Gas Laws Chapter 10 Boyles Law The volume

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Gas Laws Chapter 10

Gas Laws Chapter 10

Boyle’s Law The volume of a fixed quantity of gas at constant temperature is

Boyle’s Law The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

P and V are inversely proportional • A plot of V versus P results

P and V are inversely proportional • A plot of V versus P results in an inverse graph • Therefore is the pressure is doubled, the volume will be halved.

Boyle’s Law Practice Problem • If I have 5. 6 liters of gas in

Boyle’s Law Practice Problem • If I have 5. 6 liters of gas in a piston at a pressure of 1. 5 atm and compress the gas until its volume is 4. 8 L, what will the new pressure inside the piston be? P 1 V 1 = P 2 V 2 (1. 5 atm)(5. 6 L) = (x)(4. 8 L) x = 1. 8 atm

Charles’s Law • The volume of a fixed amount of gas at constant pressure

Charles’s Law • The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature in Kelvins. • i. e. , V = k T A plot of V versus T will be a straight line.

Charles’s Law Practice Problem • If I have 45 liters of helium in a

Charles’s Law Practice Problem • If I have 45 liters of helium in a balloon at 250 C and increase the temperature of the balloon to 550 C, what will the new volume of the balloon be?

Avogadro’s Law • The volume of a gas at constant temperature and pressure is

Avogadro’s Law • The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. • V 1/n 1 = V 2/n 2 • Mathematically, this means V = kn

Avagadro’s Law Practice Problem A 6. 0 L sample at 25 °C and 2.

Avagadro’s Law Practice Problem A 6. 0 L sample at 25 °C and 2. 00 atm of pressure contains 0. 5 moles of a gas. If an additional 0. 25 moles of gas at the same pressure and temperature added, what is the final total volume of the gas? Vf = (6. 0 L x 0. 75 moles)/0. 5 moles Vf = 4. 5 L/0. 5 Vf = 9 L

Ideal-Gas Equation • So far we’ve seen that V 1/P (Boyle’s law) V T

Ideal-Gas Equation • So far we’ve seen that V 1/P (Boyle’s law) V T (Charles’s law) V n (Avogadro’s law) • Combining these, we get n. T V P

Ideal-Gas Equation The constant of proportionality is known as R, the gas constant.

Ideal-Gas Equation The constant of proportionality is known as R, the gas constant.

Ideal-Gas Equation The relationship n. T V P then becomes n. T V =

Ideal-Gas Equation The relationship n. T V P then becomes n. T V = R P or PV = n. RT

Ideal Gas Law Practice Problem • If I have 4 moles of a gas

Ideal Gas Law Practice Problem • If I have 4 moles of a gas at a pressure of 5. 6 atm and a volume of 12 L, what is the temperature? PV=n. RT 205 K

Densities of Gases If we divide both sides of the ideal-gas equation by V

Densities of Gases If we divide both sides of the ideal-gas equation by V and by RT, we get n P = V RT

Densities of Gases • We know that – moles molecular mass = mass n

Densities of Gases • We know that – moles molecular mass = mass n = m • So multiplying both sides by the molecular mass ( ) gives m P = V RT

Densities of Gases • Mass volume = density • So, m P d =

Densities of Gases • Mass volume = density • So, m P d = = V RT • Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas.

Molecular Mass We can manipulate the density equation to enable us to find the

Molecular Mass We can manipulate the density equation to enable us to find the molecular mass of a gas: P d = RT Becomes d. RT = P