© 2014 pearson education, inc. chapter 11 gases 11.8 the ideal gas law learning goal use the ideal...
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© 2014 Pearson Education, Inc.
Chapter 11 Gases11.8 The Ideal Gas Law
Learning Goal Use the ideal gas law equation to solve for P, V, T, or n of a gas when given three of the four variables in the ideal gas law equation. Calculate density, molar mass, or volume of a gas in a chemical reaction.
Chapter 11 Lecture
Basic ChemistryFourth Edition
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The ideal gas law is a combination of the four properties (P, V, n, and T), written as a single expression: PV = nRT.
Rearranging the ideal gas law equation shows that the four properties are equal to the gas law constant, R, equal to 0.0821 L atm per mol K.
The Ideal Gas Law PV = nRT
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Using a different unit for pressure, 760 mmHg, gives us another value for R, 62.4 L mmHg, per mol K.
The Ideal Gas Law
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Guide to Using the Ideal Gas Law
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How many moles of N2 gas are present if the sample occupies 215 mL at 0.813 atm and 30.0 °C?
Learning Check
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How many moles of N2 gas are present if the sample occupies 215 mL at 0.813 atm and 30.0 °C?Step 1 State the given and needed
quantities.
P V n R T
Given 0.813 atm 0.215 L 0.0821 L atmK mol
30.0 °C + 273 = 303 K
Need ? moles
Solution
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How many moles of N2 gas are present if the sample occupies 215 mL at 0.813 atm and 30.0 °C?Step 2 Rearrange the ideal gas law
equation to solve for the needed quantity.
Solution
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How many moles of N2 gas are present if the sample occupies 215 mL at 0.813 atm and 30.0 °C?Step 3 Substitute the gas data into the
equation and calculate the needed quantity.
Solution
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Butane, C4H10, is used as fuel for barbeques and as an aerosol propellant. If you have 108 mL of butane at 715 mmHg and 25 °C, what is the mass, in grams, of butane?
Learning Check
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Given 108 mL of butane, C4H10, at 715 mmHg and 25 °C, what is the mass, in grams, of C4H10?Step 1 State the given and needed quantities.
P V n R T
Given 715 mmHg 108 mL(0.108 L)
62.4 L mmHgK mol
25 °C + 273 = 298 K
Need ? moles
Solution
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Given 108 mL of butane, C4H10, at 715 mmHg and 25 °C, what is the mass, in grams, of C4H10?Step 2 Rearrange the ideal gas law equation to
solve for the needed quantity.
moles of C4H10 Molar MassMolar Mass grams of C4H10
Solution
© 2014 Pearson Education, Inc.
Given 108 mL of butane, C4H10, at 715 mmHg and 25 °C, what is the mass, in grams, of C4H10?Step 3 Substitute the gas data into the
equation and calculate the needed quantity.
Solution
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Another use of the ideal gas law is to determine the molar mass of a gas. Dividing the mass of gas by the moles of gas gives the molar mass of the gas.
Given the mass, in grams, of gas, we can calculate the number of moles of the gas using the ideal gas law equation.
Molar Mass of a Gas
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Guide to Calculating the Molar Mass of a Gas
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What is the molar mass, in grams per mole, of a 3.16-g sample of gas at 0.750 atm and 45 °C, that occupies a volume of 2.05 liters?
Learning Check
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What is the molar mass, in grams per mole, of a3.16-g sample of gas at 0.750 atm and 45 °C,
that occupies a volume of 2.05 liters?Step 1 State the given and needed
quantities.
P V n R T
Given 0.750 atm 2.05 L mass = 3.16 g
0.0821 L atmK mol
45 °C + 273 = 318 K
Need ? moles
Solution
© 2014 Pearson Education, Inc.
What is the molar mass, in grams per mole, of a 3.16-g sample of gas at 0.750 atm and 45 °C, that occupies a volume of 2.05 liters?Step 2 Rearrange the ideal gas law equation
to solve for the number of moles.
Solution
© 2014 Pearson Education, Inc.
What is the molar mass, in grams per mole, of a3.16-g sample of gas at 0.750 atm and 45 °C,
that occupies a volume of 2.05 liters?Step 2 Rearrange the ideal gas law equation
to solve for the number of moles.
Solution
© 2014 Pearson Education, Inc.
What is the molar mass, in grams per mole, of a3.16-g sample of gas at 0.750 atm and 45 °C,
that occupies a volume of 2.05 liters?Step 3 Obtain the molar mass by dividing
the given number of grams by the number of moles.
Solution