A balloon filled with 1.35 atm of dimethyl ether gas and 5.25 atm of oxygen gas at 27 °C has an initial volume 2.00L They react according to the following reaction: C2H6O (g) + 3 O2 (g) -> 2 CO2 (g) + 3 H2O (g) The system is allowed to back cool down to 27 °C following the reaction. Assuming the external pressure is still the same (6.60 atm), what is the new volume of the balloon? What is the partial pressure of carbon dioxide in the balloon?
I tried P1V1/T1=P2V2/T2 but the volume still comes out to 2. Does that mean the volume does not change since the system was allowed to cool to the original temperature? Help much appreciated!
I don't think it means that. I think the fallacy in your thinking is that you've not taken into account the change in the number of mols during the reaction. I think you must convert pether and pO2 to mols using PV = nRT, determine the limiting reagent (which I think is the ether) calculate mols remaining of each material after equilibrium, and use those new mols numbers to solve for new volume and then pCO2.
To solve this problem, we can use the ideal gas law, which states that for a given amount of gas, the pressure, volume, and temperature are related by the equation PV = nRT.
First, let's determine the moles of dimethyl ether and oxygen gas. To do this, we'll use the given pressures and the ideal gas law.
For dimethyl ether:
P1 = 1.35 atm
V1 = 2.00 L
T1 = 27 °C (convert to Kelvin: T1 = 27 + 273 = 300 K)
For oxygen gas:
P2 = 5.25 atm
V2 = 2.00 L
T2 = 27 °C (convert to Kelvin: T2 = 27 + 273 = 300 K)
To find the number of moles (n), we can use the ideal gas law rearranged as n = PV / RT.
For dimethyl ether:
n1 = (P1 * V1) / (R * T1)
For oxygen gas:
n2 = (P2 * V2) / (R * T2)
Now, let's use the balanced chemical equation and stoichiometry to determine how many moles of CO2 are formed.
From the balanced equation: C2H6O (g) + 3 O2 (g) -> 2 CO2 (g) + 3 H2O (g)
The stoichiometric ratio tells us that for every 1 mole of dimethyl ether, 2 moles of CO2 are produced. Therefore, the number of moles of CO2 is:
n_CO2 = (2/1) * n1
To find the new volume of the balloon, we can use the ideal gas law again, this time using the number of moles of CO2 and the given pressure and temperature.
P3 = 6.60 atm
T3 = 27 °C (convert to Kelvin: T3 = 27 + 273 = 300 K)
V3 = (n_CO2 * R * T3) / P3
To find the partial pressure of carbon dioxide in the balloon, we need to know the total pressure in the balloon after the reaction.
The total pressure can be obtained by adding the partial pressures of all the gases in the system, which includes the initial dimethyl ether gas, initial oxygen gas, and the carbon dioxide gas formed.
Total pressure = P1 + P2 + P_CO2
Since the initial volume doesn't change (V1 = V2 = V3), the partial pressure of carbon dioxide (P_CO2) will be the difference between the total pressure and the sum of the initial pressures.
P_CO2 = Total pressure - (P1 + P2)
Finally, substitute the values into the equations and solve for the new volume (V3) and the partial pressure of carbon dioxide (P_CO2).