• Mm Of Helium
• Molecular Weight Helium

Because of helium's relatively low molar (atomic) mass, its thermal conductivity, specific heat, and sound speed in the gas phase are all greater than any other gas except hydrogen. For these reasons and the small size of helium monatomic molecules, helium diffuses through solids at a rate three times that of air and around 65% that of hydrogen. Molar mass of helium = 4 g That means 1 mole have 4 g Or 4g have 1 mole of helium atoms Or 1 g have ¼ mole of helium atoms Or 0.15g have ¼(.15) = 0.375.6.02.10^23 =2.25.10^22 helium atoms.b. If you had 12 dozen helium atoms, what would be their mass? 4.00g/(mol) You can obtain the molar mass of any chemical element by using the periodic table: The molar mass is usually listed underneath the chemical symbol. The units associated with molar mass is grams per mole (g/(mol)). Properties of Various Ideal Gases (at 300 K) Gas: Formula: Molar Mass: Gas constant: Specific Heat at Const. Specific Heat at Const.

The Universal and Individual Gas Constants in fluid mechanics and thermodynamics. Individual gas constant is given for the most common gases.

The Universal and Individual Gas Constants are known from the Ideal Gas Law.

The Individual Gas Constant - R

The Individual Gas Constant depends on the particular gas and is related to the molecular weight of the gas. The value is independent of temperature. The induvidual gas constant, R, for a gas can be calculated from the universal gas constant, R_u (given in several units below), and the gas molecular weight, M_gas:

R = R_u/M_gas [1]

In the imperial system the most common units for the individual gas constant are ft lb/slug ^oR. In the SI system the most common units are J/kg K.

Unit conversion: 1 J/kg K = 5.97994 ft lb/slug °R, and 1 ft lb/slug °R = 0.167226 J/kg K.

The Individual Gas Constant for gases:

For full table - rotate the screen!

