Let's approach this problem step-by-step by considering the balanced chemical reaction involved, the molecular weights, and the stoichiometry.
### Step 1: Write the Balanced Chemical Equation
The balanced chemical equation for the reaction between hydrogen gas (H2) and oxygen gas (O2) to form water (H2O) is:
[tex]\[ 2 \text{H}_2 + \text{O}_2 \rightarrow 2 \text{H}_2\text{O} \][/tex]
This equation tells us that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water.
### Step 2: Calculate the Moles of Hydrogen Gas
We need to convert the given mass of hydrogen gas to moles. The molar mass of hydrogen gas (H2) is calculated as follows:
[tex]\[ \text{Molar mass of H}_2 = 2 \times 1.008 \, \text{g/mol} = 2.016 \, \text{g/mol} \][/tex]
The given mass of hydrogen gas is 6.50 grams. Using the formula:
[tex]\[ \text{Moles of H}_2 = \frac{\text{Mass of H}_2}{\text{Molar mass of H}_2} \][/tex]
[tex]\[ \text{Moles of H}_2 = \frac{6.50 \, \text{g}}{2.016 \, \text{g/mol}} \][/tex]
[tex]\[ \text{Moles of H}_2 = 3.225 \, \text{moles} \][/tex]
### Step 3: Use Stoichiometry to Find the Moles of Water Produced
From the stoichiometry of the reaction (the coefficients in the balanced equation):
[tex]\[ 2 \text{H}_2 + \text{O}_2 \rightarrow 2 \text{H}_2\text{O} \][/tex]
We see that 2 moles of H2 produce 2 moles of H2O. Hence, the number of moles of H2O produced is equal to the number of moles of H2 used, which is:
[tex]\[ \text{Moles of H}_2\text{O} = \text{Moles of H}_2 = 3.225 \, \text{moles} \][/tex]
### Conclusion
Therefore, 6.50 grams of hydrogen gas will produce 3.225 moles of water when it reacts completely with excess oxygen gas.
