What is the original volume at 101.3 kPa required to fill a 15-liter scuba tank?

What is the calculation process to determine the original volume at 101.3 kPa required to fill a 15-liter scuba tank based on the given data?

The original volume at 101.3 kPa that is required to fill the 15-liter scuba tank is approximately 31.56 liters. Given the pressure in the scuba tank (P1 = 212.8 kPa), the volume of the scuba tank (V1 = 15 liters), and the pressure required to fill the scuba tank (P2 = 101.3 kPa), we can calculate the original volume required using the Ideal gas law.

Calculating Original Volume at 101.3 kPa

Step 1: Determine the formula to calculate the original volume required.

Using the Ideal gas law equation PV = nRT, where P is pressure, V is volume, n is moles of gas, R is the gas constant, and T is the temperature of the gas, we can derive the formula V = nRT/P.

Step 2: Substitute the given values into the formula.

Using the equation V1/P1 = V2/P2, we can calculate V2 (the original volume required) as V2 = V1 × P2 / P1, which results in V2 ≈ 7.12 liters at 101.3 kPa.

Step 3: Calculate the volume of the scuba tank at 101.3 kPa.

Using V2/P2 = V/P1, we find that the volume of the scuba tank at 101.3 kPa (V) is approximately 15 liters, which confirms that the original volume required to fill a 15-liter scuba tank at 101.3 kPa is approximately 31.56 liters.

Therefore, the process involves understanding the Ideal gas law equation, manipulating the variables to solve for the original volume, and confirming the result by calculating the volume of the scuba tank at the given pressure.