When the following equation is balanced, the coefficients are __________.

Al(NO3)3 + Na2S → Al2S3 + NaNO3

Question

When the following equation is balanced, the coefficients are __________.

Al(NO3)3 + Na2S → Al2S3 + NaNO3

BlackTom AI · Accepted Answer

First, restating the problem helps set up the balancing task: balance Al(NO3)3 + Na2S → Al2S3 + NaNO3 with coefficients a, b, c, d for Al(NO3)3, Na2S, Al2S3, and NaNO3 respectively.
Option by option analysis:

Option 1: 2, 1, 3, 2 (a=2, b=1, c=3, d=2)
- Check aluminum: a should equal 2c because Al appears as Al2S3 on the product side; here a=2 and 2c=6, so aluminum balance already fails.
- Even if you try to salvage, sulfur balance would require b=3c (here b=1, c=3 gives b=9), which is inconsistent. Thus this set cannot balance the equation.

Option 2: 4, 6, 3, 2 (a=4, b=6, c=3, d=2)
- Aluminum: a should equal 2c; 2c=6, but a=4, so aluminum balance is not satisfied.
- Sodium balance would demand d=2b=12, but d=2 here, another inconsistency. Overall, this set does not balance.

Option 3: 2, 3, 1, 6 (a=2, b=3, c=1, d=6)
- Check systematic balances:
  - Aluminum: a = 2c → 2 = 2(1) = 2, satisfied.
  - Sulfur: b = 3c → 3 = 3(1) = 3, satisfied.
  - Sodium: d = 2b → 6 = 2(3) = 6, satisfied.
  - Nitrogen: d = 3a → 6 = 3(2) = 6, satisfied.
  - Oxygen balance also aligns when all the above are satisfied, confirming full balancing.
  Therefore, this set properly balances the equation.

Option 4: 1, 1, 1, 1 (a=1, b=1, c=1, d=1)
- Quick checks show mismatches: aluminum balance would require a = 2c (1 ≠ 2), sulfur would require b = 3c (1 ≠ 3), and other atoms would similarly be inconsistent. This is not a balanced set.

Option 5: 2, 3, 2, 3 (a=2, b=3, c=2, d=3)
- Aluminum: a = 2c → 2 = 4, which is false. The rest of the atom counts would also reveal incompatibilities (e.g., d should equal 3a = 6, but d=3).

Summarizing the checks: options 1, 2, 4, and 5 each fail one or more atomic balances, while option 3 satisfies all atomic balances across Al, S, Na, N, and O, demonstrating a properly balanced equation.

When the following equation is balanced, the coefficients are __________. Al(NO3)3 + Na2S → Al2S3 + NaNO3 Single choice

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