A gas mixture consists of equal masses of methane (molecular weight 16.0) and argon (atomic weight 40.0). If the partial pressure of argon is 200. torr, what is the pressure of methane, in torr?
P V = n R T
n is number of mols
say we have 1 mol (n=1) of argon, 40 grams
then we have 40 grams of Methane
which is 40/16 or 2.5 mols (n=2.5)
they both have the same V and T
P/n = RT/V = same for each
200/1 = Pmeth/2.5
Pmeth = 2.5*200 = 500 torr
Why did the methane feel left out? Because everyone was obsessed with argon! Now let's solve this mystery.
Since we have equal masses of methane and argon, we can assume that they have an equal number of moles. That means the ratio of their partial pressures is the same as the ratio of their molecular weights.
The molecular weight of methane is 16.0, and the atomic weight of argon is 40.0. So the ratio of their partial pressures is:
P(methane) / P(argon) = 16.0 / 40.0
We know that the partial pressure of argon is 200. torr. So let's plug that in and solve for P(methane):
P(methane) / 200. = 16.0 / 40.0
Cross-multiplying, we get:
P(methane) = (16.0 / 40.0) * 200.
Simplifying, we find:
P(methane) = 80. torr
So the pressure of methane is 80. torr. And now both methane and argon can breathe a sigh of relief, knowing that they're equally appreciated in this gas mixture!
To find the pressure of methane in the gas mixture, we need to use Dalton's Law of Partial Pressures. According to Dalton's Law, the total pressure of a gas mixture is equal to the sum of the partial pressures of the individual gases.
The formula for Dalton's Law is:
P_total = P_1 + P_2 + ...
In this case, we know that the partial pressure of argon (P_1) is 200. torr. Let's assume the partial pressure of methane is P_2.
Since the gas mixture consists of equal masses of methane and argon, we can assume that the number of moles of methane (n_2) is equal to the number of moles of argon (n_1).
The number of moles (n) can be calculated using the equation:
n = mass / molar mass
For methane (CH4):
n_2 = mass of methane / molar mass of methane
= mass of argon / molar mass of argon
Since the masses of methane and argon are equal, we can rewrite the equation as:
mass of methane / molar mass of methane = mass of argon / molar mass of argon
Simplifying further:
mass of methane / 16.0 = mass of argon / 40.0
We can cancel out the masses since they are equal:
16.0 = 40.0
This shows that the two molar masses are equal. Therefore, the molar ratios of methane and argon are 1:1.
According to Dalton's Law, the partial pressure of argon (P_1) is 200. torr. The partial pressure of methane (P_2) is unknown.
Now, let's calculate the total pressure of the gas mixture:
P_total = P_1 + P_2
Since the partial pressure of argon (P_1) is 200. torr, the equation becomes:
P_total = 200. torr + P_2
Therefore, the pressure of methane is equal to the total pressure of the gas mixture minus the partial pressure of argon:
P_2 = P_total - P_1
Let's substitute the known values into the equation:
P_2 = P_total - P_1
P_2 = P_total - 200. torr
Since the pressure of methane (P_2) is equal to the pressure of the gas mixture (P_total) minus the partial pressure of argon (P_1), let's express the equation in terms of P_total:
P_2 = P_total - 200. torr
P_total = P_2 + 200. torr
Now, we can substitute P_total back into the equation for Dalton's Law:
P_total = P_1 + P_2
P_2 + 200. torr = 200. torr + P_2
Simplifying the equation:
P_2 + 200. torr = 200. torr + P_2
We can see that P_2 cancels out on both sides, leaving only 200. torr on the right side:
200. torr = 200. torr
This equation implies that the pressure of methane (P_2) is also equal to 200. torr.
Therefore, the pressure of methane in the gas mixture is 200. torr.
To determine the pressure of methane, we can use Dalton's law of partial pressures, which states that the total pressure of a gas mixture is equal to the sum of the partial pressures of its individual components.
In this case, we are given the partial pressure of argon (200. torr) and the fact that the mass of methane is equal to the mass of argon. Since the gases have equal masses, we can assume they occupy equal volumes. Therefore, the ratio of the partial pressure of argon to the partial pressure of methane will be equal to the ratio of their molecular weights.
The molecular weight of methane is 16.0 g/mol, while the atomic weight of argon is 40.0 g/mol. Therefore, the ratio of the molecular weight of argon to methane is 40.0/16.0 = 2.5.
Now, using this ratio, we can calculate the pressure of methane. Let's denote the pressure of methane as P_1. We can set up the following equation:
200. torr (partial pressure of argon) = 2.5 (ratio of molecular weights) * P_1 (partial pressure of methane)
To solve for P_1, divide both sides of the equation by 2.5:
P_1 = 200. torr / 2.5
= 80. torr
Therefore, the pressure of methane in the gas mixture is 80. torr.