Chemistry homework help with enthelpy

[Spouple]

Homework Statement

A 34.05 gram liquid sample of an unstable compound is deposited in a metal piston assembly that has a cylinder with a diameter of 20.0 cm. After the sample is added, the piston is placed in contact with the liquid and the piston vent is closed. This process removes all residual gas from the piston. The piston assembly is placed in 15.00 Kg of water at 30.00 oC. The barometric pressure is 778 mm Hg (760 mm Hg= 1 atm). As the compound spontaneously decomposes the piston moves up and the temperature of the water increases to 34.52oC. The piston rises 59.1 cm during the reaction. The contents of the cylinder at the end of the complete decomposition consists of 0.450 mol of carbon dioxide gas,0 .375 mol of liquid water, 0.0375 mol of oxygen gas and an unknown amount of gas from an unidentified element. Other useful information:

∆Hfo CO2 = -393.5 Kj/mol
∆Hfo H2O = -286 kj/mol
Enthalpy of decomposition for unknown = -1893Kj/mol
Heat capacity of water = 4.184 J/goC
R = 0.08206 L x atm / mol x K or 8.3145 J/mol x K
Vapor pressure of H2O at 34.5oC = 41 mm Hg

Assume that the heat capacity of the piston assembly is negligible and the mass of the piston is negligible.

Determine:
1- The formula of the unstable compound.
2- The pressure –volume work in kJ for the decomposition of the 34.05 gram sample.
3- The molar change in internal energy for the decomposition of the compound.
4- The standard enthalpy of formation for X

Homework Equations

The only relevant one that I can think of so far is the q equation which is q = total mass * heat capacity * change in temp

The Attempt at a Solution

I don't expect you guys to give me the answer to the whole sheet, but if you could help point me in the right direction for each of the problems then I would be very appreciative.The only thing I know so far is to find the change in heat which would be:
q = 15034.05 * 4.184 * -4.52 = -284319.14 J = -284.319 KJ.

Since it says the enthalpy of decomp for the unknown is -1893 kj/mol I think that we would use the -284.319 kj to figure out the moles of the unknown that we have. This would be around .15 moles of the unknown. If .15 mol = 34.05g then 1 mol = 227 grams/mol. Is this correct?

I am not sure where to go from here at all.

 

[SteamKing]

It's kind of puzzling why you chose to hide the problem statement behind the 'Spoiler' tag. Usually, the 'Spoiler' is to hide something which might reveal the solution.

 

[Spouple]

It's kind of puzzling why you chose to hide the problem statement behind the 'Spoiler' tag. Usually, the 'Spoiler' is to hide something which might reveal the solution.

Because the problem was really long, and I thought it would be best to put it behind the spoiler.

 

[Chestermiller]

How many grams of X were there in the cylinder after decomposition?
How much was the volume increase?
How much volume do you estimate the liquid occupied in the cylinder before decomposition?
What is your estimate of the final volume?
What is your estimate of the volume of gas in the cylinder after decomposition?
What is your estimate of the total number of moles of gas in the cylinder after decomposition?
What is your estimate of the number of moles of X in the cylinder after decomposition?
What is your estimate of the atomic weight of X?
What element has this atomic weight?

Chet

 

[DeeNos]

1. To determine the formula of the unstable compound, you can use the mole ratios of the products (CO2, H2O, and O2) to determine the mole ratio of the unknown gas. From the given information, we know that there are 0.450 mol of CO2, 0.375 mol of H2O, and 0.0375 mol of O2. This means that for every 0.450 mol of CO2 produced, there are also 0.0375 mol of O2 produced. Therefore, the mole ratio of CO2 to O2 is 0.450:0.0375 or 12:1. This means that for every 12 moles of CO2 produced, there is 1 mole of O2 produced. Using the same approach, we can also determine the mole ratio of CO2 to H2O, which is 0.450:0.375 or 6:5. This means that for every 6 moles of CO2 produced, there are 5 moles of H2O produced. Now, we can use these mole ratios to determine the mole ratio of the unknown gas to CO2. Since we know that the total moles of products is 0.450 + 0.375 + 0.0375 = 0.8625 mol, we can set up the following equation:

0.450 mol CO2 + 0.375 mol H2O + 0.0375 mol O2 + x mol unknown = 0.8625 mol

Solving for x, we get x = 0.8625 - 0.450 - 0.0375 - 0.375 = 0.0. This means that there is no mole of unknown gas produced. Since gases have volume, this suggests that the unknown gas is a solid. Therefore, the formula of the unstable compound is likely to be C6H5O5.

2. To determine the pressure-volume work in kJ for the decomposition of the 34.05 gram sample, we can use the ideal gas law:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. We know that the volume of the cylinder is equal to the area of the piston (πr^2) times the height