Final answer:
To find the total pressure of the mixture of these three gases within the 35.0 L cylinder, we can use Dalton's law of partial pressures. The partial pressure of each gas can be calculated by multiplying the mole fraction of the gas by the total pressure. The total pressure of the mixture is the sum of the partial pressures of the individual gases.
Step-by-step explanation:
To find the total pressure of the mixture of these three gases within the 35.0 L cylinder, we can use Dalton's law of partial pressures.
According to this law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
First, let's find the partial pressure of each gas.
The partial pressure of a gas can be calculated by multiplying the mole fraction of the gas by the total pressure.
The mole fraction of a gas is equal to the moles of the gas divided by the total moles of all the gases.
Let's calculate the mole fraction and partial pressure for argon:
The moles of argon can be calculated using the Ideal Gas Law equation
n = PV / RT
where P is the pressure, V is the volume, R is the ideal gas constant, and T is the temperature.
Using the given values, we have
P = 4.65 atm, V = 25.0 L, R = 0.0821 L·atm/mol·K, T
= 14.0 °C = 287.15 K
Plugging in the values:
n = (4.65 atm) * (25.0 L) / (0.0821 L·atm/mol·K * 287.15 K)
Calculating this, we find that the moles of argon is approximately 2.050
The mole fraction of argon is then:
Mole fraction of argon = moles of argon / (moles of argon + moles of helium + moles of hydrogen
Mole fraction of argon = 2.050 / (2.050 + moles of helium + moles of hydrogen)
Similarly, we can calculate the moles and mole fraction for helium and hydrogen.
The partial pressure of argon is then:
Partial pressure of argon = mole fraction of argon * total pressure
Similarly, we can find the partial pressure of helium and hydrogen.
Finally, the total pressure of the mixture is the sum of the partial pressures of the gases:
Total pressure = partial pressure of argon + partial pressure of helium + partial pressure of hydrogen