What would be the value for the ideal gas constant R if pressure P is in kilopascals temperature T is in Kelvins volume V is in liters and amount of gas n is in moles?

Ideal gas equation

The equation of state refers to a fixed mass of gas. From Avogadro's law we know that the same volume of all gases contain the same number of moles and from this, it follows that the volume is proportional to the number of moles.

Volume ∝ number of moles (n)

These two equations can be combined to obtain an expression involving all the quantities:

After rearrangement, for 'n' moles of gas the proportionality constant is called the Universal Gas Constant and is given the symbol 'R'

This gives the ideal gas equation:

Ideal Gas Equation: PV = nRT

where:

P = pressure in Pa
V = volume in m3
n = number of moles of gas
R = Universal Gas constant = 8.314 JK-1mol-1
T = the absolute temperature in Kelvin

It is often more convenient to express the pressure in kPa and the volume in litres (dm3). This leaves the value of R the same (see below).

Example: Calculate the number of moles of gas present in 2.6 dm3 at a pressure of 1.01 x 105 Pa and 300 K.

PV = nRT

2.6 dm3 = 0.0026 m3

0.0026 x 1.01 x 105 = n x 8.314 x 300

n = 0.0026 x 1.01 x 105 / 8.314 x 300

n = 0.105 moles

There are several units used for gas volume, gas pressure and temperature. It is important to be consistent with the use of units when carrying out gas law calculations. The Syllabus states that SI units will be used wherever possible.

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Universal gas constant - R

Although called "Universal", its value depends on the units used for P, V and T.

With the SI units of metres, kilograms, Kelvin and Joules, using P, V and T values at STP gives:

	PV=nRT
therefore:	R=PV/nT
for 1 mole of gas at STP (using accepted values of P = 1.00 x 105 Pa, V = 0.02271 m3, T = 273.15 K)
R =	(1.00 x 105) x 0.02271)/273.15
R =	8.314 J K-1 mol-1

In chemistry, the units of volume used are the decimetre cubed (dm3) and pressure in kiloPascals (kPa), so one unit is 100x greater and the other 100x smaller than the SI equivalent. Consequently the differences in the product, PV, both cancel out (multiplying AND dividing by 1000), so that the final value for R is the same as in SI units.

The Universal gas constant, R, calculated using atmospheres Pressure and volume in litres, then:

	PV=nRT
	R=PV/nT
at STP:	P = 1 atm, V = 22.7 dm3, T = 273
	n = 1
	R = 0.0821 dm3 atm mol-1 K-1

There are, of course, several other values of R as there are many ways of measuring both the volume and the pressure of a gas. .

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SI units and 'R'

The SI units of P, V and T give rise to the previously used value for the universal gas constant, R = 8.314 J K-1 mol-1.

How does this happen when chemists do not use these SI units?

Remember:

1 litre = 1 dm3 = 1000 cm3

Consequently, if litres are used in the Ideal Gas equation then the pressure units must also be divided by 1000 (as PV = constant). Pressure is measured in Pa or Nm-1, and so the unit of the kPa correct for the difference in volume units.

Atmospheric pressure in Pa = 1.00 x 105 Pa

Atmospheric pressure in kPa = 1.00 x 102 kPa

Provided that you are consistent with the application of units there will be no problem. It is always a good idea when carrying out calculations to look at the value of your answer and ask yourself, "does it seem reasonable?"

The IBO is consistent with the use of litres (dm3) and kPa in gas law questions.

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Page 3

This section covers the behaviour of pure and mixtures of ideal gases. Chemical reactions involving gases are required.

Understandings

Reactants can be either limiting or excess.

Avogadro's law enables the mole ratio of reacting gases to be determined from volumes of the gases.

The molar volume of an ideal gas is a constant at specified temperature and pressure.

Applications and skills

Calculation of reacting volumes of gases using Avogadro's law.

Solution of problems and analysis of graphs involving the relationship between temperature, pressure and volume for a fixed mass of an ideal gas.

Solution of problems relating to the ideal gas equation.

Explanation of the deviation of real gases from ideal behaviour at low temperature and high pressure.

Obtaining and using experimental values to calculate the molar mass of a gas from the ideal gas equation.

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Kinetic theory of gases

Gas particles, in common with all particles, are in constant motion. Gases are substances in which the force of attraction between the particles has been overcome by their energetic motion. The gas particles can simply no longer be held together by attractive forces.

As the particles fly around at high speed, they collide many times per second with each other and with the walls of any container. If the container has no walls, the gas particles spread out to fill all the available space.

To deal with gases in chemistry some assumptions are made:

1
The gas particles themselves occupy no volume.
2
The forces of attraction between particles are so small as to be negligible.
3

Collisions involving gas particles are perfectly elastic.

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Gas volume

In chemistry, volumes are usually measured in litres (decimetres cubed, dm3) and centimetres cubed (cm3), rather than metres cubed (m3). The reason for this is purely practical, the metre cubed is a very large volume compared to the test tubes and flasks used in laboratories. See apparatus, section 1.62.

Gas volumes may be quoted in metres cubed (m3), litres (L), centimetres cubed (cm3) or millilitres (mL), depending on the textbook consulted.

1m3 (1 metre cubed) = 1000 dm3 (1000 decimetres cubed) = 1,000,000 cm3 (1 million centimetres cubed)

1 decimetre cubed (1 dm3) is also called 1 litre (= 1000 cm3)

1 centimetre cubed (cm3) is also called 1 millilitre (mL) as it is 1/1000 of a litre.

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Conversion between volume units

To convert from cm3 or ml to dm3 or litres divide by 1000

To convert from dm3 or litres to cm3 or ml multiply by 1000

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Gas pressure

The pressure of a gas is caused by the gas particles colliding with the walls of the container. Each small collision exerts a force on the wall. The sum of these forces over an area of the wall is called the gas pressure. The SI unit of force is the Newton and the unit for area is the metre squared (m2). Pressure is measured in Newtons per metre squared = Nm-2. This combined unit is called the Pascal, Pa.

1 Nm-2 = 1 Pa

The Pascal is a fairly small quantity and atmospheric pressure = 100.0 kPa (approximately) - this is the value used for gas calculations in the IB chemistry exams.

Note: In SI units the atmospheric pressure = 100.0 kPa = 1.00 x 105 Pa. Older measurements for pressure may be encountered in textbooks, for example: mmHg (Torr), where atmospheric pressure = 760 mmHg (Torr). However, the IB is fairly consistent with the use of kPa as a pressure measurement.

Conversion of pressure units

1000 Pa = 1 kPa

To convert from Pa into kPa divide by 1000

To convert from atm (atmospheres) to kPa multiply by 100

To convert from kPa to atmospheres divide by 100

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Temperature

The SI unit of temperature is the kelvin (K), although problems are often set in degrees Celsius (ºC). It is important to ALWAYS carry out gas calculations using absolute (kelvin) temperature values.

0K is called absolute zero. It is the temperature at which particles have no energy. This temperature is equal to -273.16ºC, approximated to -273ºC. The magnitude of 1 kelvin is the same as that of 1º Celsius, therefore;

0K = -273ºC

273K = 0ºC

373K = 100ºC

Conversion of temperature units

To convert from degrees Celsius to Kelvin add 273

To convert from Kelvin to degrees Celsius subtract 273

Absolute temperature in Kelvin = degrees Celsius + 273

Temperature in degrees Celsius = Absolute temperature in Kelvin - 273

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