A 24L sample of a gas at fixed mass and constant temperature exerts a pressure of 3.0 atm. What pressure will the gas exert if the volume is changed to 16L?

4.5atm

Use Boyle's Law (P1V1=P2V2)

3.0atm*24L=P2*16
)3.0atm*24)/16=P2
After calculating, the pressure ends up being 4.5atm (:

P1V1 = P2V2

Well, look at it this way - the gas must be feeling a little squeezed in that smaller volume, like trying to fit into skinny jeans after a holiday feast! To find the new pressure, we can use the "pressure-volume inverse relationship" known as Boyle's Law. It states that if the volume of a gas decreases, the pressure increases, and vice versa.

So, we can set up an equation using the initial pressure (P1) and volume (V1), and the final volume (V2) as follows:

P1 x V1 = P2 x V2

Substituting the given values, we have:

3.0 atm x 24 L = P2 x 16 L

Now, let's solve for P2, the unknown pressure value. *cue dramatic mathematical calculations* And after some number crunching:

P2 = (3.0 atm x 24 L) / 16 L

P2 = 72.0 atm / 16 L

P2 = 4.5 atm

So, if you compress that gas clown-car style into 16 liters, it will exert a pressure of 4.5 atmospheres. Surely, the gas must be quite relieved to have some breathing room again!

To find the pressure of the gas when the volume is changed, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the mass and temperature are constant.

Boyle's Law formula:
P1V1 = P2V2

Where:
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume

Now let's substitute the given values into the formula:

P1 = 3.0 atm (initial pressure)
V1 = 24 L (initial volume)
V2 = 16 L (final volume)

P2 = (P1 * V1) / V2
P2 = (3.0 atm * 24 L) / 16 L
P2 = 72 atm / 16 L
P2 ≈ 4.5 atm

Therefore, the gas will exert a pressure of approximately 4.5 atm when the volume is changed to 16L.