To solve the problem of decomposing water (H₂O) into its components, let's go through the detailed steps involving the reaction stoichiometry.
1. Understanding the Chemical Equation:
The given chemical equation is:
[tex]\[
H_2O (\text{l}) \rightarrow H_2 (\text{g}) + \frac{1}{2} O_2 (\text{g})
\][/tex]
This equation represents the decomposition of one molecule of water into hydrogen gas and oxygen gas.
2. Stoichiometry of the Reaction:
The stoichiometric coefficients of the reactants and products in the balanced equation indicate how many moles of each substance are involved in the reaction:
- 1 mole of H₂O decomposes to produce:
- 1 mole of H₂ (hydrogen gas)
- [tex]\( \frac{1}{2} \)[/tex] mole of O₂ (oxygen gas)
3. Interpreting the Reaction:
- For each mole of water decomposed, you get 1 mole of hydrogen gas (H₂).
- Additionally, you obtain [tex]\( \frac{1}{2} \)[/tex] mole of oxygen gas (O₂) which means that two moles of water would produce one mole of oxygen gas.
4. Visual Representation:
Imagine if you start with a container having water (H₂O), after decomposition:
- If you start with 18 grams of water (which is 1 mole of H₂O), it will produce:
- 2 grams of hydrogen (H₂), since the molar mass of hydrogen gas (H₂) is 2 grams per mole.
- 16 grams of oxygen (O₂), since the molar mass of oxygen gas (O₂) is 32 grams per mole, and half of this amount is produced.
5. Summarizing the Reaction:
The chemical equation [tex]\( H_2O (\text{l}) \rightarrow H_2 (\text{g}) + \frac{1}{2} O_2 (\text{g}) \)[/tex] succinctly captures the essence of the decomposition:
- Water (liquid) decomposes into hydrogen gas and half a mole of oxygen gas per mole of water decomposed.
By breaking down the reaction step-by-step and understanding the mole-to-mole relationships, we can clearly see how the decomposition of water into hydrogen and oxygen gases takes place.
