High School

How many grams of [tex]CO_2[/tex] will be produced by the combustion of 38.2 liters of [tex]C_2H_6[/tex] gas? Assume excess [tex]O_2[/tex].

A. [tex]2.05 \times 10^{24} \, \text{g} \, CO_2[/tex]
B. [tex]75.1 \, \text{g} \, CO_2[/tex]
C. [tex]150. \, \text{g} \, CO_2[/tex]
D. [tex]150 \, \text{g} \, CO_2[/tex]

Answer :

Sure! Let's solve the problem of determining how many grams of CO₂ are produced by the combustion of 38.2 liters of C₂H₆ gas.

Step 1: Calculate the moles of C₂H₆.

We are given the volume of C₂H₆ as 38.2 liters. According to the ideal gas law, at standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters. Therefore, we can calculate the moles of C₂H₆ gas as:

[tex]\[ \text{Moles of C}_2\text{H}_6 = \frac{38.2 \text{ liters}}{22.4 \text{ liters/mole}} \][/tex]

Step 2: Determine the moles of CO₂ produced.

From the balanced chemical equation for the combustion of ethane ([tex]\( \text{C}_2\text{H}_6 \)[/tex]):

[tex]\[ 2 \text{C}_2\text{H}_6 + 7 \text{O}_2 \rightarrow 4 \text{CO}_2 + 6 \text{H}_2\text{O} \][/tex]

We see that 2 moles of C₂H₆ produce 4 moles of CO₂. Hence, for each mole of C₂H₆, 2 moles of CO₂ are produced. So, we multiply the moles of C₂H₆ by 2 to get the moles of CO₂:

[tex]\[ \text{Moles of CO}_2 = \text{Moles of C}_2\text{H}_6 \times 2 \][/tex]

Step 3: Convert moles of CO₂ to grams.

The molar mass of CO₂ is 44.01 grams/mole. We'll use this to convert the moles of CO₂ to grams:

[tex]\[ \text{Mass of CO}_2 = \text{Moles of CO}_2 \times 44.01 \text{ g/mole} \][/tex]

Final Calculation:

Calculating all these, you will find approximately 150 grams of CO₂ are produced.

Therefore, the correct answer is 150 g CO₂.

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