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TRANSCRIPT
Gas Laws Honors chemistry – Semester 2
Objectives
Understand and use four gas laws
Boyle’s law
Charles’s law
Gay-Lussac’s law
Avogadro’s law
Measurable properties of gas
Pressure = P
Temperature = T (in kelvins!)
Volume = V
Number of moles = n
Memory Aid!
Write the letters below in the order shown
“On Pressure TV, you can’t buy goats!” - Angie Nguyen
P T V C B G
Boyle’s law
At constant temperature,
pressure times volume is constant
PV = k
If the amount of gas remains the same
PiVi = PfVf = k
In other words, ½ the volume = 2x the pressure!
Boyle’s Law
• Constant temp (pinch “T”), note “B” underneath
• Move “P” up - down (inc. – dec. pressure)
• What happens to “V”?
As P gets bigger, V gets smaller
As P gets smaller, V gets bigger
P T V C B G
Example
A sample of gas fills 523 mL at 1.00 atm. If pressure increases to 1.97 atm, what is the new volume?
P1 = 1.00 atm V1 = 523 mL
P2 = 1.97 atm V2 = ?
P1V1 = P2V2
V2 = P1V1 / P2
= (1.00 atm)(523 mL) / 1.97 atm = 265 mL
Example
A sample of gas has a volume of 150.0 mL at 0.947 atm. What is the volume if pressure decreases to 0.750 atm?
P1 = 0.947 atm V1 = 150.0 mL
P2 = 0.750 atm V2 = ?
P1V1 = P2V2
V2 = P1V1 / P2
= (0.947 atm)(150.0 mL) / 0.750 atm = 189 mL
Practice
A balloon with a volume of 456 mL at a pressure of 1.0 atm is submerged in water so that the new pressure is 3.3 atm. Assuming constant temperature, what is the new volume of the balloon?
1.4 x 102 mL or 140 mL
Charles’s Law
If the temperature changes, a gas will expand or contract to maintain constant pressure
At constant pressure, the volume of gas divided by temperature is constant
V / T = k V1 / T1 = V2 / T2
Example
A balloon with a volume of 15.5 L is inflated at 20.0 C. The balloon is cooled to 7.0 C. What will be the volume of the balloon?
V1 = 15.5 L T1 = 20.0 C = 293.0 K
V2 = ? T2 = 7.0 C = 280.0 K
V1 / T1 = V2 / T2 V2 = V1T2 / T1
V2 = (15.5 L)(280 K) / 293 K = 14.8 L
Practice
1.50 x 103 L of air is heated from 5.00 C to 30.0 C in a furnace. What is the new volume of the air?
1.63 x 103 L
Gay-Lussac’s Law
At constant volume, pressure is proportional to temperature
P = kT
P/T = k
P1/T1 = P2/T2
Example
A can containing gas at 101 kPa and 22 °C is heated to 55 °C. Calculate the pressure in the heated can.
P1 = 101 kPa T1 = 22 °C = 295 K
P2 = ? T2 = 55 °C = 328 K
P1/T1 = P2/T2
P2 = P1T2/T1 = (101 kPa)(328 K)/295 K = 112 kPa
Example
The pressure in tire at 20 °C is 29.8 psi. After being driven on a hot road, the temperature rises to 48 °C . What is the pressure in the hot tire?
P1 = 29.8 psi T1 = 20 °C = 293 K
P2 = ? T2 = 48 °C = 321 K
P1/T1 = P2/T2
P2 = P1T2/T1 = (29.8 psi)(321 K)/293 K = 32.6 psi
Practice
A sample of nitrogen has a pressure of 1.07 atm at 122 °C. The gas is cooled and the new pressure measured as 0.880 atm. What is the temperature of the cooled gas?
325 K or 52 °C
Avogadro’s Law
Equal volumes of gas under the same pressure and temperature have the same # of particles
Example:
He H2 CO2
Avogadro’s Law
The volume of a gas is proportional to the number of moles of particles
V = kn
k = constant
n = number of moles
Avogadro’s Law
But volume changes with different T and P!
Use standard temperature and pressure (STP)
• 0 °C and 1 atm pressure
At STP:
• volume of 1 mol of any gas = 22.41 L
• mass of 22.41 L of any gas = molar mass
• 22.41 L of any gas = 6.022 x 1023 particles
Example
1 mol of He, H2 and CO2 at STP
volume mass particles
He 22.41 L 4.0 g 6.022 x 1023
H2 22.41 L 2.0 g 6.022 x 1023
CO2 22.41 L 44.0 g 6.022 x 1023
He H2 CO2
Gas Law Recap
Boyle’s Law: P1V1 = P2V2 (constant T)
Charles’s Law: V1/T1 = V2/T2 (constant P)
Gay-Lussac’s Law: P1/T1 = P2/T2 (constant V)
Avogadro’s Law: V = kn
P T V C B G
Review
As popcorn heats up, the pressure inside the kernel builds. What law describes this pressure increase?
Gay-Lussac’s Law (P1/T1 = P2/T2, V is constant)
Once the popcorn kernel breaks open, its volume increases and the pressure drops. What law describes this?
Boyle’s Law (P1V1 = P2V2, T is constant)
Review
Video: What two gas laws are in play with this video clip?
Gay-Lussac’s law – heating with pressure increase
Boyle’s Law – Volume expansion when pressure drops