A mixture of helium and neon gases at 317 K contains 3 times the number of helium atoms as neon atoms. The concentration (π/π) of the mixture is found to be 0.150 mol/L. Assuming ideal behavior, what is the partial pressure of helium?
Calculate the total pressure of the 1 L as
PV = nRT
V = 1 L, n = 0.150, R = 0.08205, T = 317 K
Ptotal = 3.9 atm
PHe = XHe x Ptotal where XHe = 3/4 or 0.75
PHe = 0.75 x 3.9 atm = ?
Well, you've got a helium and neon party going on in that mixture! Let's break it down step by step.
First, let's assign some variables. Let π_π» be the number of moles of helium and π_π be the number of moles of neon. Since the number of helium atoms is 3 times the number of neon atoms, we can say that π_π» = 3π_π.
The total number of moles in the mixture is π_π‘ππ‘ππ = π_π» + π_π.
Now, the concentration (π/π) of the mixture is given as 0.150 mol/L, which means π_π‘ππ‘ππ/π = 0.150. Let's assume a volume of 1 L for simplicity, so π_π‘ππ‘ππ = 0.150 mol.
Substituting π_π» = 3π_π, we have 0.150 = 3π_π + π_π, which simplifies to 0.150 = 4π_π. Solving for π_π, we get π_π = 0.150/4 = 0.0375 mol.
Since π_π» = 3π_π, π_π» = 3 * 0.0375 = 0.1125 mol.
Now, assuming ideal behavior, we know that the partial pressure of a gas is given by the product of the moles of the gas and the gas constant (R) and the temperature (T). Symbolically, it's written as π = ππ
π, where π is the number of moles and π
is the ideal gas constant.
For helium, the partial pressure (π_π») is given by π_π»π
π, and for neon, the partial pressure (π_π) is given by π_ππ
π.
Using the ideal gas constant π
= 0.0821 Lβ
atm/(molβ
K) and the temperature π = 317 K, we can calculate the partial pressure.
For helium (π_π»): π_π» = π_π»π
π = 0.1125 * 0.0821 * 317 = 0.926 atm.
So, the partial pressure of helium in the mixture is approximately 0.926 atm. Let the heliums party on!
To find the partial pressure of helium, we need to determine the mole fractions of helium and neon in the mixture.
Let:
π_β = number of moles of helium
π_π = number of moles of neon
Given:
π/π = 0.150 mol/L (concentration of the mixture)
π_β = 3π_π (helium is three times more abundant than neon)
We can use the mole fraction formula to find the mole fractions of helium and neon:
π₯_β = π_β / (π_β + π_π)
π₯_π = π_π / (π_β + π_π)
Let's solve for π_β and π_π:
Since π = π_β + π_π (total moles of the mixture), we have π = 0.150 mol/L.
So, π_β + π_π = 0.150 mol/L.
Since π_β = 3π_π, we can substitute in the above equation:
3π_π + π_π = 0.150 mol/L
4π_π = 0.150 mol/L
π_π = 0.150 mol/L / 4
π_π = 0.0375 mol/L
Now, let's calculate π_β:
π_β = 3π_π
π_β = 3 * 0.0375 mol/L
π_β = 0.1125 mol/L
The mole fractions are:
π₯_β = π_β / (π_β + π_π)
= 0.1125 mol/L / (0.1125 mol/L + 0.0375 mol/L)
= 0.1125 mol/L / 0.150 mol/L
= 0.75
π₯_π = π_π / (π_β + π_π)
= 0.0375 mol/L / (0.1125 mol/L + 0.0375 mol/L)
= 0.0375 mol/L / 0.150 mol/L
= 0.25
To calculate the partial pressure of helium, we can use Dalton's Law of partial pressures:
π_β = π₯_β * π * π
* π
Given:
π = 317 K (temperature)
π
= 0.0821 L * atm / mol * K (ideal gas constant)
Substituting the values, we get:
π_β = 0.75 * 0.150 mol/L * 0.0821 L * atm / mol * K * 317 K
Calculating the partial pressure of helium:
π_β β 0.015 atm
Therefore, the partial pressure of helium in the mixture is approximately 0.015 atm.
To find the partial pressure of helium, we need to determine the mole fraction of helium in the mixture and then use the ideal gas law.
Let's start by finding the mole fraction of helium (π_π»π). The mole fraction is defined as the ratio of the number of moles of a component to the total number of moles in the mixture.
Given that the mixture contains 3 times the number of helium atoms as neon atoms, we can calculate the mole fraction of helium as follows:
π_π»π = π_π»π / π_π‘ππ‘ππ
where π_π»π is the number of moles of helium and π_π‘ππ‘ππ is the total number of moles in the mixture.
Since the concentration of the mixture (π/π) is given as 0.150 mol/L, we can calculate the total number of moles using the formula:
π_π‘ππ‘ππ = πΆ Γ π
where πΆ is the concentration of the mixture and π is the volume of the mixture.
Now, assuming we have the volume of the mixture, we can solve for π_π‘ππ‘ππ:
π_π‘ππ‘ππ = 0.150 mol/L Γ π
Next, we know that the number of moles of helium (π_π»π) is three times the number of moles of neon (π_Nπ):
π_π»π = 3 Γ π_Nπ
Now, we can substitute the value of π_π»π into the mole fraction equation:
π_π»π = 3 Γ π_Nπ / (0.150 mol/L Γ π)
Finally, using the ideal gas law equation:
π_π»π = π_π»π Γ π_π‘ππ‘ππ
where π_π»π is the partial pressure of helium and π_π‘ππ‘ππ is the total pressure of the gas mixture.
Given the temperature of the mixture (317 K), we can determine the total pressure using the ideal gas law:
π_π‘ππ‘ππ = π_π‘ππ‘ππ Γ π
Γ π
where π
is the ideal gas constant (0.0821 LΒ·atm/(molΒ·K)).
Substituting the values into the equation, we can calculate π_π»π.