Helium is collected over water at 20.°C and 1.16 atm total pressure. What total volume of gas must be collected to obtain 0.597 g of helium? (At 20.°C the vapor pressure of water is 17.5 torr.)
I would do this.
pHe + pH2O = 1.16 atm. Calculate pHe alone but be careful that you use the same units.
Then use PV = nRT and solve for V for the dry He.
Using that number for n dry He, solve PV = nRT for n for H2O at 17.5 torr.
Add n H2O + n He for total mols, then
PV = nRT and use total mols for n and total pressure for P. Calculate total V.
To solve this problem, we need to 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/mol.K)
- T is the temperature in Kelvin
First, we need to find the number of moles of helium gas using the given mass. The molar mass of helium (He) is approximately 4 g/mol.
Step 1: Convert the temperature from Celsius to Kelvin.
The given temperature is 20.°C. To convert it to Kelvin, we add 273.15 to the Celsius temperature.
T = 20.°C + 273.15 = 293.15 K
Step 2: Convert the vapor pressure of water from torr to atm.
The vapor pressure of water is given as 17.5 torr. To convert it to atm, we divide it by 760.
Vapor pressure of water = 17.5 torr / 760 torr/atm = 0.023 atm
Step 3: Calculate the partial pressure of helium.
The total pressure is given as 1.16 atm. To find the partial pressure of helium, we subtract the vapor pressure of water:
Partial pressure of helium = Total pressure - Vapor pressure of water
Partial pressure of helium = 1.16 atm - 0.023 atm = 1.137 atm
Step 4: Calculate the number of moles of helium gas.
We can rearrange the ideal gas law equation to solve for n:
n = PV / RT
n = (Partial pressure of helium * Volume) / (Ideal gas constant * Temperature)
Since we want to find the volume, we rearrange the equation:
Volume = (n * R * T) / Partial pressure of helium
Substituting the known values into the equation:
Volume = (0.597 g / 4 g/mol) * (0.0821 L.atm/mol.K) * (293.15 K) / (1.137 atm)
Step 5: Calculate the volume of the gas.
Volume = (0.597/ 4) * (0.0821 * 293.15) / (1.137)
Volume = 0.0894 L
Therefore, the total volume of gas that must be collected to obtain 0.597 g of helium is 0.0894 L.