A mass of 0.4 g of hydrogen (H2) and 3.2 g of helium (He) are mixed in a rigid 500 mL container.
What is the partial pressure of helium when the container is cooled to 77 K ?
Use PV = nRT
P = unknown to be calculated.
V = 500 mL but convert to L.
n = grams He/molar mass He.
R = 0.08206 L*atm/mol*K
T = 77 K.
Note this calculation does not involve H2. Dalton's Law tells us that EACH gas exerts its own partial pressure regardless of other gases present. You could calculate the partial pressure of the H2 the same way and you could calculate the TOTAL pressure by added the partial pressure of He to partial pressure H2.
To calculate the partial pressure of helium (He) when the container is cooled to 77 K, we need to use the ideal gas law and the concept of partial pressures.
The ideal gas law is expressed as:
PV = nRT
Where:
P is the pressure
V is the volume
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/(mol·K) in the given units)
T is the temperature in Kelvin
To find the partial pressure of helium, we first need to determine the number of moles for each gas present in the container.
For hydrogen (H2):
Given mass = 0.4 g
Molar mass of H2 = 2 g/mol
Using the formula:
n = mass / molar mass
n(H2) = 0.4 g / 2 g/mol = 0.2 mol
For helium (He):
Given mass = 3.2 g
Molar mass of He = 4 g/mol
Using the formula:
n = mass / molar mass
n(He) = 3.2 g / 4 g/mol = 0.8 mol
Now, we can find the total number of moles in the container:
n(total) = n(H2) + n(He) = 0.2 mol + 0.8 mol = 1 mol
Next, we need to convert the volume of the container to liters (L):
Given volume = 500 mL = 500/1000 = 0.5 L
We also have the temperature given as 77 K.
Now, using the ideal gas law, we can calculate the total pressure in the container:
PV = nRT
P(total) * V = n(total) * R * T
P(total) = (n(total) * R * T) / V
Substituting the known values:
P(total) = (1 mol * 0.0821 L·atm/(mol·K) * 77 K) / 0.5 L
P(total) = 12.6478 atm
Now, to find the partial pressure of helium (P(He)) specifically, we need to consider that the partial pressure is proportional to the number of moles of helium present. Since we know the total pressure and the total moles of gas in the container, we can calculate the partial pressure of helium using the following equation:
P(He) = (n(He) / n(total)) * P(total)
Substituting the known values:
P(He) = (0.8 mol / 1 mol) * 12.6478 atm
P(He) = 10.11824 atm
Therefore, when the container is cooled to 77 K, the partial pressure of helium (He) will be approximately 10.12 atm.