Gas		Molecular Weight	Individual Gas Constant - R
Name	Formula	[g/mol], [kg/kmol]	[J/kg K]	[kJ/kg K]	[Wh/(kg K)]	[kcal/(kg K)], [Btu(IT)/lb °F]	[kcal/(lb °F)]	[ft lbf/lb °R]	[ft lbf/slug °R]
Acetylene	C2H2	26.038	319.32	0.3193	0.08870	0.07627	0.0623	59.350	1910
Air	A mixture	28.9647	287.05	0.2871	0.07974	0.06856	0.0560	53.353	1717
Ammonia	NH3	17.031	488.21	0.4882	0.13561	0.11661	0.0952	90.740	2919
Argon	Ar	39.948	208.13	0.2081	0.05781	0.04971	0.0406	38.684	1245
Butane	C4H10	58.122	143.05	0.1431	0.03974	0.03417	0.0279	26.588	855
Butene	C4H8	56.106	148.19	0.1482	0.04116	0.03539	0.0289	27.543	886
Carbon Dioxide	CO2	44.010	188.92	0.1889	0.05248	0.04512	0.0368	35.114	1130
Carbon Monoxide	CO	28.010	296.84	0.2968	0.08246	0.07090	0.0579	55.171	1775
Carbonic acid	H2CO3	62.025	134.05	0.1341	0.03724	0.03202	0.0261	24.915	802
Chlorine	Cl2	70.906	117.26	0.1173	0.03257	0.02801	0.0229	21.794	701
Chloromethane	CH3Cl	50.488	164.68	0.1647	0.04575	0.03933	0.0321	30.608	985
Dichlorofluorumethane	CHCl2F	102.923	80.78	0.0808	0.02244	0.01929	0.0158	15.015	483
Ethane	C2H6	30.069	276.51	0.2765	0.07681	0.06604	0.0539	51.393	1654
Ethene	C2H4	28.053	296.38	0.2964	0.08233	0.07079	0.0578	55.086	1772
Fluorine	F2	37.997	218.82	0.2188	0.06078	0.05226	0.0427	40.670	1309
Helium	He	4.003	2077.1	2.0771	0.57696	0.49610	0.4050	386.047	12421
Hydrogen	H2	2.016	4124.2	4.1242	1.14563	0.98506	0.8043	766.541	24663
Hydrogen bromide	HBr	80.912	102.76	0.1028	0.02854	0.02454	0.0200	19.099	614
Hydrogen chloride	HCl	36.461	228.04	0.2280	0.06334	0.05447	0.0445	42.384	1364
Hydrogen sulfide	H2S	34.081	243.96	0.2440	0.06777	0.05827	0.0476	45.344	1459
Krypton	Kr	83.798	99.22	0.0992	0.02756	0.02370	0.0193	18.441	593
Methane (natural gas)	CH4	16.042	518.28	0.5183	0.14397	0.12379	0.1011	96.329	3099
Neon	Ne	20.180	412.02	0.4120	0.11445	0.09841	0.0803	76.579	2464
Nitrogen	N2	28.013	296.80	0.2968	0.08245	0.07089	0.0579	55.165	1775
Nitrogen dioxide	NO2	46.006	180.73	0.1807	0.05020	0.04317	0.0352	33.590	1081
Nitrogen trifluoride	NF3	71.002	117.10	0.1171	0.03253	0.02797	0.0228	21.765	700
Nitrous oxide	N2O	44.012	188.91	0.1889	0.05248	0.04512	0.0368	35.112	1130
Oxygen	O2	31.999	259.84	0.2598	0.07218	0.06206	0.0507	48.294	1554
Propane	C3H8	44.096	188.56	0.1886	0.05238	0.04504	0.0368	35.045	1128
Propene	C3H6	42.080	197.59	0.1976	0.05489	0.04719	0.0385	36.724	1182
Sulfur dioxide	SO2	64.064	129.78	0.1298	0.03605	0.03100	0.0253	24.122	776
Sulfur hexafluoride	SF6	146.055	56.93	0.0569	0.01581	0.01360	0.0111	10.581	340
Sulfur trioxide	SO3	80.063	103.85	0.1038	0.02885	0.02480	0.0203	19.302	621
Water vapor	H2O	18.015	461.52	0.4615	0.12820	0.11023	0.0900	85.780	2760
Xenon	Xe	131.293	63.33	0.0633	0.01759	0.01513	0.0123	11.770	379

The Universal Gas Constant - R_u

The Universal Gas Constant - R_u - appears in the ideal gas law and can be expressed as the product between the Individual Gas Constant - R - for the particular gas - and the Molecular Weight - M_gas - for the gas, and is the same for all ideal or perfect gases:

R_u = M_gas R [2]

The Universal Constant defined in Terms of the Boltzmann's Constant

The universal gas constant can be defined in terms of Boltzmann's constant k as:

R_u = k N_A [3]

where
k = Boltzmann's constant = 1.381 x 10^-23 [J/K]
N_A = Avogadro Number = 6.022 x 10²³ [1/mol]

The Molecular weight of a Gas Mixture

The average molecular weight of a gas mixture is equal to the sum of the mole fractions of each gas multiplied by the molecular weight of that particular gas:

M_mixture = Σx_i*M_i = (x₁*M₁ + ......+ x_n*M_n) [4]

where

x_i = mole fractions of each gas
M_i = the molar mass of each gas

The Universal Gas Constant - R_u - in alternative Units

• atm.cm³/(mol.K) : 82.057338
• atm.ft³/(lbmol.K) : 1.31443
• atm.ft³/(lbmol.^oR) : 0.73024
• atm.l/(mol.K) : 0.082057338
• bar.cm³/(mol.K) : 83.144598
• bar.l/(mol.K) : 0.083144598
• Btu/(lbmol.^oR) : 1.9872036
• cal/(mol.K) : 1.9859
• erg/(mol.K) : 83144598
• hp.h/(lbmol.^oR) : 0.0007805
• inHg.ft³/(lbmol.^oR) : 21.85
• J/(mol.K) : 8.3144598
  
