- Identify the coefficients in the balanced equation \(N_2 + 3H_2 \rightarrow 2NH_3\), which are 3 for \(H_2\) and 2 for \(NH_3\).
- Determine the mole ratio of hydrogen to ammonia by taking the ratio of their respective coefficients.
- Conclude that the mole ratio is \(3 : 2\), which corresponds to option c.
- The final answer is \(\boxed{3 : 2}\).
Explanation
- Analysis of the Balanced Chemical Equation
The problem asks for the mole ratio of hydrogen (\(H_2\)) to ammonia (\(NH_3\)) based on the provided balanced chemical equation:
\[N_2 + 3H_2 \rightarrow 2NH_3\]
The coefficients in a balanced chemical equation represent the stoichiometric amounts, or molar proportions, in which the substances participate in the reaction. In this equation, the coefficient for nitrogen (\(N_2\)) is \(1\), the coefficient for hydrogen (\(H_2\)) is \(3\), and the coefficient for ammonia (\(NH_3\)) is \(2\).
- Determining the Mole Ratio
To find the mole ratio between two substances in a chemical reaction, we look at the ratio of their coefficients. Here, we are asked for the mole ratio of hydrogen (\(H_2\)) to ammonia (\(NH_3\)). Looking at the balanced equation, we see that the coefficient for \(H_2\) is \(3\) and the coefficient for \(NH_3\) is \(2\). Therefore, the mole ratio of hydrogen to ammonia is \(3 : 2\).
- Conclusion and Final Answer
Comparing the result of \(3 : 2\) with the given options:
A\(1 : 1\)
B\(1 : 2\)
C\(3 : 2\)
D\(5 : 4\)
The correct option is c. Thus, the mole ratio of hydrogen to ammonia is \(\boxed{3 : 2}\).
Examples
Mole ratios are fundamental in stoichiometry, the branch of chemistry that deals with the quantitative relationships between reactants and products. For instance, if a chef knows that a recipe requires 3 cups of flour for every 2 cups of sugar, the "mole ratio" is 3:2. By understanding this ratio, a chemist can calculate exactly how much hydrogen gas is needed to produce a specific amount of ammonia, just as a baker calculates the necessary ingredients to produce the right number of cookies without waste. This concept helps in designing efficient industrial processes and ensures resources are used effectively.