All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds
Sections
Pressure Units
The Ideal Gas Law
The Ideal Gas Law Derivations
The Ideal Gas Law Applications
Chemistry Gas Laws
Chemistry Gas Laws: Combined Gas Law
Mole Fraction
Partial Pressure
The Ideal Gas Law: Molar Mass
The Ideal Gas Law: Density
Gas Stoichiometry
Standard Temperature and Pressure
Effusion
Root Mean Square Speed
Kinetic Energy of Gases
Maxwell-Boltzmann Distribution
Velocity Distributions
Kinetic Molecular Theory
Van der Waals Equation
Additional Practice
Manometer
Collecting Gas Over Water
Additional Guides
Boyle's Law
Charles Law
Ideal Gas Law
LearnAdditional Practice
Next SectionThe Ideal Gas Law Applications

The Ideal Gas Law Derivations are a convenient way to solve gas calculations involving 2 sets of the same variables. 

Ideal Gas Law Derivations

Concept #1: The Ideal Gas Law Derivations

Example #1: A sample of sulfur hexachloride gas occupies 8.30 L at 202 ºC. Assuming that the pressure remainsconstant, what temperature (in ºC) is needed to decrease the volume to 5.25 L?

Practice: A sample of nitrogen dioxide gas at 130 ºC and 315 torr occupies a volume of 500 mL. What will the gas pressure be if the volume is reduced to 320 mL at 130 ºC?

Practice: A cylinder with a movable piston contains 0.615 moles of gas and has a volume of 295 mL. What will its volume be if 0.103 moles of gas escaped?

Practice: On most spray cans it is advised to never expose them to fire. A spray can is used until all that remains is the propellant gas, which has a pressure of 1350 torr at 25 ºC. If the can is then thrown into a fire at 455 ºC, what will be the pressure (in torr) in the can?

