$2 C_6 H_{14}+19 O_2 \rightarrow 12 CO_2+14 H_2 O$
The molar mass of each substance is provided in the table below.
| Substance | Molar Mass $( g / mol )$ |
| :------------------------- | :----------------- |
| Hexane $\left( C _4 H _4\right)$ | 86.17 |
| Oxygen $\left( O _2\right)$ | 32.00 |
| Carbon dioxide $\left( CO _2\right)$ | 44.01 |
| Water $\left( H _2 O \right)$ | 18.02 |
What mass of oxygen would be needed?
Answer (2)
The balanced chemical equation shows that 2 moles of C 6 H 14 react with 19 moles of O 2 .
Assuming we have 2 moles of C 6 H 14 , we need 19 moles of O 2 .
The molar mass of O 2 is 32.00 g/mol.
The mass of O 2 needed is 19 × 32.00 = 608.0 grams.
Explanation
Problem Setup We are given a balanced chemical equation and the molar masses of the substances involved. The equation is: 2 C 6 H 14 + 19 O 2 → 12 C O 2 + 14 H 2 O We are asked to find the mass of oxygen ( O 2 ) needed for the reaction.
Mole Ratio From the balanced equation, we see that 2 moles of C 6 H 14 react with 19 moles of O 2 . Therefore, the mole ratio of O 2 to C 6 H 14 is 2 19 .
Moles of Oxygen However, the question does not specify the mass of Hexane ( C 6 H 14 ) , so we cannot determine the mass of oxygen needed. We need to assume that we are given 2 moles of Hexane. In that case, we need 19 moles of O 2 .
Mass of Oxygen The molar mass of O 2 is given as 32.00 g/mol. To find the mass of O 2 needed, we multiply the number of moles of O 2 by its molar mass: ma s s O 2 = m o l e s O 2 × m o l a r _ ma s s O 2 = 19 × 32.00 = 608.0
Final Answer Therefore, the mass of oxygen needed is 608.0 grams.
Examples
In combustion engines, the ratio of fuel (like hexane) to oxygen is crucial for efficient burning. This calculation helps determine the precise amount of oxygen needed to completely burn a given amount of fuel, ensuring minimal waste and maximum energy output. For example, if you're designing an engine that uses 172.34 grams of hexane, you'd need 608 grams of oxygen for complete combustion, based on the balanced chemical equation. This principle extends to various industrial processes, from power generation to waste incineration, where maintaining the correct fuel-to-oxygen ratio is vital for both efficiency and environmental control.
The mass of oxygen needed for the combustion of 2 moles of hexane is 608.0 grams, calculated from the reaction's balanced equation and the molar mass of oxygen. Since the reaction indicates that 19 moles of oxygen are required, multiplying this by the molar mass gives us the total mass needed. Thus, oxygen must be supplied in that amount to ensure complete combustion.
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