A deep sea diver uses a gas cylinder of 10.0 L and a content of 51.4 g of O2 and 32.5 g of He.
Calculate the partial pressure of each gas and the total pressure of the temperature of the gas is 16 C.
P V = n R T
T = 16 + 273
V = 10 L = .01 m^3
n of O2 = 51.4/32
n of He = 32.5/4
calculate P of each
then add to get total
To calculate the partial pressure of each gas and the total pressure, we need to use the ideal gas law equation, which is given by:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, we need to calculate the number of moles for each gas using their respective masses and molar masses. The molar mass of oxygen (O2) is 32 g/mol, and the molar mass of helium (He) is 4 g/mol.
1. Calculate the number of moles for each gas:
moles of O2 = mass of O2 / molar mass of O2
moles of O2 = 51.4 g / 32 g/mol
moles of O2 = 1.6075 mol
moles of He = mass of He / molar mass of He
moles of He = 32.5 g / 4 g/mol
moles of He = 8.125 mol
Next, we need to convert the given temperature from Celsius to Kelvin. The equation to convert Celsius to Kelvin is: K = °C + 273.15
2. Convert the temperature to Kelvin:
T = 16°C + 273.15
T = 289.15 K
Now, we can calculate the partial pressures using the ideal gas law equation:
3. Calculate the partial pressure of oxygen:
Partial pressure of O2 = (moles of O2 * R * T) / V
Partial pressure of O2 = (1.6075 mol * 0.0821 L·atm/mol·K * 289.15 K) / 10.0 L
Partial pressure of O2 = 3.852 atm
4. Calculate the partial pressure of helium:
Partial pressure of He = (moles of He * R * T) / V
Partial pressure of He = (8.125 mol * 0.0821 L·atm/mol·K * 289.15 K) / 10.0 L
Partial pressure of He = 18.691 atm
Finally, we can calculate the total pressure by summing up the partial pressures:
5. Calculate the total pressure:
Total pressure = Partial pressure of O2 + Partial pressure of He
Total pressure = 3.852 atm + 18.691 atm
Total pressure = 22.543 atm
Therefore, the partial pressure of oxygen is 3.852 atm, the partial pressure of helium is 18.691 atm, and the total pressure is 22.543 atm for a gas temperature of 16°C.