A scuba diver's tank contains 0.29kg of O2 compressed into a volume of 2.3L. Calculate the gas pressure at 8 degrees celcius.
Use PV = nRT
To calculate the gas pressure, we can use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas in Kelvin
First, let's convert the temperature from Celsius to Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius value:
T(K) = T(°C) + 273.15
T(K) = 8 + 273.15
T(K) = 281.15K
Next, let's convert the volume from liters to cubic meters. Since 1 L is equal to 0.001 m^3:
V(m^3) = V(L) * (0.001 m^3 / 1 L)
V(m^3) = 2.3 * 0.001
V(m^3) = 0.0023 m^3
Now, let's calculate the number of moles of gas using the given mass and molar mass of oxygen (O2). The molar mass of O2 is approximately 32 g/mol:
n(mol) = mass(g) / molar mass(g/mol)
n(mol) = 0.29 / 32
n(mol) = 0.0090625 mol
Now we have the values needed for the ideal gas law equation, so let's solve for the pressure (P):
P * V = n * R * T
R is the ideal gas constant, which is approximately 8.31 J/(mol·K).
P = (n * R * T) / V
P = (0.0090625 * 8.31 * 281.15) / 0.0023
P ≈ 88298.89 Pa
Therefore, the gas pressure at 8 degrees Celsius is approximately 88298.89 Pascal (Pa).