Elements
Gases
The relations known as Boyle's law, Charles' law, and Avogadro's law can be combined into an exceedingly useful formula called the
Ideal Gas Equation,
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where R denotes the gas constant:
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The temperature is, as always in gas equations, measured in Kelvin.
This formula is strictly valid only for ideal gases—those in which the molecules are far enough apart so intermolecular forces can be neglected. At high pressures, such forces cause significant departure from the Ideal Gas Equation, and more complicated equations have been devised to treat such cases. The Ideal Gas Equation, however, gives useful results for most gases at pressures less than 100 atmospheres.
The conditions of 0° C temperature and 1 atm pressure may easily be produced in the laboratory; such conditions are called standard temperature and pressure ( STP).Because the properties of gases vary with both temperature and pressure, many published values are for gases at STP. Note that room temperature differs from standard temperature.
Use the Ideal Gas Equation to calculate the volume of 1 mole of gas at STP:
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This is the value stated in the carbon dioxide reaction; you were asked to memorize that 1 mole of any gas occupies 22.40 liters at STP.
You should be able to use the Ideal Gas Equation to determine any one of the four quantities—pressure, volume, moles, or temperature—if you are given values for the other three.
One important application is to deduce the molecular weight and formula for a gas. Assume you know that the hydrocarbon propylene is, by weight, 85.6% carbon and 14.4% hydrogen. Then the atomic ratios of the compound are
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Therefore, the propylene molecule is some integral multiple of CH2: it can be CH2 or C2H4 or C3H6 or a yet larger molecule. Measuring the volume of 10 grams of propylene at STP yields 5.322 liters, which you can use to calculate its molecular weight.
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Because the atomic weights of 1 CH2 unit add to 14.03, the molecule contains 3 such units. Consequently, the molecular formula for propylene is C3H6.
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Problem 1: What is the volume occupied by 1 kilogram of carbon monoxide at 700° C and 0.1 atm?
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Problem 2: The ozone molecule contains only oxygen atoms. Determine the molecular formula of ozone given that 2.3 grams occupies 1,073 milliliters at standard temperature and pressure.
