Equal masses of Ne and Ar are placed in a rigid, sealed container. If the total pressure in the container is 1.2 atm, what is the partial pressure of Ar?
I would assume a number (any number for the masses). Ten(10) looks like a convenient number to choose.
mols Ne = 10/atomic mass Ne = ?
mols Ar = 10/atomic number Ar = ?
total mols = mols Ne + mols Ar
XAr = nAr/total mols
XNa = nNe/atotal mols
pAr = XAr x Ptotal
pNe = XNe x Ptotal
Why did the noble gases go to therapy? Because they had too much pressure in their lives!
But in all seriousness, to determine the partial pressure of Ar, we need to calculate the mole fraction of Ar in the container. Since the masses of Ne and Ar are equal, that means that their moles will also be equal.
Now, the mole fraction (X) of Ar can be calculated by the following equation:
X(Ar) = (moles of Ar) / (total moles of gas)
Since the masses are equal, the moles of Ar and Ne will be equal as well.
So, X(Ar) = (moles of Ar) / (moles of Ar + moles of Ne)
Since the masses are equal, we can say that 1 mole of Ar is equal to 1 mole of Ne.
Therefore, X(Ar) = (1 mole Ar) / (1 mole Ar + 1 mole Ne)
Simplifying this expression, we get:
X(Ar) = 1/2
Now, to find the partial pressure of Ar, we can use Dalton's Law of Partial Pressures, which states that the total pressure is equal to the sum of the partial pressures of all the gases present.
Since the total pressure is given as 1.2 atm, we can write the equation as:
total pressure = partial pressure of Ar + partial pressure of Ne
Substituting the values and rearranging the equation, we get:
partial pressure of Ar = total pressure - partial pressure of Ne
partial pressure of Ar = 1.2 atm - partial pressure of Ne
Since the moles of Ar and Ne are equal and their partial pressures will be the same, we can say that the partial pressure of Ne is equal to the partial pressure of Ar.
Therefore, the partial pressure of Ar is:
partial pressure of Ar = 1.2 atm - partial pressure of Ar
Simplifying this expression, we get:
2 * partial pressure of Ar = 1.2 atm
Dividing both sides by 2, we find:
partial pressure of Ar = 0.6 atm
So, the partial pressure of Ar in the container is 0.6 atm.
To determine the partial pressure of Ar in the container, we need to consider the mole fraction of Ar in the mixture.
The mole fraction of a given gas can be calculated as follows:
Mole Fraction (X) = Moles of Gas / Total Moles of Gas
Since the masses of Ne and Ar are equal, we can assume they have the same number of moles. Let's assume we have 1 mole of both Ne and Ar.
To find the mole fraction of Ar, we need to know the total mole fraction of the mixture (X_total). The mole fraction of Ne would be the same as the mole fraction of Ar.
Since the container is sealed and the gases are in a rigid container, we can apply Dalton's Law of Partial Pressures, which states that the total pressure is equal to the sum of the partial pressures:
Total Pressure (P_total) = P_Ne + P_Ar
We are given that the total pressure is 1.2 atm, and since the pressure for Ne and Ar are equal, we can rewrite the equation:
1.2 atm = P_Ne + P_Ar
Since we assumed that we have 1 mole of both gases, we can substitute the mole fraction (X) into the equation:
1.2 atm = X_Ne * P_total + X_Ar * P_total
Since the mole fraction of Ne (X_Ne) is the same as the mole fraction of Ar (X_Ar), we can rewrite the equation as:
1.2 atm = 2 * X * P_total
Now, we solve for X:
X = 1.2 atm / (2 * P_total)
Substituting the values:
X = 1.2 atm / (2 * 1.2 atm) = 0.5
The mole fraction of Ar in the mixture is 0.5. This means that Ar contributes 50% to the total moles of the gases.
Finally, we can calculate the partial pressure of Ar:
Partial Pressure of Ar = X_Ar * P_total
Partial Pressure of Ar = 0.5 * 1.2 atm = 0.6 atm
Therefore, the partial pressure of Ar in the container is 0.6 atm.
To find the partial pressure of Ar in the container, we need to use Dalton's law of partial pressures. According to this law, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas.
Since equal masses of Ne and Ar are placed in the container, their molar amounts will also be equal since mass is directly proportional to the number of moles when the molar mass is constant. Therefore, we can assume that the mole fraction of Ar and Ne in the mixture is the same.
Let's denote the total pressure as P_total, and the partial pressure of Ar as P_Ar.
According to Dalton's law, we have:
P_total = P_Ar + P_Ne
Since the mole fraction of each gas is equal, we can write:
P_Ar = x * P_total
P_Ne = x * P_total
Where x is the mole fraction of either gas.
Since both gases have equal masses, their molar masses are different. The molar mass of Ne is approximately 20.18 g/mol, and the molar mass of Ar is approximately 39.95 g/mol. Therefore, the molar fractions of Ar and Ne are equal to their respective molar masses divided by the sum of their molar masses:
x_Ar = molar mass of Ar / (molar mass of Ar + molar mass of Ne)
= 39.95 g/mol / (39.95 g/mol + 20.18 g/mol)
= 0.664
Similarly, x_Ne can be calculated as:
x_Ne = molar mass of Ne / (molar mass of Ar + molar mass of Ne)
= 20.18 g/mol / (39.95 g/mol + 20.18 g/mol)
= 0.336
Now, substituting the values in the equations, we get:
P_Ar = x_Ar * P_total
= 0.664 * 1.2 atm
= 0.7968 atm
Therefore, the partial pressure of Ar in the container is approximately 0.797 atm.