Suppose two 100.0 L tanks are to be filled separately with the gases helium and hydrogen. What mass of each gas is needed to produce a pressure of 155 atm in its respective tank at 22°C?
Use PV = nRT and solve for n in each tank. Then n = grams/molar mass. You know molar mass and n, solve for grams in each tank.
DrBob222, I still don't understand
You have a 100 L tank and you want to fill it with He to a pressure of 155 atm at 22 C.
This problem is two problems in one. One for He and the other for H2. Here is the He one done for you. It's just a matter of substituting into PV = nRT and using n for solve for grams.
PV = nRT or
n = PV/RT =
P = 155 atm
V = 100 L
R = 0.08205
T = 273C + 22C = 295K
n = (155*100)/(0.08205*295)=640 more or less. You can do it more accurately.
Then grams = mols x molar mass
g He = mols He x molar mass He
g He = 640 x 4 = about 2.6 kg.
Thank!
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To find the mass of each gas needed to produce a certain pressure in its respective tank, we can use the ideal gas law, which states:
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:
T(K) = T(°C) + 273.15
T(K) = 22°C + 273.15
T(K) = 295.15 K
Given:
V = 100.0 L
P = 155 atm
T = 295.15 K
Next, we need to calculate the number of moles (n) for each gas.
For helium (He):
Using the ideal gas law equation and rearranging it to solve for n:
n = (PV) / (RT)
Substituting the values into the equation:
n(He) = (155 atm * 100.0 L) / (0.0821 L*atm/mol*K * 295.15 K)
n(He) ≈ 529.93 mol
For hydrogen (H2):
Using the ideal gas law equation and rearranging it to solve for n:
n = (PV) / (RT)
Substituting the values into the equation:
n(H2) = (155 atm * 100.0 L) / (0.0821 L*atm/mol*K * 295.15 K)
n(H2) ≈ 529.93 mol
Now that we have the number of moles for each gas, we can calculate the mass of each gas using their respective molar masses.
The molar mass of helium (He) is approximately 4.00 g/mol.
The molar mass of hydrogen (H2) is approximately 2.02 g/mol.
For helium (He):
Mass(He) = n(He) * molar mass(He)
Mass(He) = 529.93 mol * 4.00 g/mol
Mass(He) ≈ 2119.72 g or 2.12 kg
For hydrogen (H2):
Mass(H2) = n(H2) * molar mass(H2)
Mass(H2) = 529.93 mol * 2.02 g/mol
Mass(H2) ≈ 1070.86 g or 1.07 kg
Therefore, approximately 2.12 kg of helium gas and 1.07 kg of hydrogen gas are needed to produce a pressure of 155 atm in their respective tanks at 22°C.