A scuba diver’s tank contains 0.29 kg of O2 compressed into a volume of 2.3L. A)calculate the gas pressure inside the tank at 7 Celsius. B) what volume would this oxygen occupy at 27 Celsius and 0.93atm?

Question

The answer is a)91atm B) 2.3 x 10^2 L Trying to find out how they got these. Please do it step by step with me.

Answer 1

To solve these problems, we can use the Ideal Gas Law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature

A) Calculate the gas pressure inside the tank at 7 Celsius.
To solve for the pressure, we need to find the number of moles of oxygen in the tank.

1. Convert the temperature to Kelvin:
T = 7 Celsius + 273.15 = 280.15 K

2. Convert the mass of oxygen to moles:
We know that the molar mass of oxygen (O2) is approximately 32 g/mol.
Convert the mass in kg to grams: 0.29 kg * 1000 g/kg = 290 g
Now, divide the mass by the molar mass: 290 g / 32 g/mol = 9.0625 mol

3. Convert the volume to liters:
The given volume is already in liters: 2.3 L

4. Convert the pressure unit:
Since the question asks for the pressure in atm, we divide by the conversion factor 1 atm = 101.325 kPa.

Let's plug in the values into the Ideal Gas Law equation:

P * V = n * R * T

P * 2.3 = 9.0625 * 0.0821 * 280.15

P * 2.3 = 21.2128

P = 21.2128 / 2.3

P ≈ 91 atm

Therefore, the gas pressure inside the tank at 7 Celsius is approximately 91 atm.

B) Calculate the volume at 27 Celsius and 0.93 atm.
To solve for the volume, we need to find the number of moles of oxygen in the new conditions.

1. Convert the temperature to Kelvin:
T = 27 Celsius + 273.15 = 300.15 K

2. Convert the pressure unit:
Since the given pressure is in atm, we multiply by the conversion factor 101.325 kPa = 1 atm.

0.93 atm * 101.325 kPa/atm = 94.269225 kPa

3. Let's plug in the values into the Ideal Gas Law equation:

P * V = n * R * T

0.93 * V = 9.0625 * 0.0821 * 300.15

0.93 * V = 22.17940625

V = 22.17940625 / 0.93

V ≈ 23.8484 L

Therefore, the volume that the oxygen would occupy at 27 Celsius and 0.93 atm is approximately 23.8484 L.