The mass of `CO_(2)` produced from 620 gm mixture of `C_(2)H_(4)O_(2)` & `O_(2)` prepared to produce maximum energy is ( combustion reaction is exothermic )

Options

A. 413.33 gm
B. 593.04 gm
C. 440 gm
D. 320 gm

Answer

To solve the problem of finding the mass of CO₂ produced from a 620 g mixture of C₂H₄O₂ and O₂, we will follow these steps:

### Step 1: Write the balanced chemical equation
The balanced equation for the combustion of acetic acid (C₂H₄O₂) is:
\[ C_2H_4O_2 + 2 O_2 \rightarrow 2 CO_2 + 2 H_2O \]

### Step 2: Define the variables
Let:
- \( x \) = mass of C₂H₄O₂ in grams
- \( 620 - x \) = mass of O₂ in grams

### Step 3: Calculate the number of moles
The molar masses are:
- Molar mass of C₂H₄O₂ = 60 g/mol
- Molar mass of O₂ = 32 g/mol

Using the molar masses, we can express the number of moles:
- Moles of C₂H₄O₂ = \( \frac{x}{60} \)
- Moles of O₂ = \( \frac{620 - x}{32} \)

### Step 4: Set up the stoichiometric ratio
From the balanced equation, the stoichiometric ratio of C₂H₄O₂ to O₂ is 1:2. Therefore, we can set up the equation:
\[ \frac{\text{Moles of } C_2H_4O_2}{\text{Moles of } O_2} = \frac{1}{2} \]
Substituting the expressions for moles, we have:
\[ \frac{\frac{x}{60}}{\frac{620 - x}{32}} = \frac{1}{2} \]

### Step 5: Cross-multiply and solve for \( x \)
Cross-multiplying gives us:
\[ 2 \cdot \frac{x}{60} = \frac{620 - x}{32} \]
This simplifies to:
\[ \frac{2x}{60} = \frac{620 - x}{32} \]
Cross-multiplying leads to:
\[ 2x \cdot 32 = 60(620 - x) \]
\[ 64x = 37200 - 60x \]
\[ 64x + 60x = 37200 \]
\[ 124x = 37200 \]
\[ x = \frac{37200}{124} = 300 \text{ g} \]

### Step 6: Calculate the mass of CO₂ produced
From the balanced equation, 1 mole of C₂H₄O₂ produces 2 moles of CO₂. Therefore, the number of moles of CO₂ produced is:
\[ \text{Moles of CO₂} = 2 \cdot \frac{x}{60} = 2 \cdot \frac{300}{60} = 10 \text{ moles} \]

Now, calculate the mass of CO₂:
\[ \text{Mass of CO₂} = \text{Moles of CO₂} \times \text{Molar mass of CO₂} = 10 \times 44 = 440 \text{ g} \]

### Final Answer
The mass of CO₂ produced is **440 g**.

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