A flask of unknown volume was filled with air at a pressure of 389.0 kPa. The flask was attached to an evacuated flask of 32.0 L and the air was allowed to expand into the second flask. At equilibrium, the final pressure was 154.0 kPa. Calculate the volume of the unknown flask.

(a) Use Boyle's law to calculate the volume the gas will occupy if the pressure is increased to 1.79 atm while the temperature is held constant.



3.17 L

(b) Use Charles's law to calculate the volume the gas will occupy if the temperature is increased to 175°C while the pressure is held

Intuitively you see that the pressure has decreased which means the volume must have increased; therefore, the volume of the old flask is v and the volume of the combined flasks is 32+v

Since p1v1 = p2v2, then
389*v = 154(32+v) and solve for v.

To solve this problem, we can use the combined gas law equation, which relates the initial and final conditions of a gas sample. The equation is as follows:

(P1 * V1) / T1 = (P2 * V2) / T2

Where:
P1 and P2 are the initial and final pressures, respectively.
V1 and V2 are the initial and final volumes, respectively.
T1 and T2 are the initial and final temperatures, respectively.

In this problem, we have the following information:
- Initial pressure (P1): 389.0 kPa
- Final pressure (P2): 154.0 kPa
- Final volume (V2): 32.0 L

We need to calculate the volume of the unknown flask (V1).

Since the temperature is not provided, we can assume that it remains constant. Therefore, we can rewrite the equation as:

(P1 * V1) / T = (P2 * V2) / T

Now, we can rearrange the equation to solve for V1:

V1 = (P2 * V2 * T) / P1

Substituting the given values:

V1 = (154.0 kPa * 32.0 L) / 389.0 kPa

Now, we can calculate the volume of the unknown flask:

V1 = (154.0 kPa * 32.0 L) / 389.0 kPa
= 12.685 L

Therefore, the volume of the unknown flask is approximately 12.685 L.