How Many dm3 of Oxygen at STP are Required to React Completely with 38.8g of Propane?
Understanding the chemical reaction between propane and oxygen is essential in various industrial and scientific applications. This article explores the calculation of the amount of oxygen required to completely combust 38.8 grams of propane under standard temperature and pressure (STP) conditions. We will break down the problem step-by-step, ensuring clarity and accuracy in our stoichiometric calculations.
Stoichiometric Equation for Propane Combustion
The balanced chemical equation for the combustion of propane ((C_{3}H_{8})) with oxygen ((O_{2})) is as follows:
[C_{3}H_{8}(g) 5O_{2}(g) rightarrow 3CO_{2}(g) 4H_{2}O(g)]
From this equation, we can see that one mole of propane reacts with five moles of oxygen to produce three moles of carbon dioxide and four moles of water. This relationship forms the basis of our stoichiometric calculations.
Calculating the Mole Ratio of Propane
To determine the amount of oxygen required, we first need to find the number of moles of propane present in 38.8 grams of the compound. The molar mass of propane ((C_{3}H_{8})) is 44.10 g/mol. Using this information, we can calculate the moles of propane:
[n_{text{propane}} frac{38.8,text{g}}{44.10,text{g/mol}} 0.869,text{mol}]
Using Stoichiometry to Determine Oxygen Requirement
According to the stoichiometric equation, 1 mole of propane requires 5 moles of oxygen for complete combustion. Therefore, the number of moles of oxygen required can be calculated as follows:
[text{Moles of }O_{2} 0.869,text{mol} times 5 4.345,text{mol}]
Since 1 mole of gas occupies 22.4 liters at STP, we can now find the volume of oxygen required:
[text{Volume of }O_{2} 4.345,text{mol} times 22.4,text{L/mol} 97.04,text{L}]
It is worth noting that 1 liter is equivalent to 1 dm3. Therefore, we can convert the volume to cubic decimeters (dm3):
[97.04,text{L} 97.04,text{dm}^3]
Conclusion and Practical Applications
Understanding the stoichiometric relationship between propane and oxygen is crucial for designing and optimizing combustion processes in various industrial applications. Whether it is for chemical plants, automotive engine design, or spacecraft propulsion systems, the proper calculation of the required reactants ensures efficiency and safety.
The detailed step-by-step approach provided here can be applied to other similar stoichiometric problems, making it a valuable skill for students and professionals in chemistry and related fields.