Select the correct answer.
In the following reaction, how many liters of oxygen will react with 270 liters of ethene [tex]$\left( C _2 H _4\right)$[/tex] at STP?
[tex]$C_2 H_{4(g)}+3 O_{2(g)} \rightarrow 2 CO_{2(g)}+2 H_2 O_{(g)}$[/tex]
The volume of one mole of gas at STP is 22.4 liters.
A. 810 liters
B. 135 liters
C. 90 liters
D. 540 liters
Answer (2)
The balanced chemical equation shows that 1 mole of C 2 H 4 reacts with 3 moles of O 2 .
At STP, the volume of gases is directly proportional to the number of moles.
Calculate the volume of O 2 by multiplying the volume of C 2 H 4 by 3: V O 2 = 3 × 270 = 810 liters.
The volume of oxygen that will react with 270 liters of ethene is 810 liters .
Explanation
Problem Setup and Given Information We are given the balanced chemical equation for the reaction between ethene ( C 2 H 4 ) and oxygen ( O 2 ) : C 2 H 4 ( g ) + 3 O 2 ( g ) i g h t ha r p oo n u p 2 C O 2 ( g ) + 2 H 2 O ( g ) We are told that 270 liters of ethene react at STP (Standard Temperature and Pressure), and we need to find the volume of oxygen required for this reaction.
Mole Ratio and Volume Relationship From the balanced equation, we see that 1 mole of ethene ( C 2 H 4 ) reacts with 3 moles of oxygen ( O 2 ) . Since the reaction occurs at STP, the volume of gases is directly proportional to the number of moles. This means that the volume of O 2 required is 3 times the volume of C 2 H 4 .
Calculating the Volume of Oxygen To find the volume of oxygen, we multiply the volume of ethene by 3: V O 2 = 3 × V C 2 H 4 = 3 × 270 liters = 810 liters
Final Answer Therefore, 810 liters of oxygen will react with 270 liters of ethene at STP.
Examples
In combustion engines, the ratio of fuel to oxygen is crucial for efficient burning. If you know the volume of fuel being used, you can calculate the amount of oxygen needed for complete combustion using stoichiometry, similar to the problem we solved. This ensures that the engine operates efficiently and minimizes the production of harmful emissions. For instance, if an engine uses 100 liters of a fuel similar to ethene, you would need 300 liters of oxygen for complete combustion, following the 1:3 ratio.
The volume of oxygen that reacts with 270 liters of ethene ( C 2 H 4 ) at STP is 810 liters. This is calculated based on the reaction ratio that indicates 1 volume of ethene requires 3 volumes of oxygen. The correct answer is 810 liters of oxygen.
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