[Aegis6]

My AP Chem teacher gave us a problem (from last year's AP Chemistry test) which went like this:

"A sample of a pure, gaseous hydrocarbon is introduced into a previously evacuated rigid 1.00L chamber. The pressure of the gas is 0.200ATM at 127°C. O₂ is introduced into the same vessel. After the addition of the O₂, total pressure of the gas mixture is 1.40ATM at 127°C.
The mixture of the hydrocarbon and oxygen is sparked so that a complete combustion reaction occurs, producing CO2(g) and H2O(g). The partial pressures of these gasses at 127°C are 0.600ATM for CO2 and 0.800ATM for H2O.

Use the partial pressures of CO2 and H2O to calculate the partial pressure of the O2 consumed in the combustion."

We went over the question in class and saw the AP test's reasoning which went something like this:

0.600 ATM CO2 * 1 ATM O2/1 ATM CO2 = 0.600 ATM O2
0.800 ATM H2O * 1 ATM O2/2 ATM H2O = 0.400 ATM O2

0.600 + 0.400= 1 ATM O2

My question for you is, why is it that you are able to relate the number of Oxygen atoms within the molecules with the pressure of the gas in the container?

[Borek]

My question for you is, why is it that you are able to relate the number of Oxygen atoms within the molecules with the pressure of the gas in the container?

Please elaborate, I am not sure I understand your question.

In general it is all about stoichiometry - we know one mole of oxygen produces two moles of water (assuming enough hydrogen). Similarly we know 1 mole of oxygen produces 1 mole of CO₂. We also know PV=nRT.

[Aegis6]

I don't understand how they converted from the pressure of the reactants to the pressure of the products. And I couldn't use PV=nRT as I did not have a value for the moles of O₂

[Borek]

From the reaction stoichiometry it is obvious that 1 mole produces 1 mole (or 2 moles) of other gas. Now there are two ways of looking at it. One is that from the Avogadro's principle under the same condition of temperature and pressure, equal volumes of all gases contain the same number of molecules - so if there was 1 mole of gas and 1 mole of gas is produced (and the temperature has not changed) pressure must be the same. The other way is to use PV=nRT - for example we know n_O2=n_CO2 (stoichiometry), V_O2=V_CO2 (volume of the vessel is constant), T_O2=T_CO2 (127°C) - it can be easily shown that the only way to keep these things identical is to have P_O2=P_CO2.

There is no substantial difference between these approaches, as Avogadro's principle was a stepping stone to the ideal gas equation.

Note that for a given vessel and temperature it can be generalized - number of moles of gas is directly proportional to its partial pressure (so if you have a mixture containing 1 atm of oxygen and 2 atm of hydrogen, they are mixed in 1:2 molar ratio).