The Ideal Gas Law Chapter 11 Section 3
Standard Molar Volume of a Gas Assume the gas is an ideal gas. Standard molar volume of a gas: the volume occupied by one mole of a gas at STP, the value is 22.4 L Therfore, if you know the volume of gas at STP, you can find the number of moles by using conversion factor 1 mole 22.4 L
Continued Knowing the mol of the gas at STP, you can find the volume of the gas 22.4 L 1 mole At STP, what is the volume of 7.08 mol of nitrogen gas? 159 L N2
Another Problem A sample of hydrogen gas occupies 14.1 L at STP. How many moles of the gas are present? 0.629 mol H2
PV = nRT The Ideal Gas Law Ideal gas law: the mathematical relationship among pressure, volume, temperature, and the number of moles of a gas behaving ideally. PV = nRT “R” is a constant (.0821 L*atm/mol*K) “n” is the number of moles of gas in sample
The Ideal Gas Constant The constant “R” is the ideal gas constant The value and units of “R” vary according to the units used for P and V If P is in kPa, and V is in L, then R = 8.314 Temperature has to be K
Problem A tank of hydrogen gas has a volume of 22.9 L and holds 14.0 mol of the gas at 12°C. What is the pressure of the gas in kPa? Given: V = 22.9 L n = 14.0 mol T = 12 + 273 = 285 K R = 8.314 L*kPa/mol*K P = ?
Solution PV = nRT P = 1448.596507 P = 1450 kPa
Another Relationship You can use the ideal gas law to find the molar mass of a substance. Remember that molar mass = grams/mole. M = molar mass m = mass of the substance R, T, P, and V stand for the same quantities.
Problem What is the molar mass of a gas which has a mass of 20.24 g and a volume of 8.13 L at 20.0 °C and 99.2 kPa? = 61.1 g/mol
Problems Calculate the volume that a 0.323-mol sample of a gas will occupy at 265 K and a pressure of 91.2 kPa. 7.80 L What is the pressure in kPa of a 0.108-mol sample of helium gas at a temperature of 20.0°C if its volume is 0.505 L? 521 kPa
Another Problem Determine the kelvin temperature required for 0.0470 mol of gas to fill a balloon to 1.20 L under 100.0 kPa 307 K