Question

You’re at the zoo and have a big red 3.20 L helium balloon. The barometric pressure is 790.0 mm Hg. Then you hear the roar of a lion. Startled, you accidently release the balloon. It flies away. By the time it reaches the clouds the atmospheric pressure is only 0.300 atm. What is the new volume of the balloon?

Answer 1

The new volume, when the pressure drops to 0.300 atm, is 11.09 L

Step-by-step explanation:

Step 1: Data given

The volume of the helium balloon = 3.20 L

The pressure in the balloon is 790.0 mmHg = 790 / 760 = 1.03947 atm

The pressure decreases to 0.300 atm

Step 2: Calculate the new volume

P1*V1 =P2*V2

⇒with P1 = the initial pressure = 1.03947 atm

⇒with V1 = the initial volume = 3.20 L

⇒with P2 = the reduced pressure = 0.300 atm

⇒with V2 = the new volume = TO BE DETERMINED

1.03947 atm * 3.20 L = 0.300 atm * V2

V2 = (1.03947 atm * 3.20 L) / 0.300 atm

V2 = 11.09 L

The new volume, when the pressure drops to 0.300 atm, is 11.09 L

Answer 2

V = 11.093 L

Step-by-step explanation:

In order to solve this question, let's gather the data once again:

We have a ballon with a 3.2 L of volume and the pressure of it, is 790.0 mmHg. When the lion roar, the balloon is released and then, the balloon pressure is 0.3 atm.

To get the new volume, we can assume here that the temperature is constant, and the content of the balloon remains the same, so we ca use Raoult's law here and use the following expression:

P₁V₁ = P₂V₂

From this expression, all we have to do is solve for the volume. In this case, we will say that the new volume is V₂, so solving from the above expression we have:

V₂ = P₁V₁ / P₂

Before we use this expression, we need to convert the pressure of mmHg to atm (You can also convert the atm to mmHg if you like), and is reported that in 1 atm we have 760 mmHg so:

P₁ = 790/760 = 1.04 atm

Now, let's use the expression of volume:

V₂ = 1.04 * 3.2 / 0.3

V₂ = 11.093 L

And this would be the new volume of the balloon.