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Which of the following reactions occur t...

Which of the following reactions occur to completion ? .
`{:(,,2A+,3B,rarr,C,+,2D,),((a)"Initial moles",20,,30,,,0,,0),((b)"Initial moles",40,,60,,,10,,0),((c)"Initial moles",40,,90,,,0,,0),((d)"Initial moles",50,,75,,,0,,10):}`

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To determine which of the given reactions occurs to completion, we need to analyze the stoichiometry of each reaction based on the initial moles provided. The reaction is: \[ 2A + 3B \rightarrow C + 2D \] We will evaluate each option one by one. ### Step 1: Analyze Option A **Initial Moles**: - A = 20 - B = 30 - C = 0 - D = 0 Assuming \( x \) moles of A are used: - From the reaction, 2 moles of A react with 3 moles of B. - If we use \( x = 10 \) moles of A, then: - Moles of B used = \( \frac{3}{2} \times 10 = 15 \) - Remaining moles of B = \( 30 - 15 = 15 \) Since we have enough moles of both A and B to react completely, this reaction will proceed to completion. ### Step 2: Analyze Option B **Initial Moles**: - A = 40 - B = 60 - C = 10 - D = 0 Assuming \( y \) moles of A are used: - If we use \( y = 20 \) moles of A, then: - Moles of B used = \( \frac{3}{2} \times 20 = 30 \) - Remaining moles of B = \( 60 - 30 = 30 \) Since we have enough moles of both A and B to react completely, this reaction will also proceed to completion. ### Step 3: Analyze Option C **Initial Moles**: - A = 40 - B = 90 - C = 0 - D = 0 Assuming \( z \) moles of A are used: - If we use \( z = 20 \) moles of A, then: - Moles of B used = \( \frac{3}{2} \times 20 = 30 \) - Remaining moles of B = \( 90 - 30 = 60 \) In this case, we have leftover moles of B (60 moles), indicating that not all reactants are consumed. Therefore, this reaction does not proceed to completion. ### Step 4: Analyze Option D **Initial Moles**: - A = 50 - B = 75 - C = 0 - D = 10 Assuming \( w \) moles of A are used: - If we use \( w = 25 \) moles of A, then: - Moles of B used = \( \frac{3}{2} \times 25 = 37.5 \) - Remaining moles of B = \( 75 - 37.5 = 37.5 \) Here, we have enough moles of both A and B to react completely, hence this reaction will also proceed to completion. ### Conclusion The reactions that occur to completion are: - Option A - Option B - Option D **Final Answer**: Options A, B, and D occur to completion. ---
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