Combined Gas Law
Summary
TLDRThis educational video script introduces the Combined Gas Law, which unifies Boyle's Law, Charles's Law, and Gay-Lussac's Law to describe the relationship between pressure, volume, and temperature of a gas. The script walks through an example problem where a gas's initial conditions and changes in pressure and temperature are given, and the new volume is calculated using the Combined Gas Law. The process involves converting temperatures to Kelvin, setting up the equation, and solving for the unknown volume, resulting in a new volume of 580.58 liters.
Takeaways
- 📚 The lesson introduces three fundamental gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law, which describe the relationships between pressure, volume, and temperature of a gas.
- 🔍 Boyle's Law relates pressure and volume, stating that at a constant temperature, the pressure of a gas is inversely proportional to its volume.
- 🌡️ Charles's Law connects volume and temperature, indicating that at a constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin.
- 🔄 Gay-Lussac's Law shows the relationship between pressure and temperature, asserting that at a constant volume, the pressure of a gas is directly proportional to its temperature in Kelvin.
- 🔗 The Combined Gas Law is formed by combining Boyle's, Charles's, and Gay-Lussac's Laws, accounting for changes in pressure, volume, and temperature simultaneously.
- 🧩 The formula for the Combined Gas Law is \( \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \), where \( P \) stands for pressure, \( V \) for volume, and \( T \) for temperature in Kelvin.
- 📘 An example problem is presented involving a gas at 110 kilopascals and 30°C with an initial volume of 2 liters, which is then heated to 80°C and the pressure increased to 440 kilopascals.
- ⚖️ The problem requires converting Celsius temperatures to Kelvin by adding 273, which is done for both the initial and final temperatures.
- 🔢 The solution process involves substituting the given values into the Combined Gas Law equation and solving for the unknown variable, which in this case is the new volume (\( V_2 \)) of the gas.
- 📝 The calculation involves cross-multiplying and isolating \( V_2 \) to find the new volume, which is determined to be 0.58 liters.
- 📚 The lesson concludes with a demonstration of how to apply the Combined Gas Law to practical problems involving changes in the state of a gas.
Q & A
What are the three gas laws mentioned in the script?
-The three gas laws mentioned are Boyle's Law, Charles's Law, and Gay-Lussac's Law.
What does Boyle's Law relate to?
-Boyle's Law relates the pressure and volume of a particular gas, stating that at a constant temperature, the pressure of a gas is inversely proportional to its volume.
What is the relationship described by Charles's Law?
-Charles's Law relates the volume and temperature of a particular gas, stating that at a constant pressure, the volume of a gas is directly proportional to its temperature in Kelvin.
How does Gay-Lussac's Law connect pressure and temperature?
-Gay-Lussac's Law states that at a constant volume, the pressure of a gas is directly proportional to its temperature in Kelvin.
What is the Combined Gas Law and why is it used?
-The Combined Gas Law is a single law that combines Boyle's Law, Charles's Law, and Gay-Lussac's Law to describe the relationship between pressure, volume, and temperature of a gas when all three variables are changing.
What formula represents the Combined Gas Law?
-The formula for the Combined Gas Law is P1V1/T1 = P2V2/T2, where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures in Kelvin.
What is the initial condition of the gas in the example problem?
-The initial condition of the gas in the example is 110 kilopascals pressure, 30°C temperature, and 2 liters volume.
How is the temperature converted from Celsius to Kelvin?
-The temperature is converted from Celsius to Kelvin by adding 273 to the Celsius temperature.
What are the final conditions of the gas in the example problem after the changes?
-The final conditions are 440 kilopascals pressure and 80°C temperature, with the volume to be determined.
How is the new volume calculated in the example problem?
-The new volume is calculated by using the Combined Gas Law formula and cross-multiplying to isolate V2, the unknown variable.
What is the final answer for the new volume of the gas in the example problem?
-The final answer for the new volume of the gas is 0.58 liters.
Outlines
📚 Introduction to Gas Laws
The script begins with an introduction to the three fundamental gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. Boyle's Law explains the relationship between pressure and volume of a gas, Charles's Law discusses the relationship between volume and temperature, and Gay-Lussac's Law addresses the relationship between pressure and temperature. The video then introduces the concept of the combined gas law, which integrates these laws to account for changes in pressure, volume, and temperature simultaneously.
🔍 Applying the Combined Gas Law
The script proceeds with an example to demonstrate the application of the combined gas law. It involves a scenario where a gas initially at 110 kilopascals and 30°C fills a container with a volume of 2 liters. The challenge is to find the new volume when the temperature is increased to 80°C and the pressure is raised to 440 kilopascals. The script guides through the process of converting Celsius to Kelvin, identifying the initial and final states of the gas, and setting up the combined gas law equation to solve for the unknown volume.
🧐 Solving for the New Volume
The script concludes with a step-by-step calculation to determine the new volume of the gas using the combined gas law. It involves cross-multiplying the known values of pressure, volume, and temperature to isolate the variable V2, which represents the new volume. The calculation is detailed, showing the process of converting units, setting up the equation, and solving for V2, which is found to be 0.58 liters. This final step illustrates the practical application of the combined gas law in solving for changes in gas volume under varying conditions.
