Understanding Boyle's Law and the Ideal Gas Law in Chemistry

1. Boyle's law Topic 3.2 ExtendedA – The gas laws BOYLE'S LAW All of what we discuss in this section has been presented to you in your chemistry class. Boyle's law states that if the temperature of a gas is kept constant, then the product of the pressure and the volume is constant. Thus If T = constant then pV= constant p1V1 = p2V2

2. 20 10 30 0 Topic 3.2 ExtendedA – The gas laws BOYLE'S LAW Consider the following demonstration: A graduated syringe which is partially filled with air is placed in an ice bath and allowed to reach the temperature of the water. T1 = 0°C p1 = 15 V1 = 10 T2 = 0°C V2 = 5 p2 = 30 Why is the graduated syringe placed in the ice water? p1V1 = 150 p2V2 = 150 Why doesn't it matter what the units are for pressure and volume? Does it matter what the units are for temperature?

3. Charles' law Topic 3.2 ExtendedA – The gas laws CHARLES' LAW Charles' law states that if the pressure of a gas is kept constant, then the quotient of the volume and the temperature is constant. Thus If P = constant then V T = constant V1 T1 V2 T2 where T is ABSOLUTE TEMPERATURE = We will define absolute temperature shortly.

4. The Ideal Gas Law The Ideal Gas Law Boltzmann's constant Topic 3.2 ExtendedA – The gas laws THE IDEAL GAS LAW We can put Boyle's and Charles' laws together into one law that we call the ideal gas law: pV T = constant p1V1 T1 p2V2 T2 where T is ABSOLUTE TEMPERATURE = If you memorize the IGL it reduces to Boyle's law if T is constant, and Charles' law if p is constant. No need to memorize all three. By the way, the great Wallahs of chemistry even figured out a value for the constant: NkB, where N is the number of molecules in the sample, and kB = 1.3810-23 J/K Thus we can write pV = NKBT

5. 20 10 30 0 FYI: We can extrapolate our points to find the temperature at which we expect the pressure of the gas to become 0: FYI: Different gases will have different slopes. But all will extrapolate to the same value of T when their pressure reaches 0: Topic 3.2 ExtendedA – The gas laws ABSOLUTE ZERO AND THE KELVIN SCALE FYI: That temperature is -273.15 °C. Now we are ready to talk about the Kelvin temperature scale. FYI: Since there is no pressure less than zero, there is no temperature less than -273.15 °C. We take this temperature to be ABSOLUTE ZERO. Suppose we have a fixed volume filled with an ideal gas of some kind, and suppose we attach a pressure gauge to it, and a thermometer: Now we apply a heat source, and plot pressure vs. temperature: p -273.15 °C T (°C) 300 200 100 0 -200 -100 -300

6. The Ideal Gas Law Universal Gas Constant Avagadro's Number Topic 3.2 ExtendedA – The gas laws THE IDEAL GAS LAW (ANOTHER FORM) An alternate, and perhaps more useful form, of the ideal gas law looks like this: pV = nRT where R is the universal gas constant and n (lower case) in the number of moles (mol) of the gas. R = 8.31 J/mol·K R = 0.0821 L·atm/mol·K The second form is probably the one you used in chemistry, where volumes are in liters and pressures are in atmospheres. Don't forget, a mole of a substance is the quantity of it that contains Avagadro's numberNAof molecules: NA = 6.021023 molecules/mole