• kJ/(kmol.K) : 8.3144598
  
• J/(kmol.K) : 8314.472
• (kgf/cm²).l/(mol.K) : 0.084784
• kPa.cm³/(mol.K) : 8314.4598
• kWh/(lbmol.^oR) : 0.000582
• lbf.ft/(lbmol.^oR) : 1545.349
• mmHg.ft³/(lbmol.K) : 999
• mmHg.ft³/(lbmol.^oR) : 555
• mmHg.l/(mol.K) : 62.363577
• Pa.m³/(mol.K) : 8.3144598
• psf.ft³/(lbmol.^oR) : 1545.3465
• psi.ft³/(lbmol.^oR) : 10.73
• Torr.cm³/(mol.K) : 62364

See also:
- More material properties
- The Ideal Gas Law - Gases are highly compressible with changes in density directly related to changes in temperature and pressure.
- A Mixture of Gases - Properties of mixtures of gases.
- More about temperature

Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involves velocity, pressure, density and temperature as functions of space and time
• Gases and Compressed Air - Air, LNG, LPG and other common gas properties, pipeline capacities, sizing of relief valves
• Air Psychrometrics - The study of moist and humid air - psychrometric charts, Mollier diagrams, air-condition temperatures and absolute and relative humidity and moisture content
• Material Properties - Material properties for gases, fluids and solids - densities, specific heats, viscosities and more

Related Documents

• Acetone - Thermophysical Properties - Chemical, physical and thermal properties of acetone, also called 2-propanone, dimethyl ketone and pyroacetic acid. Phase diagram included.
• Air - Molecular Weight and Composition - Dry air is a mixture of gases where the average molecular weight (or molar mass) can be calculated by adding the weight of each component
• Air - Thermophysical Properties - Thermal properties of air - density, viscosity, critical temperature and pressure, triple point, enthalpi and entropi, thermal conductivity and diffusicity, and more
• Benzene - Thermophysical properties - Chemical, physical and thermal properties of benzene, also called benzol. Phase diagram included.
• Dry Air Properties - Dry air properties at temperatures ranging 175 - 1900 K - specific heat, ratio of specific heats, dynamic viscosity, thermal conductivity, Prandtl number, density and kinematic viscosity
• Ethylene - Thermophysical Properties - Chemical, physical and thermal properties of ethylene, also called ethene, acetene and olefiant gas. Phase diagram included.
• Gas Mixture Properties - Special care must be taken for gas mixtures when using the ideal gas law, calculating the mass, the individual gas constant or the density
• Gases - Dynamic Viscosity - Absolute viscosities of gases
• Gases - Molar Specific Heat - Molar specific heats of gases at constant volume
• Humid Air and the Ideal Gas Law - Pressure, temperature and volume for an ideal or perfect gas like air with water vapor - or moist air
• Ideal Gas Law - The relations between volume, pressure, temperature and quantity of a gas, including definition of density of a gas
• Mole Fraction of Water Vapor in Moist Air - Mole fraction of water vapor is the ratio of water molecules - to air and water molecules
• Mollier Diagram for Water-Steam - Enthalpy-entropy diagram for water and steam
• Nitrogen - Enthalpy, Internal Energy and Entropy - Enthalpy, internal energy and entropy of Nitrogen as ideal gas
• Non-ideal gas - Van der Waal's Equation and Constants - Listing of van der Waals constants for more than 200 gases, used to correct for non-ideal behavior of gases caused by intermolecular forces and the volume occupied by the gas particles
• Rankine Efficiency - The efficiency of the Rankine cycle
• Ratios of Specific Heat of Gases - Ratios of specific heat for gases in constant pressure and volume processes
• Sulfur Dioxide Liquid - Thermal Properties - Density, specific heat, thermal conductivity and more
• Temperature - Introduction to temperature - including Celsius, Fahrenheit, Kelvin and Rankine definitions - an online temperature converter
• Thermodynamic Terms, Functions and Relations - Common thermodynamic terms and functions - potential energy, kinetic energy, thermal or internal energy, chemical energy, nuclear energy and more
• Total and partial pressure - Dalton's law of partial pressures - How to calculate total pressure and partial pressures for gas mixtures from Ideal Gas Law

