A mixture consists of 45% oxygen, 12% argon, and 43% nitrogen by volume. A sample of this mixture has a pressure of 2.0 atm in a 5.3 L container at 350 K temperature. How many moles of gas are in the container?

To find the number of moles of gas in the container, we need to use the ideal gas law.

The ideal gas law is represented by the equation: PV = nRT

Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)

We are given:
Pressure (P) = 2.0 atm
Volume (V) = 5.3 L
Temperature (T) = 350 K

Let's plug in the values into the ideal gas law and solve for n:

PV = nRT
(2.0 atm)(5.3 L) = n(0.0821 L.atm/mol.K)(350 K)

10.6 L.atm = n(28.735 L.atm/mol)

Now, let's isolate n by dividing both sides of the equation by (28.735 L.atm/mol):

n = (10.6 L.atm) / (28.735 L.atm/mol)

n ≈ 0.369 mol

Therefore, there are approximately 0.369 moles of gas in the container.

To find the number of moles of gas in the container, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)

Given:
Pressure (P) = 2.0 atm
Volume (V) = 5.3 L
Temperature (T) = 350 K

First, let's convert the percentage compositions of the mixture into decimal values:

Oxygen: 45% = 0.45
Argon: 12% = 0.12
Nitrogen: 43% = 0.43

Next, we need to calculate the mole fraction of each gas in the mixture. To do this, we divide the partial pressure of each gas by the total pressure of the mixture:

Oxygen mole fraction (Xoxygen) = partial pressure of oxygen / total pressure of the mixture
Argon mole fraction (Xargon) = partial pressure of argon / total pressure of the mixture
Nitrogen mole fraction (Xnitrogen) = partial pressure of nitrogen / total pressure of the mixture

The partial pressure of each gas can be obtained by multiplying the mole fraction of each gas by the total pressure:

Partial pressure of oxygen = Xoxygen * total pressure
Partial pressure of argon = Xargon * total pressure
Partial pressure of nitrogen = Xnitrogen * total pressure

Once we have the partial pressures, we can calculate the moles of each gas using the ideal gas law equation. Then, we sum up the moles of each gas to get the total number of moles.

Let's calculate step-by-step:

1. Calculate the mole fractions of each gas in the mixture:

Xoxygen = 0.45
Xargon = 0.12
Xnitrogen = 0.43

2. Calculate the partial pressure of each gas:

Partial pressure of oxygen = Xoxygen * total pressure
Partial pressure of argon = Xargon * total pressure
Partial pressure of nitrogen = Xnitrogen * total pressure

Partial pressure of oxygen = 0.45 * 2.0 atm = 0.9 atm
Partial pressure of argon = 0.12 * 2.0 atm = 0.24 atm
Partial pressure of nitrogen = 0.43 * 2.0 atm = 0.86 atm

3. Now, let's calculate the moles of each gas using the ideal gas law equation:

Moles of oxygen (noxygen) = (Partial pressure of oxygen) * (Volume) / (Ideal gas constant * Temperature)
Moles of argon (nargon) = (Partial pressure of argon) * (Volume) / (Ideal gas constant * Temperature)
Moles of nitrogen (nnitrogen) = (Partial pressure of nitrogen) * (Volume) / (Ideal gas constant * Temperature)

Moles of oxygen = (0.9 atm * 5.3 L) / (0.0821 L·atm/mol·K * 350 K)
Moles of argon = (0.24 atm * 5.3 L) / (0.0821 L·atm/mol·K * 350 K)
Moles of nitrogen = (0.86 atm * 5.3 L) / (0.0821 L·atm/mol·K * 350 K)

4. Finally, sum up the moles of each gas to get the total number of moles:

Total moles of gas = Moles of oxygen + Moles of argon + Moles of nitrogen

Now you can substitute the values into the equations and calculate the answer.