Laws: Determination of Gas Constant R Learning Goals: 1. Use a chemical reaction to generate and collect oxygen, O2, gas over water. 2. Use Dalton's Law of Partial Pressures to determine the pressure of oxygen gas collected. 3. Use the ideal gas law, PV = nRT, to calculate the Gas Constant R. (Assuming O2 is an Ideal Gas) Abstract:

TABLE A-2—UNIVERSAL GAS CONSTANT FOR DIFFERENT … Most gases at low pressure follow the ideal-gas law. Application of the ideal-gas law results in two useful engineering approxima-tions. First, the standard molar volume representing the volume oc-cupied by one mole of gas at standard conditions is independent of the gas composition. gv g sc v g V sc n RT sc p 10.73146(60 459.67) 14.7 379.4 ...

Ideal Gas Equation of State - Simon Fraser University Since R is a constant for a gas, one can write: where subscripts 1 and 2 denote two states of an ideal gas. Note that the constant R is different for each gas; see Tables A1 and A2 in Cengel book. where / is the molar specific volume. That is the volume per unit mole. Ru = 8.314 kJ / (kmol. K) is the universal gas constant, R = Ru /M.

VALUES OF THE GAS CONSTANT IN DIFFERENT UNIT … This table gives the appropriate value of R for use in the ideal gas equation, PV = nRT, when the variables are expressed in other units. The following conversion factors for pressure units were used in generating the table:

PROPERTY TABLES AND CHARTS (ENGLISH UNITS) - Wright … 10.732 psia·ft3/lbmol·R is the universal gas constant and M is the molar mass. Source: Specific heat values are mostly obtained from the property routines prepared by The National Institute of Standards and Technology (NIST), Gaithersburg, MD. *Sublimation temperature.

THE IDEAL GAS CONSTANT AND THE MOLAR VOLUME OF … In this experiment you will determine both, the numerical value of the ideal gas constant R using the ideal gas law and the molar volume of hydrogen gas at STP.

The Universal Gas Constant R - University of Notre Dame The Universal Gas Constant R by William B. Jensen Question Why is the universal gas constant in PV = nRT represented by the letter R? Donald R. Paulson Department of Chemistry California State University Los Angeles, CA 90032 Answer This is best answered by tracing the origins of the ideal gas law itself. One of the first persons to combine ...

LECT05. Ideal Gas Calculations - Che 31. Introduction to … What is an ideal gas? An ideal gas is an imaginary gas that obeys exactly the following relationship: PV = nRT where P = absolute pressure of the gas V = total volume occupied by the gas n = number of moles of the gas R = ideal gas constants in appropriate units T = absolute temperature of the gas

Contents Chapter 2: Revision 2.3 The Ideal Gas Law and Water … 5.The ideal gas equation applies to partial pressures as well as total pressure, P . The partial pressure of the dry part of the air is P e where e is the vapour pressure. Use this to work out an equation for total density, r = r d + r v in terms of e, P , T , R d and e ( rst work out r d and r v) r d = (P e)M d R T; r v = eM w R T = ) r = (P e ...

The Ideal Gas Law Lecture 2: Atmospheric Thermodynamics Gas Constant The ideal gas law can be applied to the combination of atmospheric gases or to individual gases. The value of gas constant for the particular gas under consideration depends on its molecular weight: R gas = R* / M gas where R* = universal gas constant = 8314.3 J deg-1 kg-1 The gas constant for dry atmospheric air is: R air = R* / M

Thermodynamics - Basic Concepts - Durham College The ideal gas law is: pV = nRT, where n is the number of moles, and R is universal gas constant. The value of R depends on the units involved, but is usually stated with S.I. units as: R = 8.314 J/mol·K. For air, one mole is 28.97 g (=0.02897 kg), so we can do …

VALUES OF THE GAS CONSTANT IN DIFFERENT UNIT … VALUES OF THE GAS CONSTANT IN DIFFERENT UNIT SYSTEMS In SI units the value of the gas constant, R, is: R = 8.314472 Pa m3 K-1 mol = 8314.472 Pa L K-1 mol = 0.08314472 bar L K-1 mol This table gives the appropriate value of R for use in the ideal gas equation, PV = nRT, when the variables are expressed in other units.

Thermodynamics Heat Content and the First Law (Mostly of Ideal … Ideal Gas: Diluted ensemble of N structure-less, independent particles with macroscopic, observable properties described by an Equation of State. When enclosed in a container of volume V, IG exerts a measurable pressure p on the container walls. = capacity to perform work w.