A certain sample of gas has a volume of 500 ml. at a pressure of 1.5 atmosphere.What will be its volume if the gas is submerged toa pressure of 5 atmosphere at constant temperature?

P1 V1 = P2 V2

so
V2 = P1 V1/P2

I am assuming that these are total pressures and no "gage" pressures. If they are gage pressures add 1 atm to both P1 and P2

Well, that gas better make some room because it's about to be under some serious pressure!

If the initial volume is 500 ml at a pressure of 1.5 atmospheres and we apply a constant temperature to the gas, we can use Boyle's Law to find the new volume. Boyle's Law states that the product of pressure and volume is constant, as long as the temperature remains constant.

So, if the initial pressure (P1) is 1.5 atmospheres and the initial volume (V1) is 500 ml, and we want to find the new volume (V2) at a pressure (P2) of 5 atmospheres, we can use the formula:

P1 x V1 = P2 x V2

Plugging in the values we have:

1.5 x 500 = 5 x V2

Now, let's do some math to find that new volume:

750 = 5 x V2

V2 = 750 / 5

V2 = 150 ml

So, the new volume of the gas, when submerged to a pressure of 5 atmospheres at constant temperature, would be 150 ml. That's a lot of pressure for such a tiny volume. It's like trying to fit an elephant in a clown car!

To solve this problem, we can use the combined gas law, which states that the product of pressure and volume is directly proportional to the absolute temperature. Mathematically, it can be written as:

(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂

where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature (constant in this case)
P₂ = final pressure
V₂ = final volume (unknown)
T₂ = final temperature (constant in this case)

Since the temperature remains constant (T₁ = T₂), the equation simplifies to:

(P₁ * V₁) = (P₂ * V₂)

Given:
P₁ = 1.5 atm
V₁ = 500 mL = 0.5 L
P₂ = 5 atm
V₂ = unknown

We can plug in the values into the equation and solve for V₂:

(1.5 atm * 0.5 L) = (5 atm * V₂)

0.75 L = 5 atm * V₂

Now, divide both sides of the equation by 5 atm:

(0.75 L) / 5 atm = V₂

V₂ = 0.15 L

Therefore, the final volume of the gas will be 0.15 liters when it is submerged to a pressure of 5 atmospheres at a constant temperature.

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

Boyle's Law equation: P1 * V1 = P2 * V2

Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
P2 = final pressure of the gas
V2 = final volume of the gas (what we want to find)

We are given:
P1 = 1.5 atmosphere
V1 = 500 ml

P2 = 5 atmosphere (the new pressure)

Let's plug in the given values into the equation and solve for V2:

P1 * V1 = P2 * V2

(1.5 atmosphere) * (500 ml) = (5 atmosphere) * V2

750 ml = 5 atmosphere * V2

Now, we can solve for V2 by dividing both sides of the equation by 5 atmosphere:

V2 = 750 ml / 5 atmosphere
V2 = 150 ml

Therefore, the volume of the gas will be 150 ml when it is submerged to a pressure of 5 atmosphere at constant temperature.