8.7 Ideal Gas Law When camping, butane is used as a fuel for a portable gas stove. Given the pressure, volume, and temperature of the gas in the tank, we can use the ideal gas law equation to determine the amount of gas present. 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 values in the ideal gas law equation. Calculate mass or volume of a gas in a chemical reaction.

The Ideal Gas Law The ideal gas law is the combination of the four properties used in the measurement of a gas—pressure (P), volume (V), temperature (T), and amount of a gas (n)—to give a single expression, which is written as Ideal Gas Law PV = nRT Core Chemistry Skill Calculating Mass or Volume of a Gas in a Chemical Reaction

R, Ideal Gas Constant Rearranging the ideal gas law equation shows that the four gas properties equal a constant, R. To calculate the value of R, we substitute the STP conditions (273 K, 1 atm) for molar volume into the expression: 1 mole of gas = 22.4 L at STP. Real gases show some deviations in behavior; however, the ideal gas law closely approximates the behavior of real gases at typical conditions.

R, Ideal Gas Constant The value for the ideal gas constant, R, is 0.0821 L atm per mole K. If we use 760 mmHg for the pressure, we obtain another useful value for R of 62.4 mmHg per mole K. In working problems using the ideal gas law, the units of each variable must match the units in the R you select.

Guide to Using the Ideal Gas Equation

Study Check Dinitrogen oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas. What is the pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container?

Solution Dinitrogen oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas. What is the pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container? STEP 1 State the given and needed quantities.

Solution Dinitrogen oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas. What is the pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container? STEP 2 Rearrange the ideal gas law equation to solve for the needed quantity.

Solution Dinitrogen oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas. What is the pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container? STEP 3 Substitute the gas data into the equation and the needed quantity. × ×

R, Unit Summary for Ideal Gas Constant

Gas Laws and Chemical Reactions Gases are involved as reactants and products in many chemical reactions. Typically, the information given for a gas in a reaction is its pressure (P), volume (V), and temperature (T). We can use the ideal gas law equation to determine the moles of a gas in a reaction if we are given the number of moles for one of the gases in a reaction. the moles of any other substance using a mole–mole factor.

Guide to Using the Ideal Gas Law for Reactions

Study Check Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g)  2NH3(g)

Solution Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g)  2NH3(g) STEP 1 State the given and needed quantities.

Solution Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g)  2NH3(g) STEP 2 Write a plan to convert the given quantity to the needed moles. grams Molar moles Mole−mole moles liters of N2 mass of N2 factor of NH3 of NH3 Ideal gas law

Solution Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g)  2NH3(g) STEP 3 Write the equalities for molar mass and mole– mole factors.

Solution Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g)  2NH3(g) STEP 4 Set up the problem to calculate moles of needed quantity. × ×

Solution Nitrogen gas reacts with hydrogen gas to produce ammonia (NH3) gas. How many liters of NH3 can be produced at 0.93 atm and 24 °C from a 16.0-g sample of nitrogen gas and an excess of hydrogen gas? N2(g) + 3H2(g)  2NH3(g) STEP 5 Convert moles of needed quantity to mass or volume using the molar mass or ideal gas law equation. × ×