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The Ideal Gas Equation

The ideal gas equation is given by [latex]PV = nRT[/latex].

Learning Objectives

Apply the ideal gas law to solve problems in chemistry

Mm Of Helium

Key Takeaways

Key Points

• An ideal gas exhibits no attractive forces between particles.
• In the ideal gas equation, both pressure and volume are directly proportional to temperature.

Key Terms

• ideal gas constant: R = 8.3145 J·mol-1·K-1
• ideal gas: a gas whose particles exhibit no attractive interactions whatsoever; at high temperatures and low pressures, gases behave close to ideally
• kinetic energy: the energy possessed by an object because of its motion; in Kinetic Gas Theory, the kinetic energy of gas particles is dependent upon temperature only

Kinetic Theory and Ideal Gases

All gases are modeled on the assumptions put forth by the Kinetic Theory of Matter, which assumes that all matter is made up of particles (i.e. atoms or molecules); there are spaces between these particles, and attractive forces become stronger as the particles converge. Particles are in constant, random motion, and they collide with one another and the walls of the container in which they are enclosed. Each particle has an inherent kinetic energy that is dependent upon temperature only.

Translational motion of helium: Real gases do not always behave according to the ideal model under certain conditions, such as high pressure. Here, the size of helium atoms relative to their spacing is shown to scale under 1,950 atmospheres of pressure.

A gas is considered ideal if its particles are so far apart that they do not exert any attractive forces upon one another. In real life, there is no such thing as a truly ideal gas, but at high temperatures and low pressures (conditions in which individual particles will be moving very quickly and be very far apart from one another so that their interaction is almost zero), gases behave close to ideally; this is why the Ideal Gas Law is such a useful approximation.

Ideal Gas Law Introduction: Discusses the ideal gas law PV = nRT, and how you use the different values for R: 0.0821, 8.31, and 62.4.

Ideal Gas Law Equation

The Ideal Gas Equation is given by:

[latex]displaystyle{PV=nRT}[/latex]

The four variables represent four different properties of a gas:

• Pressure (P), often measured in atmospheres (atm), kilopascals (kPa), or millimeters mercury/torr (mm Hg, torr)
• Volume (V), given in liters
• Number of moles of gas (n)
• Temperature of the gas (T) measured in degrees Kelvin (K)

R is the ideal gas constant, which takes on different forms depending on which units are in use. The three most common formulations of R are given by:

[latex]displaystyle{8.3145frac{text{L} cdot text{kPa}}{text{K} cdot text{mol}}=0.0821frac{text{L} cdot text{atm}}{text{K} cdot text{mol}}=62.4frac{text{L} cdot text{mm Hg}}{K cdot text{mol}}}[/latex]

Example 1

A 20 L box contains a fixed amount of gas at a temperature of 300 K and 101 kPa of pressure. How many moles of gas are contained in the box?

[latex]PV=nRT[/latex]

[latex]displaystyle{n=frac{PV}{RT}=frac{text{(101 kPa)(20 L)}}{text{(8.3145 }text{L} cdot text{kPa} cdot K^{-1} cdot text{mol}^{-1}) cdot text{300 K}}=text{0.8 } text{mol}}[/latex]

Example 2

Calculate the number of moles of gas contained within a bouncy house with a volume of 20.63 cubic meters, a temperature of 300 Kelvin, and a pressure of 101 kPa.

