Solve Gas Stoichiometry: Find CH2 Molecular Formula from 2.56atm

[Hollysmoke]

Homework Statement

A sealed 1.00 L vessel contains 0.3475 g of argon gas and 6.766 g of an unknown gas at 350 K. If the total pressure of the gas mixture is 2.56 atm, and the unknown gas has an empirical formula of CH2, what is the molecular formula of the unknown gas?

Homework Equations

I get stuck about halfway. I find the mole fraction of Ar but I'm not sure if its right, if someone could help me on how to finish the problem please? How do I find the molar mass of the unknown?

The Attempt at a Solution

I used the mass of the Argon Gas to find the number of moles (0.00869 mols), then ideal gas law to find the pressure of argon gas (2.49 atm). Then using mole fractions, P1=X1*Ptot,I get X for Argon as 0.097, or 9.7% Argon Gas.

Is CH2 = 90.3% then, so X = 0.903? What do I do afterwards?

 

[chemisttree]

You know the temperature, volume and pressure of the vessel. Assume that the mixture of gases acts in an ideal fashion (PV=nRT). From this you will know the total number of moles of the binary mixture. You already precisely know the number of moles of one of the components.

 

[Blueshift5]

it is important to carefully read and understand the given information before attempting to solve the problem. In this case, we are given the total pressure of the gas mixture, the volume of the vessel, and the masses of two gases present. The first step is to convert the given masses of argon and the unknown gas into moles. This can be done by dividing the given masses by their respective molar masses. The molar mass of argon is 39.948 g/mol and the molar mass of the unknown gas can be calculated using its empirical formula of CH2, which has a molar mass of 14.03 g/mol. This gives us 0.00869 moles of argon and 0.4834 moles of the unknown gas.

Next, we can use the ideal gas law (PV = nRT) to calculate the partial pressure of the unknown gas. We know the total pressure (2.56 atm), volume (1.00 L), and temperature (350 K), and we have just calculated the number of moles of the unknown gas. Solving for the unknown pressure gives us 2.32 atm.

Now, we can use the mole fraction formula (X = n1/(n1+n2)) to calculate the mole fraction of the unknown gas. We know the total number of moles (0.4921 moles) and we just calculated the number of moles of the unknown gas (0.4834 moles). Plugging these values into the formula gives us a mole fraction of 0.982, or 98.2% for the unknown gas. This means that the remaining 1.8% is argon.

Finally, to determine the molecular formula of the unknown gas, we need to find the ratio of the number of atoms of each element present. Since the empirical formula of CH2 only has one carbon atom and two hydrogen atoms, we can assume that for every mole of the unknown gas, there is one mole of carbon and two moles of hydrogen. However, we have to take into account the fact that only 98.2% of the gas is the unknown gas. This means that for every 0.982 moles of the unknown gas, there is 1 mole of carbon and 2 moles of hydrogen. This gives us a molecular formula of C0.982H1.964, which can be simplified to CH2.