Question

n-Butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\) is burned with stoichiometric amount of oxygen. Determine the mole fraction of carbon dioxide and water in the products. Also, calculate the mole number of carbon dioxide in the products per unit mole of fuel burned.

Short answer

Answer: The mole fractions of CO2 and H2O in the products are 4/9 and 5/9, respectively. The mole number of CO2 in the products per unit mole of fuel burned is 4.

Step-by-step solution

1. Write the balanced combustion reaction for n-butane

The combustion reaction of n-butane can be written as: C4H10 (g) + O2 (g) → CO2 (g) + H2O (g) Now, we balance the reaction: C4H10 (g) + 13/2 O2 (g) → 4 CO2 (g) + 5 H2O (g) From the balanced reaction, we can see that for every 1 mole of n-butane burned, 4 moles of CO2 and 5 moles of H2O are produced.

2. Calculate the moles of products formed

Let's assume that we burned 1 mole of n-butane. According to the stoichiometric coefficients, the moles of each product formed will be: - Moles of CO2: n(CO2) = 4 moles - Moles of H2O: n(H2O) = 5 moles

3. Determine the mole fraction of carbon dioxide and water

The mole fractions can be calculated using the formula: Mole fraction (X) = (moles of the component) / (total moles in the mixture) Total moles in the mixture = moles of CO2 + moles of H2O = 4 + 5 = 9 moles Mole fraction of CO2 (X_CO2) = n(CO2) / Total moles = 4/9 Mole fraction of H2O (X_H2O) = n(H2O) / Total moles = 5/9

4. Calculate the mole number of CO2 per unit mole of fuel burned

To find the mole number of CO2 per unit mole of fuel burned (n-butane), we just follow the stoichiometric coefficients in the balanced combustion reaction: Mole number of CO2 = Moles of CO2 / Moles of n-butane = 4 CO2 moles / 1 n-butane mole = 4 So, for every 1 mole of n-butane burned, 4 moles of CO2 are produced. In conclusion: - Mole fraction of CO2 in the products: X_CO2 = 4/9 - Mole fraction of H2O in the products: X_H2O = 5/9 - Mole number of CO2 per unit mole of fuel burned: 4