[latex]displaystyle{PV=nRT}[/latex]

[latex]displaystyle{frac{PV}{RT}=n cdot n=frac{101text{ kPa} cdot (20.63text{ cubic meters})}{(8.3143text{ J/mol}) cdot K(300K)} cdot n=835.34text{ mols}}[/latex]

The ideal gas equation enables us to examine the relationship between the non-constant properties of ideal gases (n, P, V, T) as long as three of these properties remain fixed.

For the ideal gas equation, note that the product PV is directly proportional to T. This means that if the gas’ temperature remains constant, pressure or volume can increase as long as the complementary variable decreases; this also means that if the gas’ temperature changes, it may be due in part to a change in the variable of pressure or volume.

The ideal gas equation is a valuable tool that can give a very good approximation of gases at high temperatures and low pressures.

Interactive: Pressure Equilibrium: There are gases on both sides of a moveable barrier (piston), which stays in the same place (more or less) when you run the model because the gas pressure on the piston is in equilibrium. Add purple gas molecules and watch what happens to the piston. Reset the model. Now add yellow gas molecules. What happens to the piston? Try heating or cooling the gas molecules. Explain the change in equilibrium with each change. Which has a greater effect on equilibrium — changing the number of gas molecules or changing the temperature? Why?

Interactive: The Temperature-Pressure Relationship: Explore the relationship between the temperature of a gas and the pressure it exerts on its container.

Density Calculations

Molecular Weight Helium

A reformulation of the Ideal Gas Equation involving density allows us to evaluate the behaviors of ideal gases of unknown quantity.

Learning Objectives

Apply the reformulated Ideal Gas Equation in your calculations

Key Takeaways

Key Points

• Density calculations allow us to evaluate the behaviors of gases of unknown volume.
• We can determine the density of an ideal gas using knowledge of three properties of the evaluated ideal gas.
• This reformulation of the Ideal Gas Equation relates pressure, density, and temperature of an ideal gas independent of the volume or quantity of gas.

Key Terms

• density: a measure of the amount of matter contained by a given volume

The Ideal Gas Equation in the form [latex]PV=nRT[/latex] is an excellent tool for understanding the relationship between the pressure, volume, amount, and temperature of an ideal gas in a defined environment that can be controlled for constant volume. However, in its most common form, the Ideal Gas Equation is not useful for examining the behavior of gases of undetermined volume, such as the gases in the clouds that surround the stars in our solar system or the atmospheric gases that support life on our planet.

Astronomical applications of the Ideal Gas Law: The Taurus Molecular Cloud consists of dust and various gases, including hydrogen and helium. The density form of the Ideal Gas Equation may be of theoretical use when studying such astronomical phenomena as star formation.

To derive a form of the ideal gas equation that has broader applications, we can use calculations that employ the physical property of density.

Atmosphere composition: Atmospheric science offers one plausible real-life application of the density form of the ideal gas equation. Earth’s atmosphere is composed of gases that support life—as the image shows, oxygen involved in the water cycle, sulfur emissions from oceans, methane from agriculture, and more. The density form of the Ideal Gas Law enables us to study the behavior of these gases without enclosing them in a container of known volume.

Derivation of the Volume-Independent Ideal Gas Law

We know the Ideal Gas Equation in the form [latex]PV=nRT[/latex]. We also know that:

[latex]n=text{# moles of gas}=frac{text{mass of gas (m)}}{text{molecular weight (M)}}=frac{m}{M}[/latex]

If we substitute [latex]frac{m}{M}[/latex] for n:

[latex]PV= frac{m}{M}RT[/latex]

Rearranging the above equation, we get:

[latex]frac{P}{RT}=frac{m}{MV}[/latex]

Now, recall that density is equal to mass divided by volume:

[latex]D=frac{m}{V}[/latex]

The term [latex]frac{m}{V}[/latex] appears on the right-hand side of the above rearranged Ideal Gas Law. We can substitute in density, D, and get the following:

[latex]frac{P}{RT}=frac{D}{M}[/latex]

Rearranging in terms of D, we have:

[latex]D=frac{MP}{RT}[/latex]

This derivation of the Ideal Gas Equation allows us to characterize the relationship between the pressure, density, and temperature of the gas sample independent of the volume the gas occupies; it also allows us to determine the density of a gas sample given its pressure and temperature, or determine the molar mass of a gas sample given its density.

