A scuba diver's tank contains .25 kg of oxygen compressed into a volume of 4.3 L (for oxygen, 32g = 1 mole)
Calculate the gas pressure inside the tank at 9 degrees Celsius
What volume would this occupy at 26 degrees Celsius and .95 atmospheres?
See above.
I looked at that guys and i still don't get it.
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,
V is the volume of the gas,
n is the number of moles of gas,
R is the ideal gas constant (0.0821 L·atm/(K·mol)),
T is the temperature of the gas in Kelvin.
First, let's convert the initial temperature from Celsius to Kelvin. To convert Celsius to Kelvin, we use the following formula:
K = °C + 273.15
So, the initial temperature of 9 degrees Celsius is equal to 9 + 273.15 = 282.15 Kelvin.
Now we can calculate the initial gas pressure using the ideal gas law. Rearranging the equation to solve for pressure, we get:
P = nRT / V
We know the number of moles (n) is equal to the mass of oxygen divided by the molar mass:
n = mass / molar mass
n = 0.25 kg / 32 g/mol
n = 0.25 kg / 0.032 kg/mol
n = 7.81 mol
Substituting the known values into the equation:
P = (7.81 mol)(0.0821 L·atm/(K·mol))(282.15 K) / 4.3 L
By calculating this expression, we find that the gas pressure inside the tank at 9 degrees Celsius is approximately 12.731 atm.
To calculate the volume at different temperature and pressure, we can use the ideal gas law again, but this time solving for the volume (V). Rearranging the equation:
V = nRT / P
Given:
T = 26 degrees Celsius = 26 + 273.15 = 299.15 Kelvin
P = 0.95 atm
Substituting the known values into the equation:
V = (7.81 mol)(0.0821 L·atm/(K·mol))(299.15 K) / 0.95 atm
Calculating this expression, we find that the volume at 26 degrees Celsius and 0.95 atmospheres is approximately 204.73 L.