Question

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 9 Celsius.
B) what volume would this oxygen occupy at 26 Celsius and 0.95atm?

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 in atm
V = volume in liters
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K) for this problem)
T = temperature in Kelvin

So let's solve A):

Given:
Mass of O2 = 0.29 kg
Volume = 2.3 L
Temperature = 9 Celsius

Step 1: Convert temperature from Celsius to Kelvin.
Kelvin = Celsius + 273.15
T = 9 + 273.15 = 282.15 K

Step 2: Convert mass of O2 to moles.
To do this, we need to know the molar mass of O2, which is 32 g/mol. Since we have the mass in kg, we need to convert it to grams first.
Mass of O2 in grams = 0.29 kg x 1000 g/kg = 290 g
Number of moles = Mass / Molar mass
n = 290 g / 32 g/mol = 9.06 mol

Step 3: Plug the values into the ideal gas law equation to solve for the pressure.
PV = nRT
P * 2.3 = 9.06 * 0.0821 * 282.15
P = (9.06 * 0.0821 * 282.15) / 2.3
P ≈ 91 atm

Therefore, the gas pressure inside the tank at 9 Celsius is approximately 91 atm.

Now let's solve B):

Given:
Volume = 2.3 L
Temperature = 26 Celsius
Pressure = 0.95 atm

Step 1: Convert temperature from Celsius to Kelvin.
T = 26 + 273.15 = 299.15 K

Step 2: Plug the values into the ideal gas law equation to solve for the number of moles.
PV = nRT
(0.95) * V = n * (0.0821) * (299.15)
n = (0.95 * V) / (0.0821 * 299.15)
n ≈ 0.118 mol

Step 3: Use the number of moles to calculate the new volume at the given conditions.
PV = nRT
V = (n * R * T) / P
V = (0.118 * 0.0821 * 299.15) / 0.95
V ≈ 2.3 x 10^2 L

Therefore, the volume that this oxygen would occupy at 26 Celsius and 0.95 atm is approximately 2.3 x 10^2 L.