Mindmap
Keywords
💡Boyle's Law
💡Charles's Law
💡Gay-Lussac's Law
💡Combined Gas Law
💡Numerator
💡Denominator
💡Kilopascals
💡Temperature Conversion
💡Cross Multiplication
💡Variable
💡Isolate
Highlights
Introduction to the three gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law, which describe the relationships between pressure, volume, and temperature of a gas.
Combining the three gas laws to form the Combined Gas Law, which accounts for changes in pressure, volume, and temperature simultaneously.
The Combined Gas Law formula: P1V1/T1 = P2V2/T2, where P, V, and T represent pressure, volume, and temperature respectively, with subscripts 1 and 2 denoting initial and final states.
Example problem: A gas at 110 kPa and 30°C fills a flexible container with an initial volume of 2 L. The temperature is raised to 80°C and the pressure increased to 440 kPa. The task is to find the new volume.
Conversion of Celsius temperatures to Kelvin by adding 273, to maintain consistency in units for temperature.
Identifying the initial conditions: P1 = 110 kPa, T1 = 303 K, V1 = 2 L.
Identifying the final conditions after changes: P2 = 440 kPa, T2 = 353 K, and the unknown V2 to be calculated.
Ensuring units are consistent, especially for pressure which can be measured in different units.
Using the Combined Gas Law formula to set up the equation for calculating the new volume V2.
Cross-multiplying to isolate the variable V2 in the equation.
Performing the calculation: 353 * 110 * 2 equals 77760.
Setting up the second part of the equation: 303 * 440 * V2 equals 133320V2.
Isolating V2 by dividing 77760 by 133320.
Calculating the new volume V2 to be approximately 0.58 L.
Demonstration of the step-by-step process of using the Combined Gas Law to solve for an unknown variable in a gas law problem.
Emphasis on the importance of unit consistency and the correct application of the Combined Gas Law in practical problems.
Conclusion summarizing the method and result of using the Combined Gas Law to find the new volume of a gas under changed conditions.
Transcripts
[Music]
all right in class you should have
learned about the three different gas
laws uh the first one being boils law
and it talks about the relationship
between pressure and volume of a
particular gas um the next one should be
Charles's Law which talks about the
volume and temperature of a particular
gas and um the last one should be gayc
law which talks about the relationship
between pressure and temperature of a
particular gas okay but what happens
when you have pressure volume and
temperature all changing well we're
actually going to combine these gas laws
to form one Giant gas law called the
combined gas law okay if you notice in
these three gas laws the pressure and
volume are always on the on the
numerator so we're going to keep them on
the numerator P1 V1 and notice the
temperature is in the is in the
denominator over T1 so all these things
are just squished into one and then P2
V2 over T2 okay so this is what we're
going to call the combined gas law so
let's actually go an example and do one
together all right so I have a problem
up here that says a gas at 110 kilop
sces and 30° C fills a flexible
container with an initial volume of 2 L
okay if the temperature is raised to 80°
C and the pressure increased to 440
kilopascals what is the new volume okay
so notice we have three variables we're
talking about pressure temperature and
um volume okay so now we're going to
employ the combined Gasol dealing with
all three of those variables so we're
going to look at our first um our first
number 110 kilopascals and that's that
is a unit of pressure so we know it's
our
P1 P1 is 110
kilopascals at 30° C I don't like things
in Celsius so I'm going to change this
to Kelvin so I'm going to add 273 to
that um which makes it uh 303 Kelvin
that's our
temperature and my initial volume is 2 L
so I'm going to say V1 equals 2 L okay
then I continue reading if the
temperature is raised to 80° C again we
want it in kelvin so we're going to add
270
3 making it 353 so our T2 is
353 Kelvin and the pressure increased to
440 kilopascals the pressure P2 is equal
to 440 kilopascals which I'm very happy
that I kept it in kilopascal so to make
sure these units are the same because
pressure can be measured in several
different units we want to make sure our
units are the
same and what is the new volume so our
V2 is our variable what we're trying to
find okay so let's basically plug all
these variables in into our combined gas
law to figure out what the new volume
would be okay so I'm going to erase
this and say our pressure one is 110
kilopascals our volume 1 is 2
L our temperature one is 303
Kelvin our uh pressure 2 is 440
kilopascals we don't know our volume so
we're going to just say
V2 over uh
353 Kelvin okay when I'm looking for a
variable I'm going to cross multiply
these guys so I'm going to say 353 * 110
* 2 and that should give me 7
77660 if you put that in your
calculator so I just cross multiplied
these guys and then cross multiply these
guys uh 303 * 440 *
V2 gives me um 13
3320 V2 okay so then I want to get my I
want to isolate my variable so I'm going
to divide by 1 3 3 32 0 1 3 3 32 0 and I
find that my new volume is.
58
0.58
L and that is how you do the combined
guas law
[Music]
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