a) 750 torr

b) 1800 torr

c) 2190 torr

d) 2850 torr

e) 3300 torr

Previous SectionThe Ideal Gas Law
Next SectionThe Ideal Gas Law Applications
Additional Problems
What do you expect the temperature change to be for a rapid, adiabatic compression of a gas from 1.0 atm to 3.0 atm? a. -10K b. 100K c. 0.001K d. -100K e. -0.001K
A 4.0 L flask containing N2 at 15 atm is connected to a 4.0 L flask containing H 2 at 7.0 atm and the gases are allowed to mix. What is the mole fraction of N2? 1. 0.75 2. Cannot be determined 3. 0.93 4. 0.26 5. 0.32 6. 0.68
1 mole of an ideal gas is kept at constant pressure but its temperature is lowered. What is the value of T when the volume of the gas reaches zero (extrapolation)?   a. 0.0°C b. 100.00°C c. - 273.15K d. - 273.15°C e. 373.15K
The gas in a gas thermometer that has been placed in an oven has a volume that is 3.68 times larger than the volume that it occupies at 158°C. Determine the temperature in the oven (in degrees Celsius).   a. 1313 b. 1586 c. 581 d. 43 e. 117
A gas has a volume of 2.00 liters at a temperature of 127ºC. What will be the volume of the gas if the temperature is increased to 327ºC? (Assume the pressure remains constant.)   1. 2.00 liters 2. 3.00 liters 3. 4.00 liters 4. 6.00 liters
The gas in a gas thermometer that has been placed in an oven has a volume that is 5.42 times larger than the volume that it occupies at 125°C. Determine the temperature of the oven (in degrees Celsius). a) none of the given answers b) 1884 c) 2430 d) 2157 e) 73.4
A sample of propane gas is placed in a 10.0 L container at 25.0°C and 725 mmHg. The gas sample is then transferred from the 10.0 L container to a 7.50 L container at 25.0°C for shipping. What is the gas pressure in the second container? a) 760 torr b) 0.95 atm c) 1062 mmHg d) 1.40 atm e) 967 mmHg
If 0.300 moles of nitrogen gas occupies 0.600 L under certain conditions, what number of moles occupies 1.500 L under the same conditions?
What volume (in mL) will a sample of F2 gas occupy in a syringe at 5.5 atm, if the F 2 has a volume of 25.0 mL at 1.2 atm? A) 7.6 mL B) 11 mL C) 5.5 mL D) 3.8 mL E) 17 mL
A gas has a volume of 9.0 liters at a pressure of 1520 torr. If the pressure is decreased to 380 torr, what will be its new volume? (Assume the temperature remains constant.) A. 36 liters B. 4.6 liters C. 2.3 liters D. 0.28 liters
A certain quantity of a gas occupies 61.3 mL at 68°C. If the pressure remains constant, what would the volume of the gas be at 17°C? A. 52 mL B. 72 mL C. 32 mL D. 92 mL
An oxygen tank of 500 L is 80 atm in a room 25°C and 1.0 atm is used for supplying oxygen to a patient. If the flow rate of oxygen coming out from the tank is set to me 1.00 L/s, about how long will this tank last for this purpose?a. 11 hrb. 5.5 hrc. 2.3 hrd. 16 mine. 8.3 min
A sample of a gas occupies 460 mL at 70.0 °C and 1.00 atmosphere. At what temperature would the gas occupy 650 mL at the same pressure?1. 99 °C2. 111 °C3. 188 °C4. 212 °C5. 435 °C6. 154 °C7. –30.0 °C
A weather balloon filled with hydrogen gas has a volume of 2.5 x 10 4 L at 1.3 atm and 32.0°C. At one point during its ascent, the balloon has the same volume as when it was launched, although its temperature is -8.00°C. Compute the pressure (in atm) at that point.  a) 0.0667 b) 4.5 x 10-3 c) 1.13 d) 1.50 e) 0.885
The gas in a gas thermometer that has been placed in an oven, has a volume that is 3.68 times larger than the volume that it occupied at 86°C. Determine the temperature in the oven (in degrees Celsius)a) 1048b) 316c) 3850d) 25.9e) 1321
Some students believe that professors are full of hot air. If I inhale 2.20 liters of gas at a temperature of 18.0°C and it heats to a temperature of 38.0°C in my lungs, what is the new volume of the gas (in liters)?a) 1.04b) 4.64c) 0.425d) 2.35e) 2.06 
A sample of gas has an initial volume of 13.9 L at a pressure of 1.22 atm. If the sample is compressed to a volume of 10.3 L, what is its pressure? 
A syringe containing 1.55 mL of oxygen gas is cooled from 95.3°C to 0.0°C. What is the final volume of oxygen gas? 
A cylinder with a moveable piston contains 0.553 mol of gas and has a volume of 253 mL. What will its volume be if an additional 0.365 mol of gas is added to the cylinder? (Assume constant temperature and pressure.) 
A sample of nitrogen gas in a 1.75-L container exerts a pressure of 1.35 atm at 25 °C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 355 °C? 
A particular balloon can be stretched to a maximum surface area of 1257 cm 2. The balloon is filled with 3.0 L of helium gas at a pressure of 755 torr and a temperature of 298 K. The balloon is then allowed to rise in the atmosphere. If the atmospheric temperature is 273 K, at what pressure will the balloon burst? (Assume the balloon to be in the shape of a sphere.) 
A sample of carbon dioxide gas at 125°C and 248 torr occupies a volume of 275 L. What will the gas pressure be if the volume is increased to 321 L at 125°C?a. 441 torrb. 289 torrc. 356 torrd. 359 torre. 212 torr
