To determine the correct equation for the reaction of hydrogen gas (H₂) with oxygen gas (O₂) in the presence of a platinum catalyst, we need to consider the nature of the reaction and the role of the catalyst.
The reaction between hydrogen gas and oxygen gas typically produces water (H₂O). A platinum catalyst is used to speed up the reaction without being consumed in the process. Therefore, the catalyst is not part of the products of the reaction, although it is necessary for the reaction to proceed efficiently.
Now, let's examine the given options:
1. [tex]\( H_2(g) + O_2(g) + Pt \rightarrow H_2(g) + O_2(g) \)[/tex]
- This equation suggests that the reactants stay the same and the platinum catalyst does not induce any reaction.
2. [tex]\( H_2(g) + O_2(g) \rightarrow H_2(g) + O_2(g) + Pt \)[/tex]
- This equation suggests that the platinum catalyst appears as a product, which is not a normal scenario for a catalyst.
3. [tex]\( 2 H_2(g) + O_2(g) \xrightarrow{ Pt } 2 H_2O(g) + Pt \)[/tex]
- This equation indicates that water is produced, but it incorrectly shows that platinum is produced as well. Given that platinum is a catalyst, it should not appear as a product.
4. [tex]\( 2 H_2(g) + O_2(g) \xrightarrow{ Pt } 2 H_2O(g) \)[/tex]
- This equation correctly represents the reaction where hydrogen and oxygen react to form water in the presence of a platinum catalyst, without including platinum as a product.
Thus, the correct equation for the reaction of hydrogen gas with oxygen gas in the presence of a platinum catalyst is:
[tex]\[ 2 H_2(g) + O_2(g) \xrightarrow{ Pt } 2 H_2O(g) \][/tex]
So, the final answer is:
[tex]\( 4 \)[/tex]
