The system is isothermal, which means the temperature is constant.

 is pressure,  volume,  moles,  gas constant,  temperature. Rearrange the equation, plug in the appropriate values and solve.

 is pressure,  volume,  moles,  gas constant,  temperature. Rearrange the equation, plug in the appropriate values and solve.

Since we start with 68.8g of the unknown gas, and we have 1.81mol, we can find the molecular weight.

 is pressure,  volume,  moles,  gas constant,  temperature. Rearrange the equation, plug in the appropriate values and solve.

Since we know we have 1.82g of the unknown gas, and we have 0.5mol, we can find the molecular weight by dividing grams by moles.

Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is equal to the sum of the pressures of each of the individual gases in the container. Boyle's Law states that the volume of a fixed amount of gas varies inversely with the pressure at constant temperature. Charles's Law states that the temperature and volume of a gas at constant pressure are directly proportional. Avogadro's Law can also be expressed by saying that one mole of any gas at standard temperature and pressure occupies 22.4L.

The pressure exerted is dependent on molar concentration only (not mass). As the containers are all the same volume, the container with the most moles will exert the most pressure. 60g of 44g/mole CO₂ gives 1.4mol, 50g of O₂ gives 1.4mol, 46g N₂ gives 1.6mol, and 54g F₂ gives 1.4mol, 40g H2 gives 40mol.

Partial pressure is the amount of pressure that is the result of one gas. This is calculated by mutiplying the mole fraction of the gas by the overall pressure.  The mole fraction is calculated as the moles of the compound of interest divided by the total amount of moles present.  2 moles O₂/ 2 moles O₂ + 3 moles N₂ + 5 moles H₂ = 2/10 = mole fraction of O₂.  2/10 multiplied by the total pressure gives us the answer as 0.4 atm.  

There are a couple of things to consider in this problem. First, the problem asks for the molar fraction of the remaining gases in the mixture. As a result, we do not need to know how many different gases are in the mixture, since they all have the same effect on the pressure in the container. Second, the number of moles that one gas accounts for is not relevant since the question is asking to find the molar fraction for the remaining gases. Knowing this, we can find the molar fraction for the described gas, and then subtract it from the total in order to find the remaining molar fraction. The equation for partial pressure is written as .

Since we know how much pressure one gas accounts for, we can solve for the molar fraction of that particular gas.

In other words, the known gas accounts for 75% of the gas molecules in the container. This means that the remaining gases must account for 25% of the gas molecules in the container.

So, the molar fraction for the remaining gases is 0.25.

According to Dalton's law of partial pressures, when two or more gases are in one container without chemical interaction, each behaves independently of the others. The partial pressure of oxygen can, therefore, be found by multiplying the molar fraction of oxygen in the container by the total pressure of the three gases.

This is an equation which requires us to find the partial pressures of each gas in the container. The equation for partial pressure is  where  is the molar fraction of one of the gases. Since there are twice as many moles of gas A as there are gas B, we know that gas A accounts for 2/3 of the moles in the container.