A scuba diver's tank contains 0.39 kg of O2 compressed into a volume of 2.5 L.
Calculate the gas pressure inside the tank at 12°C.
I'll do my best to help.
You know the ideal gas equation right?
PV=nRT
P=pressure (atm)
V=volume (L)
n=number moles of gas
R=gas constant=.08206 (atm L/mol K)
T=Temperature (Kelvin)
So convert the temperature to kelvin.
Then convert the mass of O2 gas to moles (In one mole of O2, there are 31.9988 grams of O2, so convert the given mass to grams and then to moles of O2). Plug stuff in... solve for P.
Do you still need more help?
To calculate the gas pressure inside the tank, we can use the Ideal Gas Law equation:
PV = nRT
where:
P is the pressure of the gas (in Pascals)
V is the volume of the gas (in liters)
n is the number of moles of gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature of the gas (in Kelvin)
First, let's convert the given values to appropriate units:
- The volume of the gas is given as 2.5 L.
- The temperature is given as 12°C. To convert it to Kelvin, we add 273.15 to the Celsius value: T = 12 + 273.15 = 285.15 K.
Next, we need to determine the number of moles of gas, n. We can do this by using the molar mass of O2, which is 32 g/mol.
Given that the mass of O2 in the tank is 0.39 kg, we can convert it to grams: 0.39 kg * 1000 g/kg = 390 g.
Then, we divide the mass by the molar mass to find the number of moles: n = 390 g / 32 g/mol = 12.188 mol.
Now we can substitute the values into the Ideal Gas Law equation:
PV = nRT
P * 2.5 L = 12.188 mol * 8.314 J/(mol·K) * 285.15 K
To find the pressure, P, we need to solve for P:
P = (12.188 mol * 8.314 J/(mol·K) * 285.15 K) / 2.5 L
Calculating this expression:
P = 35207.67 J / 2.5 L
P ≈ 14083.07 Pa
Therefore, the gas pressure inside the scuba diver's tank at 12°C is approximately 14083.07 Pa.