By the end of this section, you will be able to:
To this point, four separate laws have been discussed that relate pressure, volume, temperature, and the number of moles of the gas:
Combining these four laws yields the ideal gas law, a relation between the pressure, volume, temperature, and number of moles of a gas: [latex]\large PV=nRT[/latex] where P is the pressure of a gas, V is its volume, n is the number of moles of the gas, T is its temperature on the kelvin scale, and R is a constant called the ideal gas constant or the universal gas constant. The units used to express pressure, volume, and temperature will determine the proper form of the gas constant as required by dimensional analysis, the most commonly encountered values being 0.08206 L atm mol–1 K–1 and 8.314 J L mol–1 K–1. Gases whose properties of P, V, and T are accurately described by the ideal gas law (or the other gas laws) are said to exhibit ideal behavior or to approximate the traits of an ideal gas. An ideal gas is a hypothetical construct that may be used along with kinetic molecular theory to effectively explain the gas laws as will be described in a later module of this chapter. Although all the calculations presented in this module assume ideal behavior, this assumption is only reasonable for gases under conditions of relatively low pressure and high temperature. In the final module of this chapter, a modified gas law will be introduced that accounts for the non-ideal behavior observed for many gases at relatively high pressures and low temperatures. The ideal gas equation contains five terms, the gas constant R and the variable properties P, V, n, and T. Specifying any four of these terms will permit use of the ideal gas law to calculate the fifth term as demonstrated in the following example exercises. Methane, CH4, is being considered for use as an alternative automotive fuel to replace gasoline. One gallon of gasoline could be replaced by 655 g of CH4. What is the volume of this much methane at 25 °C and 745 torr? Check Your LearningCalculate the pressure in bar of 2520 moles of hydrogen gas stored at 27 °C in the 180-L storage tank of a modern hydrogen-powered car. Standard Conditions of Temperature and PressureWe have seen that the volume of a given quantity of gas and the number of molecules (moles) in a given volume of gas vary with changes in pressure and temperature. Chemists sometimes make comparisons against a standard temperature and pressure (STP) for reporting properties of gases: 273.15 K and 1 atm (101.325 kPa). At STP, an ideal gas has a volume of about 22.4 L—this is referred to as the standard molar volume (Figure 10). Figure 1. Since the number of moles in a given volume of gas varies with pressure and temperature changes, chemists use standard temperature and pressure (273.15 K and 1 atm or 101.325 kPa) to report properties of gases. The equations describing these laws are special cases of the ideal gas law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of the gas, T is its kelvin temperature, and R is the ideal (universal) gas constant. Key Equations
Glossaryideal gas: hypothetical gas whose physical properties are perfectly described by the gas laws ideal gas constant (R): constant derived from the ideal gas equation R = 0.08226 L atm mol–1 K–1 or 8.314 L kPa mol–1 K–1 ideal gas law: relation between the pressure, volume, amount, and temperature of a gas under conditions derived by combination of the simple gas laws standard conditions of temperature and pressure (STP): 273.15 K (0 °C) and 1 atm (101.325 kPa) standard molar volume: volume of 1 mole of gas at STP, approximately 22.4 L for gases behaving ideally Kit L. asked • 04/20/201) What is the mass of 75.0 L of methane gas (CH₄) measured at STP? 2) What volume, in liters, will be occupied by 48.8 g of helium gas at STP? 3) What volume, in liters, at STP, is occupied by 3.30 X 10²³ molecules of oxygen gas? 4) What is the mass of 3.01 x 10²² molecules of carbon dioxide at STP? 1 Expert AnswerJason T. answered • 04/20/20 Experienced tutor and teacher in math, chemistry, and chem engineering These are all small gas molecules at STP (standard temperature and pressure), so we will assume ideal gas law (carbon dioxide is polar so would have the largest deviation from ideal gas behavior). 1 mol of ideal gas occupies 22.4 L at STP. 75.0 L CH4 * (1 mol / 22.4 L) = 3.348 mol CH4 molar mass of CH4 = 16.04 g / mol 3.348 mol CH4 * (16.04 g / mol) = 53.7 g CH4 We use 3 significant figures in the answer because 3 were given in the problem statement, "75.0" Keep using 22.4 L / mol and each compounds molar mass to solve the rest of the problems. Also remember Avogadro's number, that there are 6.022*10^23 molecules per mole for the last 2 problems. If you need further assistance, please book a session with me! Kit L. asked • 04/20/20
1) What is the mass of 75.0 L of methane gas (CH₄) measured at STP? 2) What volume, in liters, will be occupied by 48.8 g of helium gas at STP? 3) What volume, in liters, at STP, is occupied by 3.30 X 10²³ molecules of oxygen gas? 4) What is the mass of 3.01 x 10²² molecules of carbon dioxide at STP? 1 Expert Answer
Jason T. answered • 04/20/20 Experienced tutor and teacher in math, chemistry, and chem engineering
These are all small gas molecules at STP (standard temperature and pressure), so we will assume ideal gas law (carbon dioxide is polar so would have the largest deviation from ideal gas behavior). 1 mol of ideal gas occupies 22.4 L at STP. 75.0 L CH4 * (1 mol / 22.4 L) = 3.348 mol CH4 molar mass of CH4 = 16.04 g / mol 3.348 mol CH4 * (16.04 g / mol) = 53.7 g CH4 We use 3 significant figures in the answer because 3 were given in the problem statement, "75.0" Keep using 22.4 L / mol and each compounds molar mass to solve the rest of the problems. Also remember Avogadro's number, that there are 6.022*10^23 molecules per mole for the last 2 problems. If you need further assistance, please book a session with me! |