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 = ?
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 = ?
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!
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.
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.