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.
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To calculate the ratio of moles of CO2 produced to moles of the original gas mixture, we need to first determine the number of moles of CO2 and the number of moles of the original gas mixture.
Let's start by calculating the number of moles of CO2 produced. Since we know the pressure of CO2 (346 mmHg) and the pressure of the original gas mixture (294 mmHg) are at the same temperature and volume, we can use the ratio of their pressures to determine the ratio of their moles. This assumes that all other conditions remain constant.
The ideal gas law can be used to relate the pressures of two different gases to the respective number of moles. The equation is as follows:
(P1 * V) / (n1 * R) = (P2 * V) / (n2 * R)
Where:
P1 and P2 are the pressures of the two gases
V is the volume (which is constant for this case)
n1 and n2 are the number of moles of the two gases
R is the ideal gas constant
Since the volume and R are constant, we can simplify the equation:
P1 / n1 = P2 / n2
Rearranging this equation, we get:
n2/n1 = P2/P1
Now, we can plug in the given values:
P1 = 294 mmHg (pressure of the original gas mixture)
P2 = 346 mmHg (pressure of CO2)
n2/n1 = 346/294
Simplifying this expression, we get:
n2/n1 ≈ 1.177
This means that the ratio of moles of CO2 produced to moles of the original gas mixture is approximately 1.177.
Please note that this calculation assumes ideal gas behavior and that complete combustion of methane and ethane occurred to produce only CO2 and H2O.