Question

Hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4},\) a base like ammonia, can react with sulfuric acid. \(2 \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \rightarrow 2 \mathrm{N}_{2} \mathrm{H}_{5}+(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq})\) What mass of hydrazine reacts with \(250 .\) mL. of \(0.146 \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\)

Short answer

2.34 g of hydrazine reacts with 250 mL of 0.146 M \(\mathrm{H}_2 \mathrm{SO}_4\).

Step-by-step solution

Calculate moles of sulfuric acid

First, find the moles of sulfuric acid (\( \mathrm{H}_2 \mathrm{SO}_4 \)) using the volume and molarity given. The formula to use is: \( \text{moles} = \text{molarity} \times \text{volume in liters} \). Convert the volume from mL to L: \[250 \text{ mL} = 0.250 \text{ L}\]Then calculate the moles:\[\text{moles} = 0.146 \text{ M} \times 0.250 \text{ L} = 0.0365 \text{ moles of } \mathrm{H}_2 \mathrm{SO}_4\]

Use stoichiometry to find moles of hydrazine

From the balanced equation, the molar ratio of \( \mathrm{N}_2 \mathrm{H}_4 \) to \( \mathrm{H}_2 \mathrm{SO}_4 \) is 2:1. Therefore, the moles of hydrazine is twice the moles of sulfuric acid. Calculate the moles of \( \mathrm{N}_2 \mathrm{H}_4 \):\[\text{moles of } \mathrm{N}_2 \mathrm{H}_4 = 2 \times 0.0365 = 0.0730 \text{ moles}\]

Calculate the mass of hydrazine

Now, calculate the mass of \( \mathrm{N}_2 \mathrm{H}_4 \) using its molar mass. The molar mass of \( \mathrm{N}_2 \mathrm{H}_4 \) is calculated by adding the atomic masses: \[ (2 \times 14.01 \text{ g/mol for N}) + (4 \times 1.01 \text{ g/mol for H}) = 32.05 \text{ g/mol}\]Finally, calculate the mass:\[\text{mass} = 0.0730 \text{ moles} \times 32.05 \text{ g/mol} = 2.338 \text{ g}\]

Key concepts

Molarity in Chemical Reactions

Molarity is a fundamental concept in chemistry that refers to the concentration of a solution, specifically the number of moles of a solute per liter of solution. This is crucial when dealing with chemical reactions in aqueous solutions, as it allows for precise control over how much of a substance is involved in a reaction. In this exercise, the molarity of sulfuric acid, denoted as \[0.146 \, \text{M}\], indicates that there are 0.146 moles of sulfuric acid present in every liter of solution.

• To calculate the amount of a chemical needed or produced, we start by using the molarity equation: \[ \text{moles} = \text{molarity} \times \text{volume (L)} \]
• This implies first converting all volume measurements to liters as molarity is defined per liter.

In the original problem, we had 250 mL of sulfuric acid, which converts to 0.250 L. The number of moles of \( \text{H}_2 \text{SO}_4 \) is found by multiplying the molarity \((0.146 \, \text{M})\) by the volume \((0.250 \, \text{L})\), yielding 0.0365 moles. This step is crucial as it forms the basis for further mole calculations.

Understanding Chemical Reactions and Mole Calculations

Chemical reactions involve rearrangements of molecules, and the balanced equation provides a ratio showing how reactants transform into products. For the reaction between hydrazine \( \text{N}_2 \text{H}_4 \) and sulfuric acid \( \text{H}_2 \text{SO}_4 \), the balanced equation given is:\[ 2 \text{N}_2 \text{H}_4(\text{aq}) + \text{H}_2 \text{SO}_4(\text{aq}) \rightarrow 2 \text{N}_2 \text{H}_5^+(\text{aq}) + \text{SO}_4^{2-}(\text{aq}) \]

• This equation tells us for every mole of sulfuric acid, two moles of hydrazine are required.
• The stoichiometric coefficients (the numbers in front of the molecules) are key to understanding how much of each reactant is needed or how much product will be formed.

From our molarity calculation, we found 0.0365 moles of sulfuric acid available. Using the stoichiometric ratios from the balanced equation, we multiply by 2 (from the 2:1 ratio) to find that 0.0730 moles of hydrazine are needed to fully react with the given sulfuric acid.

Calculating the Mass from Moles

Once we ascertain the number of moles needed for a reaction, the next step often involves converting these moles into a mass for practical purposes. In our problem, we calculated that 0.0730 moles of hydrazine \( \text{N}_2 \text{H}_4 \) are necessary. To convert moles to mass, we use the molar mass, which is the weight of one mole of a given substance.

• The molar mass of hydrazine is determined by adding the atomic masses of its constituent atoms.
• For hydrazine: - \[ 2 \times 14.01 \, \text{g/mol for N} + 4 \times 1.01 \, \text{g/mol for H} = 32.05 \, \text{g/mol} \]

Using the molar mass, the relationship \( \text{mass} = \text{moles} \times \text{molar mass} \) allows us to calculate: \[ 0.0730 \, \text{moles} \times 32.05 \, \text{g/mol} = 2.338 \, \text{g} \]Thus, 2.338 grams of hydrazine are necessary to react completely with the sulfuric acid provided.