Chemistry Help - Using the Gas Laws

The final pressure will be 20.0 atmIn summary, based on the given information, the pressure of the ideal gas in the sealed container will remain at 1.00 atm and 1.00 L if the temperature is raised to 200.0 degrees Celsius and the piston is not allowed to move. This can be determined using Guy-Lussac's Law, where P1/T1 = P2/T2.
  • #1
sam.
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Homework Statement



This figure (file attached) shows a container that is sealed at the top by a movable piston. Inside the container is a ideal gas at 1.00 atm, 20.0 degrees Celsius, and 1.00 L.

The gas sample has now returned to its original state of 1.00 atm, 20.0 degrees Celsius and 1.00 L. What will the pressure become if the temperature of the gas is raised to 200.0degrees celsius and the piston is not allowed to move?

Homework Equations



Boyle's Law P_1V_1 = P_2V_2
or
Charles' Law V_1/T_1 = V_2/T_2

The Attempt at a Solution



Okay, in order for the piston not to move, this means that the volume must remain at 1.00 L. What I don't know what to do is how to relate temperature and pressure to solve for the final pressure.
 

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  • #2
Guy-Lussacs Law P1/T1 = P2/T2
 
  • #3


To solve for the final pressure, we can use the combined gas law, which states that P1V1/T1 = P2V2/T2. In this case, we know the initial pressure (1.00 atm), volume (1.00 L), and temperature (20.0 degrees Celsius). We also know the final volume (1.00 L) and temperature (200.0 degrees Celsius). Therefore, we can plug in these values and solve for the final pressure:

P1V1/T1 = P2V2/T2
(1.00 atm)(1.00 L)/(293.15 K) = P2(1.00 L)/(473.15 K)
P2 = (1.00 atm)(293.15 K)/(473.15 K)
P2 = 0.619 atm

Therefore, the final pressure of the gas will be 0.619 atm when the temperature is raised to 200.0 degrees Celsius and the piston is not allowed to move. It is important to note that this calculation assumes that the gas is still behaving as an ideal gas. If the gas deviates from ideal behavior, the results may not be accurate. Additionally, it is always important to double check units and make sure they are consistent throughout the calculation.
 

1. What are the gas laws in chemistry?

The gas laws in chemistry are a set of principles that describe the behavior of gases under different conditions. These laws include Boyle's law, Charles's law, Gay-Lussac's law, and Avogadro's law.

2. What is Boyle's law and how is it used?

Boyle's law states that at a constant temperature, the volume of a gas is inversely proportional to its pressure. This means that as pressure increases, volume decreases and vice versa. This law is commonly used to predict changes in volume or pressure of a gas when one of those variables is changed.

3. How does Charles's law relate to temperature and volume?

Charles's law states that at a constant pressure, the volume of a gas is directly proportional to its absolute temperature. This means that as temperature increases, volume also increases and vice versa. This law is commonly used to predict changes in volume of a gas when temperature is changed.

4. What is Gay-Lussac's law and how is it used?

Gay-Lussac's law states that at a constant volume, the pressure of a gas is directly proportional to its absolute temperature. This means that as temperature increases, pressure also increases and vice versa. This law is commonly used to predict changes in pressure of a gas when temperature is changed.

5. What is Avogadro's law and how is it used?

Avogadro's law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. This means that the volume of a gas is directly proportional to the number of moles of gas present. This law is commonly used to calculate the volume of a gas at a given temperature and pressure, or to determine the number of moles of gas present in a given volume.

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