What is the coefficient for NaOH(aq) when the following equation is balanced?

B2O3(s) + NaOH(aq) → Na3BO3(aq) + H2O(l)

Question

What is the coefficient for NaOH(aq) when the following equation is balanced?

B2O3(s) + NaOH(aq)  →  Na3BO3(aq) + H2O(l)

BlackTom AI · Accepted Answer

We start by identifying all species and setting up the general balanced form: a B2O3(s) + b NaOH(aq) → c Na3BO3(aq) + d H2O(l).

First, balance boron atoms: each B2O3 has 2 boron, and Na3BO3 has 1 boron per molecule. To match boron, we need c = 2a.

Next, balance sodium: Na comes from NaOH on the left and Na3BO3 on the right, which has 3 Na per molecule. So b = 3c = 3(2a) = 6a.

Now balance hydrogen: NaOH provides 1 H per molecule, and H2O has 2 H per molecule on the right. Thus b = 2d, giving d = b/2 = (6a)/2 = 3a.

Finally, check oxygen balance as a consistency check: left has 3a from B2O3 plus b from NaOH, i.e., 3a + b. Right has 3c from Na3BO3 plus d from H2O, i.e., 3c + d. Substituting c = 2a and d = 3a, both sides equal 3a + 6a = 9a and 3(2a) + 3a = 6a + 3a = 9a, so the balance holds.

With a chosen as 1 to obtain the smallest whole-number coefficients, we get: a = 1, b = 6, c = 2, d = 3. Therefore, the coefficient of NaOH(aq) is 6.

Now evaluating the provided options:
- Option 2: 2 — This would yield mismatched boron or sodium balances under any proportional scaling, so it cannot be correct.
- Option 1: 1 — A coefficient of 1 fails to satisfy the sodium and boron balance simultaneously, so it’s incorrect.
- Option 4: 4 — Reducing or increasing from the calculated set would break the derived equalities (especially Na and B balance), making this option false.
- Option 6: 6 — This matches the derived minimal integer solution (b = 6) and satisfies all element balances; it is consistent with the stoichiometric relationship b = 6a when a = 1.
- Option 3: 3 — Like the others, this does not satisfy the necessary balance equations for all elements, so it is incorrect.

What is the coefficient for NaOH(aq) when the following equation is balanced? B2O3(s) + NaOH(aq) → Na3BO3(aq) + H2O(l)

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