A 5.0 -m L, sample of CO2 gas is enclosed in a gas-tight syringe (see Figure 12.4 ) at 22^∘ C. I

step 1 Welcome back to our adventure through Chapter 12 exercises. I've got a situation set up for you

A 5.0 -m L, sample of CO2 gas is enclosed in a gas-tight...

A 5.0 -m $L$, sample of $\mathrm{CO}_{2}$ gas is enclosed in a gas-tight syringe (see Figure 12.4 ) at $22^{\circ}$ C. If the syringe is immersed in an ice bath $\left(0^{\circ} \mathrm{C}\right),$ what is the new gas volume, assuming that the pressure is held constant?

Key Concepts

Charles's Law

Charles's Law states that the volume of a given amount of gas held at constant pressure is directly proportional to its absolute temperature. This means that if the temperature of the gas decreases in Kelvin, its volume will decrease in the same proportion, and vice versa. It is a fundamental principle in understanding the behavior of gases under thermal changes.

Absolute Temperature (Kelvin Scale)

Using the absolute temperature scale (Kelvin) is essential when applying gas laws since it provides a true zero reference point. Converting temperatures from Celsius to Kelvin ensures that the proportional relationships, such as those in Charles's Law, are accurately applied, as calculations require temperatures measured on an absolute scale.

Transcript

00:01 Welcome back to our adventure through chapter 12 exercises.

00:05 I've got a situation set up for you that is almost identical to what you'll find in problem 8.

00:12 They refer you to figure 12 .4, where they have a gas -tight syringe, which is sealed off, plugged into a rubber stopper, with 5 milliliters of carbon dioxide gas inside the syringe.

00:26 Now, on top of the syringe handle, there is a mass.

00:30 Made out of lead which is pressing down on the handle which is at equilibrium with the gas whose pressure is pushing it back up so it's not moving but lead is really dangerous so i've chosen to replace the the lead with patrick decagon any similarities to patrick star are purely coincidental this is a hundred percent original character don't sue me now the weather is quite nice it is 22 degrees celsius in our syringe, but we're going to be dipping our syringe in an ice bath and let it cool down to zero degrees celsius.

01:11 Ooh, quite chilly.

01:13 Now, as our gas molecules cool off as their temperature goes down, their kinetic energy is reduced, meaning they're bouncing around in here slower, not necessarily on average, which means these gas molecules, which are smacking up against all the walls and including the top part of our syringe, which is pushing back against patrick, it's not going to be pushing back as hard.

01:36 So patrick will start to win, and he'll squish them down tighter and tighter until they get compact enough that the number of smacks against the top of our syringe increases.

01:49 So even though on average, they'll be weaker smacks, they'll occur more often.

01:54 Thus, once again, equilibrium will be restored.

01:57 So we expect our final answer to have a slightly smaller volume than our current 5 milliliters.

02:03 We'll find this final answer using charles law, which, if you haven't seen it before, is the volume of your first situation divided by its temperature in kelvin.

02:16 Very important.

02:19 If this were in degrees celsius, you could get zero degrees celsius, and then you're dividing by zero, and that makes a hot mass of infinities.

02:28 So we use kelvin in all circumstances here.

02:32 This is going to be equal to the volume of its second scenario divided by its temperature.

02:40 In kelvin, this is derived from our gas law, pivner, ideal gas law.

02:50 And you can use charles law when the pressure remains constant...

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