Here's how we can break down the problem and solve it:
1. Identify the Reaction:
The reaction is:
Metal + Water → Sodium Hydroxide + Hydrogen Gas
2. Write a Balanced Chemical Equation:
To do this, we need to know the specific metal involved. Let's assume the metal is sodium (Na). The balanced equation would be:
2 Na + 2 H₂O → 2 NaOH + H₂
3. Convert Grams to Moles:
* Sodium Hydroxide (NaOH): 40 grams of NaOH.
- The molar mass of NaOH is approximately 40 g/mol.
- Therefore, 40 grams of NaOH is equal to 1 mole.
* Hydrogen Gas (H₂): 3 grams of H₂
- The molar mass of H₂ is approximately 2 g/mol.
- Therefore, 3 grams of H₂ is equal to 1.5 moles.
4. Use the Mole Ratio from the Balanced Equation:
The balanced equation shows that for every 2 moles of NaOH produced, 2 moles of H₂O are consumed.
Since we have 1 mole of NaOH, we can set up a proportion:
2 moles NaOH / 2 moles H₂O = 1 mole NaOH / x moles H₂O
Solving for x, we find that x = 1 mole of H₂O
5. Convert Moles to Grams:
The molar mass of H₂O is approximately 18 g/mol. Therefore, 1 mole of H₂O is equal to 18 grams.
Answer: 18 grams of liquid water must have been added.
Important Note: This calculation assumes the metal is sodium (Na). If it's a different metal, the balanced equation and mole ratios will change, and the final answer will be different.
