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Ch.2 - Atoms, Molecules & Ions
Chapter 2, Problem 167

If 3.670 g of nitrogen combines with 0.5275 g of hydrogen to yield compound X, how many grams of nitrogen would combine with 1.575 g of hydrogen to make the same compound? Is X ammonia (NH3) or hydrazine (N2H4)?

Verified step by step guidance
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Step 1: Determine the ratio of nitrogen to hydrogen in the original compound by dividing the mass of nitrogen by the mass of hydrogen: \( \frac{3.670 \, \text{g N}}{0.5275 \, \text{g H}} \).
Step 2: Use the ratio from Step 1 to find out how many grams of nitrogen would combine with 1.575 g of hydrogen. Set up a proportion: \( \frac{3.670 \, \text{g N}}{0.5275 \, \text{g H}} = \frac{x \, \text{g N}}{1.575 \, \text{g H}} \) and solve for \( x \).
Step 3: Calculate the molar mass of ammonia (NH3) and hydrazine (N2H4) to compare with the ratio obtained. Ammonia has a molar mass of approximately 17.03 g/mol, and hydrazine has a molar mass of approximately 32.05 g/mol.
Step 4: Determine the nitrogen to hydrogen ratio in ammonia and hydrazine. For ammonia, the ratio is \( \frac{14.01 \, \text{g N}}{3.02 \, \text{g H}} \), and for hydrazine, it is \( \frac{28.02 \, \text{g N}}{4.04 \, \text{g H}} \).
Step 5: Compare the calculated nitrogen to hydrogen ratio from Step 2 with the ratios for ammonia and hydrazine to determine which compound matches the experimental data.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amounts of substances involved based on their molar ratios derived from balanced chemical equations. Understanding stoichiometry is essential for determining how much nitrogen will react with a given amount of hydrogen to form a specific compound.
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Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. In this question, knowing the molar masses of nitrogen (N2) and hydrogen (H2) helps in determining how much nitrogen is needed to react with a specified mass of hydrogen.
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Chemical Formula Identification

Chemical formula identification involves recognizing the composition of a compound based on its molecular formula. In this case, distinguishing between ammonia (NH3) and hydrazine (N2H4) is vital for understanding the reaction and the stoichiometric relationships. Each compound has a different ratio of nitrogen to hydrogen, which affects how much nitrogen will combine with a given amount of hydrogen.
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