If a certain gas occupies a volume of 20L when the applied pressure is 10atm , find the pressure when the gas occupies a volume of 5.0L

P1 Vi = P2 V2

10(20) = P2(5)

P2 = 40

Well, if we take the initial volume and pressure as a joke, it's like the gas was playing hide-and-seek in a big room. The gas was feeling quite cramped in that 20L room with a pressure of 10atm. It must have been thinking, "Hey, I need more space to breathe!"

So, the gas sneaked out and found itself in a smaller room of 5.0L. Now it's all cozy and comfortable, but we need to find out the pressure it feels.

To do that, we can use the ideal gas law, which is like the secret code for gases. It's PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

Since we don't know the number of moles or the temperature, we can assume those values are constant. So, we can write:

P1V1 = P2V2

Now let's plug in the values we know:
P1 = 10atm (initial pressure)
V1 = 20L (initial volume)
V2 = 5.0L (final volume)

And we need to find P2, the final pressure.

Using the formula, we have:
10atm * 20L = P2 * 5.0L

Simplifying that, we get:
200 = 5P2

To isolate P2, we divide both sides by 5:
40 = P2

So, the final pressure when the gas occupies a volume of 5.0L is 40atm. Now, that's one impressive hide-and-seek game for our gas friend!

To find the pressure when the gas occupies a volume of 5.0L, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.

Boyle's Law formula: P₁V₁ = P₂V₂

Where:
P₁ = initial pressure (10 atm)
V₁ = initial volume (20L)
P₂ = final pressure (unknown)
V₂ = final volume (5.0L)

Substituting the given values into the formula, we have:

(10 atm)(20L) = P₂(5.0L)

Solving for P₂, we can rearrange the formula:

P₂ = (10 atm)(20L) / (5.0L)

P₂ = 200 atm / 5.0

P₂ = 40 atm

Therefore, the pressure when the gas occupies a volume of 5.0L is 40 atm.

To find the pressure when the gas occupies a volume of 5.0L, we can use Boyle's Law. Boyle's Law states that the pressure of a gas is inversely proportional to its volume at constant temperature.

Boyle's Law equation is expressed as:

P1 * V1 = P2 * V2

Where:
P1 is the initial pressure (10 atm)
V1 is the initial volume (20L)
P2 is the final pressure (unknown)
V2 is the final volume (5.0L)

Plugging in the given values:
(10 atm) * (20L) = (P2) * (5.0L)

Now, we can solve for P2 (the final pressure):

(10 atm * 20L) / 5.0L = P2

(200 atm * L) / 5.0L = P2

40 atm = P2

Therefore, the pressure when the gas occupies a volume of 5.0L is 40 atm.