Chapter 9: Problem 12
Nitrogen gas reacts with hydrogen gas to produce ammonia. $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ a. If you have \(3.64 \mathrm{~g}\) of \(\mathrm{H}_{2}\), how many grams of \(\mathrm{NH}_{3}\) can be produced? b. How many grams of \(\mathrm{H}_{2}\) are needed to react with \(2.80 \mathrm{~g}\) of \(\mathrm{N}_{2}\) ? c. How many grams of \(\mathrm{NH}_{3}\) can be produced from \(12.0 \mathrm{~g}\) of \(\mathrm{H}_{2}\) ?
Short Answer
Step by step solution
Write down the balanced chemical equation
Calculate the molar masses
Convert grams of \( \mathrm{H}_{2} \) to moles for part (a)
Use stoichiometry to find moles of \( \mathrm{NH}_{3} \) for part (a)
Convert moles of \( \mathrm{NH}_{3} \) to grams for part (a)
Convert grams of \( \mathrm{N}_{2} \) to moles for part (b)
Use stoichiometry to find moles of \( \mathrm{H}_{2} \) for part (b)
Convert moles of \( \mathrm{H}_{2} \) to grams for part (b)
Convert grams of \( \mathrm{H}_{2} \) to moles for part (c)
Use stoichiometry to find moles of \( \mathrm{NH}_{3} \) for part (c)
Convert moles of \( \mathrm{NH}_{3} \) to grams for part (c)
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chemical Equations
Molar Mass
For example, the molar mass of \text{N}_2 is calculated as follows: \[ \text{Molar Mass of } \text{N}_2 = 2 \times 14.01 \text{ g/mol} = 28.02 \text{ g/mol} \] Similarly, molar masses for hydrogen gas (\text{H}_2) and ammonia (\text{NH}_3) are: \[ \text{Molar Mass of } \text{H}_2 = 2 \times 1.01 \text{ g/mol} = 2.02 \text{ g/mol} \] \[ \text{Molar Mass of } \text{NH}_3 = 1 \times 14.01 \text{ g/mol} + 3 \times 1.01 \text{ g/mol} = 17.03 \text{ g/mol} \] Knowing the molar masses is crucial for converting between grams and moles.
Mass-Mole Conversion
Use the formula: \[ \text{Moles} = \frac{\text{Mass (in grams)}}{\text{Molar Mass (in g/mol)}} \] For instance, given 3.64 g of \text{H}_2, the number of moles is: \[ \text{Moles of } \text{H}_2 = \frac{3.64 \text{ g}}{2.02 \text{ g/mol}} = 1.80 \text{ mol} \] To convert moles to grams:
Use the formula: \[ \text{Mass (in grams)} = \text{Moles} \times \text{Molar Mass (in g/mol)} \] For example, to find the mass of 1.20 moles of \text{NH}_3: \[ \text{Mass of } \text{NH}_3 = 1.20 \text{ mol} \times 17.03 \text{ g/mol} = 20.44 \text{ g} \] Such computations are vital for solving chemical reaction problems.
Balanced Equations
For the given reaction: \[ \text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \] Count the number of nitrogen and hydrogen atoms:
- Reactants: \[ \text{N}_2 = 2 \text{ N atoms}, \text{H}_2 = 3 \times 2 = 6 \text{ H atoms} \]
- Products: \[ \text{NH}_3 = 2 \times \text{NH}_3 = 2 \times (1 \text{ N atom} + 3 \text{ H atoms}) = 2 \text{ N atoms} + 6 \text{ H atoms} \]
Reactants and Products
- Reactants: \text{N}_2 (Nitrogen gas) and \text{H}_2 (Hydrogen gas)
- Products: \text{NH}_3 (Ammonia)
In stoichiometry, we use the balanced equation to relate the amounts of reactants to the amounts of products. The coefficients in the equation also indicate the mole ratios (e.g., 1 mole of \text{N}_2 reacts with 3 moles of \text{H}_2 to produce 2 moles of \text{NH}_3).