To determine the correct balanced equation for the reaction of hydrofluoric acid (HF) with silicon dioxide (SiO₂), we need to ensure that both the reactants and products are accounted for with the correct stoichiometry as well as considering the states of matter.
Let's break down the steps to balance the equation:
1. Identify the reactants and products:
- Reactants: Hydrofluoric acid (HF) and silicon dioxide (SiO₂).
- Products: Silicon tetrafluoride (SiF₄) and water (H₂O).
2. Balance the silicon (Si) atoms:
- One mole of SiO₂ provides one Si atom.
- One mole of SiF₄ also contains one Si atom.
- Therefore, the silicon atoms are already balanced with 1 mole of SiO₂ producing 1 mole of SiF₄.
3. Balance the fluorine (F) atoms:
- SiF₄ contains 4 fluorine atoms.
- Each HF molecule contains 1 fluorine atom.
- Therefore, we need 4 moles of HF to provide the 4 fluorine atoms for 1 mole of SiF₄.
4. Balance the hydrogen (H) and oxygen (O) atoms:
- Using 4 moles of HF will also provide 4 hydrogen atoms.
- 2 water molecules (H₂O) will contain these 4 hydrogen atoms (2×H₂O = 2×2 H = 4 H).
- SiO₂ provides 2 oxygen atoms, which is sufficient to form 2 moles of water (H₂O).
5. Consider the states of the reactants and products:
- HF is typically aqueous in solutions, denoted as [tex]\( HF(aq) \)[/tex].
- SiO₂ is a solid, denoted as [tex]\( SiO₂(s) \)[/tex].
- SiF₄ is a gas, denoted as [tex]\( SiF₄(g) \)[/tex].
- The water produced in the reaction is usually in the liquid state, denoted as [tex]\( H₂O(ℓ) \)[/tex].
Using the above considerations, the balanced chemical equation is:
[tex]\[
4 HF(aq) + SiO₂(s) \rightarrow SiF₄(g) + 2 H₂O(ℓ)
\][/tex]
Thus, the correct choice is:
B. [tex]\(4 HF ( aq )+ SiO _2( s ) \rightarrow SiF _4( g )+2 H _2 O (\ell)\)[/tex]
