Certainly! Let's break down the problem step by step to determine how many grams of hydrogen are required to form 3.00 moles of water, based on the given chemical reaction:
[tex]\[ 2 \ H_2 + O_2 \rightarrow 2 \ H_2O \][/tex]
### Step 1: Understanding the Stoichiometry
In the balanced chemical equation provided, 2 moles of hydrogen gas ([tex]\( H_2 \)[/tex]) react with 1 mole of oxygen gas ([tex]\( O_2 \)[/tex]) to form 2 moles of water ([tex]\( H_2O \)[/tex]).
### Step 2: Mole Ratio
From the equation, we see that the mole ratio of hydrogen to water is 1:1. This means that for every 1 mole of [tex]\( H_2O \)[/tex] formed, we need exactly 1 mole of [tex]\( H_2 \)[/tex].
### Step 3: Calculate the Moles of Hydrogen Needed
Since we are forming 3.00 moles of water, we need an equal amount of hydrogen in moles due to the 1:1 ratio. Therefore, we need 3.00 moles of hydrogen.
### Step 4: Find the Molar Mass of Hydrogen
The molar mass of hydrogen ([tex]\( H_2 \)[/tex]) is 2 grams per mole. This information is crucial because it allows us to convert the moles of hydrogen to grams.
### Step 5: Calculate the Mass of Hydrogen Needed
Using the molar mass, we convert the moles of hydrogen to grams:
[tex]\[ \text{Mass of Hydrogen} = \text{Moles of Hydrogen} \times \text{Molar Mass of Hydrogen} \][/tex]
Substituting in the values, we get:
[tex]\[ \text{Mass of Hydrogen} = 3.00 \ \text{moles} \times 2 \ \text{grams/mole} \][/tex]
[tex]\[ \text{Mass of Hydrogen} = 6.00 \ \text{grams} \][/tex]
### Conclusion
Therefore, to form 3.00 moles of water, we require 6.00 grams of hydrogen. Among the given options, the closest value is:
6.05 g
So, the correct answer is:
[tex]\[ \boxed{6.05 \ g} \][/tex]