A gas occupies 4.23 L at 2.25 atm. What is the volume at 3.46 atm? A) 6.50 L B) 1.84 L C) 2.75 L D) 32.9 L E) 0.364 L
A fuel cell car is powered by electrons harvested from the flameless, low-temperature reactionHow many liters of oxygen is needed to react with 42.0 L of hydrogen at STP?1. 21.0 L2. 32.0 L3. 63.0 L4. 84.0 L5. 22.4 L6. 672 L7. 42.0 L8. 2.02 L
A sample of carbon dioxide gas as 125 oC and 248 torr occupies a volume of 275 L. What will the gas pressure be if the volume is increased to 321 L at 125 oC? a. 441 torr b. 289 torrc. 356 torrd. 359 torre. 212 torr 
A gas is collected and found to fill a volume of 2.85 L at 25.0°C. What will be its volume at standard temperature?a. 1.3 Lb. 2.6 Lc. 4.5 Ld. 2.8 Le. 1.3 L
What volume (in mL) will a sample of F2 gas occupy in a syringe at 5.5 atm, if the F2 has a volume of 25.0 mL at 1.2 atm? a) 11 mL b) 17 mL c) 3.8 mL d) 5.5 mL e) 7.6 mL
A certain quantity of a gas occupies 61.3 mL at 68°C. If the pressure remains constant, what would the volume of the gas be at 17°C?1. 72 mL2. 92 mL3. 32 mL4. 52 mL
A sample of oxygen gas has its absolute temperature halved while the pressure of the gas remained constant. If the initial volume is 400 mL, what is the final volume?
At 25.0°C, a sample of Xe gas occupies 106.5 mL in a piston-cylider apparatus when the external pressure is 644.4 torr. At what pressure (torr) will its volume become 215.2 mL if the temperature does not change? Enter your answer with two decimal places and no units.
A sample of ideal gas at room temperature occupies a volume of 34.0 L at a pressure of 782 torr . If the pressure changes to 3910 torr , with no change in the temperature or moles of gas, what is the new volume, V2; and If the volume of the original sample in Part A (P1 = 782 torr , V1 = 34.0 L ) changes to 65.0L , without a change in the temperature or moles of gas molecules, what is the new pressure, P2. 
A sample of gas in a balloon has an initial temperature of 9°C and a volume of 1200L . If the temperature changes to 85°C , and there is no change of pressure or amount of gas, what is the new volume, V2, of the gas? What Celsius temperature, T2, is required to change the volume of the gas sample in Part A (T1 = 9°C , V1= 1200L ) to a volume of 2400L ? Assume no change in pressure or the amount of gas in the balloon. 
Oxygen used in respiratory therapy is stored at room temperature under a pressure of 150 atm in a gas cylinder with a volume of 60.0 L. What volume would the oxygen occupy at 0.730 atm? Assume no temperature change; and if the oxygen flow to the patient is adjusted to 6.00 L/min at room temperature and 0.730 atm , how long will the tank of gas last?
What volume will a balloon occupy at 1.0 atm, If the balloon has a volume of 8.8 L at 4.4 atm? a. 2.0 L b. 44 L c. 0.50 L d. 39 L
What volume will a balloon occupy at 1.0 atm, if the balloon has a volume of 7.6 L at 2888 mmHg?
A 12 liter tank contains helium gas pressurized to 160 atm. What size tank would be needed to contain the same amount of helium at atmospheric pressure (1 atm)?
A sample of gas (24.2 g) initially at 3.00 atm was compressed from 8.00 L to 2.00 L at constant temperature. After the compression, the gas pressure was  ________   atm.a) 4.00b) 8.00c) 12.0d) 16.0e) 2.00
A sample of nitrogen gas at 298 K and 745 torr has a volume of 37.42 L. What volume will it occupy if the pressure is increased to 894 torr at constant temperature? a. 22.3 L b. 31.2 L c. 44.9L d. 112 L e. 380 L
A 12 Liter tank contains helium gas pressurized to 160 atm.How many 3-liter balloons could the 12 Liter helium tank fill?(Keep in mind that an "exhausted" helium tank is not empty. In other words, once the gas inside the tank reaches atmospheric pressure, it will no longer be able to fill balloons.)
Part AA certain gas is present in a 15.0 L cylinder at 4.0 atm pressure. If the pressure is increased to 8.0 atm, the volume of the gas decreases to 7.5 L. Find the two constants ki, the initial value of k, and kf, the final volume of k, to verily whether the gas obeys Boyle's law. Express your answers to two significant figures separated by a comma. Part BIf a certain gas occupies a volume of 12 L when the applied pressure is 6.0 atm, find the pressure when the gas occupies a volume of 3.0L. Express your answer to two significant figures, and include the appropriate units.
A 0.850-mole sample of nitrous oxide, a gas used as an anesthetic by dentists, has a volume of 20.46 L at 123°C and 1.35 atm. What would be its volume at 468°C and 1.35 atm? a. 19.0 L b. 77.9 L c. 10.9 L d. 38.3 L e. 5.38 L
An arctic weather balloon is filled with 1.87 L of helium gas inside a prep shed. The temperature inside the shed is 15.°C. The balloon is then taken outside, where the temperature is - 43.°C. Calculate the new volume (L) of the balloon. You may assume the pressure on the balloon stays constant at exactly 1 atm. Round your answer to 3 significant digits.