The variables with subscript 1 indicate initial values; and those with subscript 2 indicate final values.
For one who is taking up chemistry for the first time, remembering all these equations is a little bit tricky.
Using the Ideal Gas Law equation, the above gas laws can be derived easily.
This way, you need to remember fewer equations.
The Ideal Gas Law Equation
PV = nRT
where:
- P is the pressure in atmosphere
- V is the volume in liters
- n is the amount of gas in moles
- R is the universal gas constant in L-atm/K-mol
- T is the temperature in Kelvin
This law relates the four variables of an ideal gas (pressure, volume, amount, and temperature) such that the value of PV/nT is always 0.082057.
It means that a change in the value of any of the four variables will bring about corresponding changes in the values of the other three variables so that the value of R remains constant.
Mathematically, it is equivalent to:
Deriving a Gas Law Equation
As mentioned earlier, we are dealing here with a fixed amount of gas.
It means the amount of gas remains the same from the initial state to the final state. So,
The value of nR must be constant.
Since the values of P1V1/T1 and P2V2/T2 are both equal to nR, then
Thus, we have derived the Combined Gas Law.
Using the above method, we can easily derive the other gas laws.
Suppose a problem states that the temperature must remain constant.
Using the Ideal Gas Law equation for the initial values and final values,
The value of nRT must be constant. Hence,
This is the Boyle's Law.
Now, you can derive the rest of the gas laws using the method we used here.
Problems
Improve your problem solving skill in chemistry by solving as many chemistry problems as possible. Here are some problems dealing with gas laws. The answer is provided for each problem.
For more chemistry problems on gases and other chemistry topics, you can go to www.tutorpartner.blogspot.com.
Boyle's Law Problems
| 1. | Calculate the pressure required to reduce the volume of 18.0 L of gas at a pressure of 0.333 atm to 6.0 L with the temperature remaining constant. |
| Answer: 0.999 atm | |
| 2. | Under constant temperature, 7000 mL of a sample gas was allowed to expand to a final volume of 23000 mL. If the initial pressure of the gas was 1085 torr, what was the final pressure of the gas after its expansion? |
| Answer: 330 torr | |
| 3. | A sample of a gas which occupies 0.93 L has a pressure of 3 atm. Determine the resulting volume of the gas if the pressure is changed to 9 atm and the temperature is maintained constant. |
| Answer: 0.31 L | |
| 4. | Calculate the pressure required to reduce the volume of 3000 mL of gas at a pressure of 1260 torr to 1000 mL with the temperature remaining constant. |
| Answer: 3780 torr | |
| 5. | Calculate the pressure required to reduce the volume of 24.0 L of gas at a pressure of 0.25 atm to 13.0 L with the temperature remaining constant. |
| Answer: 0.462 atm | |
| 6. | At a pressure of 7 atm, a sample of gas has a volume of 8.634 L. If the pressure is reduced to 2.75 atm, what will be the resulting volume of the gas? Temperature is maintained constant. |
| Answer: 21.977 L | |
| 7. | Under constant temperature, 10000 mL of a sample gas was allowed to expand to a final volume of 17000 mL. If the initial pressure of the gas was 21489 torr, what was the final pressure of the gas after its expansion? |
| Answer: 12641 torr | |
| 8. | At a pressure of 10 atm, a sample of gas has a volume of 0.497 L. If the pressure is reduced to 5 atm, what will be the resulting volume of the gas? Temperature is maintained constant. |
| Answer: 0.994 L | |
| 9. | A sample of a gas which occupies 2.8 L has a pressure of 1 atm. Determine the resulting volume of the gas if the pressure is changed to 8 atm and the temperature is maintained constant. |
| Answer: 0.35 L | |
| 10. | Under constant temperature, 5.0 L of a sample gas was allowed to expand to a final volume of 19.0 L. If the initial pressure of the gas was 12.088 atm, what was the final pressure of the gas after its expansion? |
| Answer: 3.181 atm | |
| 11. | Calculate the pressure required to reduce the volume of 14000 mL of gas at a pressure of 3281 torr to 3000 mL with the temperature remaining constant. |
| Answer: 15311 torr | |
| 12. | At a pressure of 10.425 atm, a sample of gas has a volume of 0.214 L. If the pressure is reduced to 1.882 atm, what will be the resulting volume of the gas? Temperature is maintained constant. |
| Answer: 1.185 L | |
| 13. | Under constant temperature, 8.0 L of a sample gas was allowed to expand to a final volume of 25.0 L. If the initial pressure of the gas was 0.342 atm, what was the final pressure of the gas after its expansion? |
| Answer: 0.109 atm | |
| 14. | At a pressure of 9.679 atm, a sample of gas has a volume of 0.397 L. If the pressure is reduced to 5.373 atm, what will be the resulting volume of the gas? Temperature is maintained constant. |
| Answer: 0.715 L | |
| 15. | At a pressure of 8.537 atm, a sample of gas has a volume of 0.45 L. If the pressure is reduced to 2.531 atm, what will be the resulting volume of the gas? Temperature is maintained constant. |
