Select the correct answer.
In the following combustion reaction of acetylene ($C_2H_2$), how many liters of $CO_2$ will be produced if 60 liters of $O_2$ is used, given that both gases are at STP?
$2 C_2 H_2+5 O_2 \rightarrow 2 H_2 O+4 CO_2$
The volume of one mole of gas at STP is 22.4 liters.
A. 48 liters
B. 0.02 liters
C. 240 liters
D. 300 liters
Answer (1)
The balanced chemical equation shows that 5 moles of O 2 produce 4 moles of C O 2 .
Set up a proportion: V o l u m e O 2 V o l u m e C O 2 = 5 4 .
Substitute the given volume of O 2 : 60 V o l u m e C O 2 = 5 4 .
Solve for V o l u m e C O 2 : V o l u m e C O 2 = 5 4 × 60 = 48 liters. The final answer is 48 .
Explanation
Problem Analysis Let's analyze the problem. We are given a combustion reaction of acetylene ( C 2 H 2 ) with oxygen ( O 2 ) producing water ( H 2 O ) and carbon dioxide ( C O 2 ). The balanced chemical equation is:
2 C 2 H 2 + 5 O 2 → 2 H 2 O + 4 C O 2
We are given that 60 liters of O 2 are used at Standard Temperature and Pressure (STP), and we need to find the volume of C O 2 produced at STP. We also know that the volume of one mole of any gas at STP is 22.4 liters.
Stoichiometric Ratio From the balanced chemical equation, we can see that 5 moles of O 2 react to produce 4 moles of C O 2 . This gives us a stoichiometric ratio between O 2 and C O 2 . Since the volume of a gas is directly proportional to the number of moles at STP, we can use the volumes directly in the ratio.
Setting up the Proportion We can set up a proportion to find the volume of C O 2 produced:
V o l u m e O 2 V o l u m e C O 2 = 5 4
We are given that V o l u m e O 2 = 60 liters. Plugging this into the proportion, we get:
60 V o l u m e C O 2 = 5 4
Calculating the Volume of CO2 Now, we can solve for V o l u m e C O 2 :
V o l u m e C O 2 = 5 4 × 60
V o l u m e C O 2 = 48 liters
Final Answer Therefore, 48 liters of C O 2 will be produced when 60 liters of O 2 are used in the combustion reaction, given that both gases are at STP.
Examples
Combustion reactions, like the one described, are fundamental in many real-world applications, such as internal combustion engines in cars or power plants that burn fuels to generate electricity. Understanding the stoichiometry of these reactions allows engineers to calculate the amount of fuel needed and the amount of emissions produced. For instance, knowing how much carbon dioxide is produced from burning a certain amount of fuel helps in assessing the environmental impact and developing strategies to reduce greenhouse gas emissions. In this specific case, if we wanted to design a system to capture the C O 2 produced, we would need to know exactly how much C O 2 is generated for a given amount of fuel consumed.
