Problem 64 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

The mass of hydrazine that reacts is 2.34 grams.

Step 1: Determine Moles of Sulfuric Acid

First, calculate the number of moles of sulfuric acid \(\mathrm{H}_2\mathrm{SO}_4\) using the formula: \(\text{moles} = \text{Molarity} \times \text{Volume (L)}\). Given that the sulfuric acid molarity is \(0.146 \) M and the volume is \(250\) mL, which is equivalent to \(0.250\) L, the moles are: \[ \text{moles of } \mathrm{H}_2\mathrm{SO}_4 = 0.146 \, \text{M} \times 0.250 \, \text{L} = 0.0365 \, \text{moles}. \]

Step 2: Use Stoichiometry to Find Moles of Hydrazine

According to the balanced equation, 1 mole of sulfuric acid \(\mathrm{H}_2\mathrm{SO}_4\) reacts with 2 moles of hydrazine \(\mathrm{N}_2\mathrm{H}_4\). Therefore, the moles of hydrazine required are twice the moles of sulfuric acid: \[ \text{moles of } \mathrm{N}_2\mathrm{H}_4 = 2 \times 0.0365 = 0.0730 \text{ moles}. \]

Step 3: Calculate the Mass of Hydrazine

To find the mass of hydrazine \(\mathrm{N}_2\mathrm{H}_4\), use its molar mass. The molar mass of \(\mathrm{N}_2\mathrm{H}_4\) is calculated as follows: \(2 \times 14.01 \, \text{g/mol (N)} + 4 \times 1.01 \, \text{g/mol (H)} = 32.05 \, \text{g/mol}.\) Now, calculate the mass: \[ \text{mass of } \mathrm{N}_2\mathrm{H}_4 = 0.0730 \, \text{moles} \times 32.05 \, \text{g/mol} = 2.34 \, \text{g}. \]

Key Concepts

Molarity

Molarity is an important concept in chemistry and it refers to the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution, usually expressed in mol/L or simply M. For example, in the exercise, the sulfuric acid has a molarity of 0.146 M. This means that there are 0.146 moles of sulfuric acid in every 1 liter of the solution.
To calculate molarity, you can use the formula:

• Molarity (M) = Moles of solute (mol) / Volume of solution (L)

In the given problem, you would first convert the volume from milliliters to liters by dividing by 1000, hence 250 mL becomes 0.250 L. Using the molarity formula, the number of moles of sulfuric acid is then calculated as:

• 0.146 M x 0.250 L = 0.0365 moles

Understanding molarity allows us to know how concentrated a particular solution is, which is essential in predicting how it will react with other substances.

Chemical Reactions

Chemical reactions involve the transformation of substances through breaking and forming chemical bonds, resulting in new products. In our example, hydrazine reacts with sulfuric acid to form hydrazinium ions and sulfate ions.
The reaction is detailed by the balanced equation:

• 2 \(\mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \rightarrow 2 \mathrm{N}_{2} \mathrm{H}_{5}^{+}(\mathrm{aq})+\mathrm{SO}_{4}^{2-}(\mathrm{aq})\)

Balancing chemical equations is crucial since it ensures the law of conservation of mass, meaning that atoms are neither created nor destroyed in a reaction.
By examining the balanced equation, we can determine the stoichiometric ratios of reactants to products. Here, 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) reacts with 2 moles of hydrazine. This ratio helps us calculate the required quantities of reactants or products in a reaction.

Mole Calculation

Mole calculations are a core aspect of stoichiometry, allowing chemists to quantify substances in a reaction. A mole serves as a bridge between the atomic scale and real-world measurements by representing 6.022 x 10²³ particles.
In this problem, you first calculate the moles of sulfuric acid, which are necessary to determine how much hydrazine will participate in the reaction. As determined:

• 0.0365 moles of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

Given the stoichiometric ratio from the balanced chemical equation (1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) reacts with 2 moles of \(\mathrm{N}_{2} \mathrm{H}_{4}\)), you then find:

• Moles of \(\mathrm{N}_{2} \mathrm{H}_{4}\) = 2 x 0.0365 = 0.0730 moles

Finally, once the moles of a substance are known, you can calculate its mass using the formula:

• Mass (g) = Moles x Molar Mass (g/mol)

For hydrazine, with a molar mass of 32.05 g/mol, the mass is calculated as:

• 0.0730 moles x 32.05 g/mol = 2.34 g

Mastering mole calculations allows us to convert between the amount of substance and measurable properties, vital for laboratory experiments and theoretical chemistry.