- The balanced chemical equation \(2H_2 + O_2 \rightarrow 2H_2O\) demonstrates a 2:2 molar ratio between hydrogen and water.
- This ratio simplifies to 1:1, meaning the moles of hydrogen required are equal to the moles of water produced.
- Calculating the requirement for \(0.253 \text{ mol}\) of water gives \(1 \times 0.253 \text{ mol} = 0.253 \text{ mol}\) of hydrogen.
- The correct choice is \(\boxed{\text{d. equal to } 0.253 \text{ mol}}\).
Explanation
- Analyzing the Stoichiometry of the Reaction
The balanced chemical equation for the reaction between hydrogen and oxygen to form water is:
\[2H_2 + O_2 \rightarrow 2H_2O\]
This equation tells us that 2 moles of hydrogen gas (\(H_2\)) react with 1 mole of oxygen gas (\(O_2\)) to produce 2 moles of water (\(H_2O\)). To find the number of moles of hydrogen required to produce a specific amount of water, we examine the stoichiometric ratio between hydrogen and water.
- Determining the Molar Ratio
From the balanced equation, the ratio of the number of moles of \(H_2\) to the number of moles of \(H_2O\) is:
\[\frac{\text{moles of } H_2}{\text{moles of } H_2O} = \frac{2}{2} = 1\]
This ratio of \(1:1\) indicates that the number of moles of hydrogen required is exactly equal to the number of moles of water produced.
- Calculating the Moles of Hydrogen Required
Given that we want to produce \(0.253 \text{ mol}\) of water, we use the molar ratio found in the previous step:
\[n(H_2) = 1 \times n(H_2O)\]
Substituting the given value:
\[n(H_2) = 1 \times 0.253 \text{ mol} = 0.253 \text{ mol}\]
Thus, the number of moles of hydrogen needed is \(0.253 \text{ mol}\). Comparing this result with the given options, we find that this amount is equal to \(0.253 \text{ mol}\), which corresponds to option d.
Examples
In industrial processes such as fuel cell production or chemical manufacturing, understanding stoichiometric ratios is vital. For example, if a fuel cell is designed to consume hydrogen and produce a specific amount of water as a byproduct, engineers must calculate the exact amount of hydrogen reactant to supply to ensure efficiency and minimize waste. By using balanced chemical equations, they can accurately predict the necessary reactants for any given production target, ensuring the system operates optimally.