Calculate Carbon to Hydrogen Ratio and Air to Fuel Ratio in Hydrocarbon Fuel

[Pammy2601]

Homework Statement

In an engine test the dry exhaust gas analysis is CO2: 5.27%; O2: 13.38%: N2: 81.35%.
Assuming that the fuel is a pure hydrocarbon of the form CxHy, and that it is completely
burnt, calculate the ratio, by mass, of carbon to hydrogen in the fuel and the air to fuel
ratio by mass.

Homework Equations

combustion equation:
Cn+H2n+1 + A*(0.21O2+0.79N2) = aCO2 + bH2O + cN2

The Attempt at a Solution

I'm pretty confused, as the question states the fuel is pure hydrocarbon so therefore one can assume the combustion is stoichiometric, but the bit that confuses me is the O2 from the dry exhaust gas analysis. I could only find the Air fuel ratio as a algebraic term:

A = (2a+b+2d)/0.42

this is done by counting the oxygens on each side, 0.21*2*A = 2a + b +2d, I added '2d' because in the exhaust gas there's oxygen. I'm not really sure how to start this question. Even a nudge in the right direction would be greatly appreciated. Thanks a lot!

 

[nate808]

Thank you for your post. Based on the information provided, it seems like you are on the right track with your attempt at a solution. Let's break down the problem step by step.

First, we can start by writing out the combustion equation for a pure hydrocarbon fuel, CxHy:

CxHy + (x + (y/2))O2 → xCO2 + (y/2)H2O

Since we know that the fuel is completely burnt, we can assume that the amount of oxygen consumed in the combustion is equal to the amount of oxygen present in the exhaust gas, which is 13.38%. This means that the coefficient in front of oxygen in the combustion equation should be equal to 0.1338.

Now, we can use the dry exhaust gas analysis to solve for the number of moles of each gas present in the exhaust. Since we are given the percentages by volume, we will need to convert them to percentages by moles. This can be done by using the ideal gas law and assuming that the volume of the exhaust gas is constant and equal to 1 mole.

CO2: (5.27% / 100%) * 1 mole = 0.0527 moles
O2: (13.38% / 100%) * 1 mole = 0.1338 moles
N2: (81.35% / 100%) * 1 mole = 0.8135 moles

Next, we can use the coefficients in the combustion equation to set up a system of equations to solve for the unknowns, x and y. Since we know that the fuel is a pure hydrocarbon, we can assume that there are no nitrogen atoms present in the fuel. This means that the coefficient in front of nitrogen in the combustion equation should be equal to 0.

0.0527 moles CO2 = x moles CO2
0.1338 moles O2 = (x + (y/2)) moles O2
0.8135 moles N2 = 0 moles N2

Solving this system of equations will give us the values for x and y, which represent the number of carbon and hydrogen atoms in the fuel, respectively.

Once we have these values, we can calculate the ratio, by mass, of carbon to hydrogen in the fuel by dividing the number of moles of carbon by the number