| Answer: 1.518 L | |
Charles' Law Problems
| 1. | Calculate the final volume of a 3.65 L gas at 92° C when the temperature is brought down to 9° C as the pressure remains unchanged. |
| Answer: 2.82 L | |
| 2. | Calculate the final volume of a 7.39 L gas at 43° C when the temperature is brought down to 13° C as the pressure remains unchanged. |
| Answer: 6.69 L | |
| 3. | A sample of gas with a volume of 6.0 L at -17° C was allowed to expand to 21.0 L while maintaining a constant pressure. What was the new temperature of the gas? |
| Answer: 623° C | |
| 4. | 18 L of gas at 294° C was compressed to 2 L at constant pressure. Determine the resulting temperature of the gas. |
| Answer: -210° C | |
| 5. | Maintaining a constant pressure, a sample of gas having a volume of 5.0 L at -127° C is heated to 369° C. What is the final volume of the gas? |
| Answer: 22.0 L | |
| 6. | 20 L of gas at 582° C was compressed to 4 L at constant pressure. Determine the resulting temperature of the gas. |
| Answer: -102° C | |
| 7. | A sample of gas with a volume of 3.0 L at -145° C was allowed to expand to 17.0 L while maintaining a constant pressure. What was the new temperature of the gas? |
| Answer: 452° C | |
| 8. | Maintaining a constant pressure, a sample of gas having a volume of 9.0 L at -210° C is heated to -7° C. What is the final volume of the gas? |
| Answer: 38.0 L | |
Gay-Lussac's Law Problems
| 1. | A sample of a gas sealed in a vessel was determined to have a pressure of 0.795 atm at 9° C. What would be the pressure of the gas if the vessel was heated to increase the temperature by 88° C? |
| Answer: 1.043 atm | |
| 2. | A gas cylinder containing a certain gas is found to have a pressure of 18.053 atm at 57° C. If the cylinder is immersed in a cooling solution so that the temperature is lowered by 0° C, calculate the resulting pressure inside the cylinder. |
| Answer: 18.053 atm | |
| 3. | A sample of a gas has a pressure of 10 atm and a temperature of 32° C. Find the corresponding change in the temperature if the pressure is (a) reduced to 5 atm, (b) tripled. Assume the volume of the gas is constant. |
| Answer: (a) -120° C, (b) 642° C | |
| 4. | A sample of a gas sealed in a vessel was determined to have a pressure of 1.007 atm at 2° C. What would be the pressure of the gas if the vessel was heated to increase the temperature by 81° C? |
| Answer: 1.304 atm | |
| 5. | A gas cylinder containing a certain gas is found to have a pressure of 147.177 atm at 50° C. If the cylinder is immersed in a cooling solution so that the temperature is lowered by 1° C, calculate the resulting pressure inside the cylinder. |
| Answer: 146.721 atm | |
| 6. | A sample of a gas sealed in a vessel was determined to have a pressure of 0.906 atm at 3° C. What would be the pressure of the gas if the vessel was heated to increase the temperature by 84° C? |
| Answer: 1.182 atm | |
Combined Gas Law Problems
| 1. | What will be the final temperature of a 51.413 L gas at 27° C if its volume is changed to 18.283 L and its pressure changed from 0.974 atm to 4.063 atm? |
| Answer: 172° C | |
| 2. | 784.96 L of a sample of gas has a pressure of 0.23 atm and a temperature of 19° C. After compressing the volume down to 1.37 L and increasing the temperature to 98° C, calculate the change in the pressure of the gas. |
| Answer: 167.435 atm | |
| 3. | 69.73 L of a sample of gas has a pressure of 0.98 atm and a temperature of 29° C. After compressing the volume down to 7.47 L and increasing the temperature to 72° C, calculate the change in the pressure of the gas. |
| Answer: 10.451 atm | |
| 4. | An expandable air balloon containing 88.2 L of a sample of a gas has a pressure of 1.039 atm at 47° C. What will be the resulting volume of the gas if the pressure is changed to 7 atm and the temperature is increased by 15° C? |
| Answer: 13.7 L | |
| 5. | What will be the final temperature of a 161.519 L gas at 12° C if its volume is changed to 24.129 L and its pressure changed from 0.225 atm to 11.314 atm? |
| Answer: 1866° C | |
| 6. | An expandable air balloon containing 8.3 L of a sample of a gas has a pressure of 31.941 atm at 42° C. What will be the resulting volume of the gas if the pressure is changed to 9 atm and the temperature is increased by 14° C? |
| Answer: 30.8 L | |
Ideal Gas Law Problems
| 1. | A 29.135 L tank containing a sample of gas has a pressure of 0.968 atm and a temperature of 70° C. Find the moles of gas contained inside the tank. |
| Answer: 1.002 mol | |
| 2. | Calculate the volume of 9.385 mol of a gas confined in a sealed vessel with a pressure of 39.66 atm and a temperature of 36° C. |
| Answer: 6 L | |
| 3. | Given a volume of 25.07 L of the following gases at STP : (a) SO2, (b) N2, (c) H2S, find the weight in grams of each gas. (mol. wt.: SO2=64.0588, N2=28.0134, H2S=34.0758) |
| Answer: (a) 71.69 g, (b) 31.35 g, (c) 38.14 g | |
| 4. | Given a weight of 8.8 g of each of the following gases: (a) NH3, (b) He, (c) NH3, calculate the volume of each gas at STP. (mol. wt.: NH3=17.0304, He=4.0026, NH3=17.0304) |
| Answer: (a) 11.57 L, (b) 49.25 L, (c) 11.57 L | |
