a mixture of methane CH4 and ethane C2H6 is stored in a container at 294 mmHg. The gases are burned in air to form CO2 and H2O. If the pressure of CO2 is 346mmHg at the same temp and volume as the original mixture, calculate the ratio of moles of CO2 produced to moles of the original gas mixture.

n = PV/RT so the ratio is

(PV/RT)of CO2 = (PV/RT)gases
Since V, R, and T are constant, then the ratio is simply PCO2/Pgases = 346/294 = ??
The problem doesn't ask for it but you can calculate the PCH4 and PC2H6 if you wish as below. I wouldn't have done this but I misread the problem and calculated the actual pressures first before I did the part above. I hated for the below to go to waste.

You must note that the CH4 produces 1 mole CO2 for every 1 mole CH4 burned while C2H6 produces 2 moles CO2 for every mole of C2H6 burned.
PCH4 + PC2H6 = 294
PCO2fromCH4 + 2PCO2fromC2H6 = 346
but 2PC2H6 = PCO2fromC2H6.
Rewrite
PCO2from CH4 + 2PCO2fromC2H6 = 346. Substitute
PCH4 + 2PC2H6 = 294
Subtract
PC2H6 = 346-394=52
Therefore, PC2H6=52 mm Hg.
PCH4 = 294-52 = 242 mm Hg.

Of course moles of the reactants are NOT equal to the moles of products. The ratio is (PV/RT)CO2/(PV/RT)gases/sub> so ratio of moles is ratio of PCO2/Pgases.

To solve this problem, we need to use the ideal gas law and stoichiometry to determine the ratio of moles of CO2 produced to moles of the original gas mixture. Here's how you can approach the problem:

Step 1: Write the balanced equation for the combustion of methane (CH4) and ethane (C2H6) to form carbon dioxide (CO2) and water (H2O):

CH4 + 2O2 → CO2 + 2H2O (Equation 1)
C2H6 + 7/2 O2 → 2CO2 + 3H2O (Equation 2)

Step 2: Calculate the number of moles of CO2 produced using the ideal gas law. The ideal gas law equation is:

PV = nRT

Where:
P is the pressure of the gas
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature in Kelvin

Since the pressure and volume are the same for the original gas mixture and the CO2, we can use the equation to calculate the number of moles of CO2:

nCO2 = (PCO2 * V) / RT (Equation 3)

Step 3: Calculate the number of moles of CH4 and C2H6 in the original gas mixture. Let's assume there are x and y moles of methane and ethane, respectively. From the balanced equations, we know that the ratio of methane to ethane is 1:2. Thus, we can write:

x/y = 1/2 (Equation 4)

Step 4: Substitute the values into Equation 3 and solve for the ratio of moles of CO2 to moles of the original gas mixture:

nCO2 / (x + y) = (PCO2 * V) / [(RT) * (x + y)]

Step 5: Substitute the given values into the equation and solve for the desired ratio.

Given:
PCO2 = 346 mmHg
P = 294 mmHg (pressure of the original gas mixture)
V (original mixture) = V (CO2)
T (temperature) is constant

By substituting these values into the equation, you can calculate the ratio of moles of CO2 produced to moles of the original gas mixture.

Please note that R in this equation is the gas constant, which is usually expressed in different units depending on the units of pressure, volume, and temperature used.