Ideal Gas Law Practice Problems with Density – YouTube: Instead of using the regular ideal gas equation, PV=nRT, we use a transformed version (D=PM/RT) to solve a problem with density and molar mass.

Molar Mass of Gas

We can derive a form of the Ideal Gas Equation, PV=nRT, that incorporates the molar mass of the gas (M, [latex]g*mol^{-1}[/latex] ).

Learning Objectives

Apply knowledge of molar mass to the Ideal Gas Law

Key Takeaways

Key Points

• The molecular weight ( molar mass ) of any gas is the mass of one particle of that gas multiplied by Avogadro’s number (6.02 x 10²³).
• Knowing the molar mass of an element or compound can help us stoichiometrically balance a reaction equation.
• The average molar mass of a mixture of gases is equal to the sum of the mole fractions of each gas (x_i) multiplied by the molar mass (M_i) of that particular gas: [latex]bar { M} =sum _{ i }^{ }{ { x }_{ i }{ M }_{ i } }[/latex].

Key Terms

• ideal gas: a hypothetical gas whose molecules exhibit no interaction and undergo elastic collision with each other and with the walls of the container
• molar mass: the mass of one mole of an element or compound
• stoichiometry: the study and calculation of quantitative (measurable) relationships of the reactants and products in chemical reactions (chemical equations)

Molar Mass of Gases and Gas Mixtures

Molar mass (M) is equal to the mass of one mole of a particular element or compound; as such, molar masses are expressed in units of grams per mole (g mol^–1) and are often referred to as molecular weights. The molar mass of a particular gas is therefore equal to the mass of a single particle of that gas multiplied by Avogadro’s number (6.02 x 10²³ ). To find the molar mass of a mixture of gases, you need to take into account the molar mass of each gas in the mixture, as well as their relative proportion.

The average molar mass of a mixture of gases is equal to the sum of the mole fractions of each gas, multiplied by their respective molar masses:

[latex]bar { M} =sum _{ i }^{ }{ { x }_{ i }{ M }_{ i } }[/latex]

The molar volumes of all gases are the same when measured at the same temperature and pressure (22.4 L at STP), but the molar masses of different gases will almost always vary.

Calculating Molar Mass using the Ideal Gas Equation

The molar mass of an ideal gas can be determined using yet another derivation of the Ideal Gas Law: [latex]PV=nRT[/latex].

We can write n, number of moles, as follows:

[latex]n=frac{m}{M}[/latex]

where m is the mass of the gas, and M is the molar mass. We can plug this into the Ideal Gas Equation:

[latex]PV=left(frac{m}{M}right)RT[/latex]

Rearranging, we get:

[latex]frac{PV}{RT}=frac{m}{M}[/latex]

Finally, putting the equation in terms of molar mass, we have:

[latex]M=frac{mRT}{PV}[/latex]

This derivation of the Ideal Gas Equation is useful in determining the molar mass of an unknown gas.

Example

• An unknown gas with a mass of 205 g occupies a volume of 20.0 L at standard temperature and pressure. What is the molar mass of the gas?
• [latex]M=frac{mRT}{PV}[/latex]

[latex]M=frac{(205)(0.0821)(273)}{(1.0)(20.0)}=230frac{g}{mol}[/latex]

Ideal Gas Law Practice Problems with Molar Mass – YouTube: How to set up and solve ideal gas law problems that involve molar mass and converting between grams and moles.