Problem 64 - Chemistry and Chemical Reactivity

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 \(0.146 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4} ?\)

Step-by-Step Solution

Answer

2.34 grams of hydrazine reacts with the given sulfuric acid.

Step 1: Calculate Moles of Sulfuric Acid

To find out how many moles of sulfuric acid are present in the given solution, use the formula for molarity and volume \( M = \frac{n}{V} \). Rearrange it to find the moles \( n = MV \). The molarity \( M \) is \( 0.146 \) M and the volume \( V \) is \( 250 \) mL or \( 0.250 \) L. Therefore, \( n = 0.146 \times 0.250 = 0.0365 \) moles of \( \mathrm{H}_2\mathrm{SO}_4 \).

Step 2: Determine Moles of Hydrazine

According to the balanced chemical equation, 2 moles of \( \mathrm{N}_2\mathrm{H}_4 \) react with 1 mole of \( \mathrm{H}_2\mathrm{SO}_4 \). Therefore, if you have 0.0365 moles of \( \mathrm{H}_2\mathrm{SO}_4 \), you will need \( 2 \times 0.0365 = 0.073 \) moles of the hydrazine \( \mathrm{N}_2\mathrm{H}_4 \).

Step 3: Calculate the Mass of Hydrazine

To find the mass of hydrazine required, use the equation \( \text{mass} = \text{moles} \times \text{molar mass} \). The molar mass of \( \mathrm{N}_2\mathrm{H}_4 \) is calculated by adding the atomic masses: \( 2 \times 14.01 + 4 \times 1.01 = 32.05 \) g/mol. Hence, the mass of hydrazine is \( 0.073 \times 32.05 = 2.33965 \) grams.

Key Concepts

Understanding Molarity

Molarity is a central concept in chemistry used to describe the concentration of a solution. It tells us how much of a substance, measured in moles, is dissolved in a given volume of liquid, often water. This is crucial when you need to know exactly how concentrated a solution is to predict the outcome of a chemical reaction.

To calculate molarity, you use the formula:

• \( M = \frac{n}{V} \)
• where \( M \) is the molarity (in moles per liter), \( n \) is the moles of solute, and \( V \) is the volume of solution in liters.

In our problem, the molarity of sulfuric acid is given as 0.146 M, and our task is to use this information to figure out how many moles are present in 250 mL of the solution. It's important to convert the volume from milliliters to liters (since molarity is moles per liter) which gives us 0.250 L. By rearranging and using the molarity formula, we find there are 0.0365 moles of sulfuric acid available for the reaction.

Balancing and Understanding Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into different substances called products. They are described using chemical equations, and balancing these equations is crucial to understanding the ratios in which substances interact.

For the reaction between hydrazine \(\mathrm{N}_2\mathrm{H}_4\) and sulfuric acid \(\mathrm{H}_2\mathrm{SO}_4\), the balanced equation is: \[ 2 \mathrm{N}_2 \mathrm{H}_4(\mathrm{aq}) + \mathrm{H}_2 \mathrm{SO}_4(\mathrm{aq}) \rightarrow 2 \mathrm{N}_2 \mathrm{H}_5^{+}(\mathrm{aq}) + \mathrm{SO}_4^{2-}(\mathrm{aq}) \] This equation tells us that two moles of hydrazine react with one mole of sulfuric acid. By following the coefficients (the numbers in front of each compound), we understand the proportions needed. For instance, if we know the moles of sulfuric acid, we can determine how many moles of hydrazine are required for complete reaction. In our problem, with 0.0365 moles of sulfuric acid, we need twice as many moles of hydrazine, totaling 0.073 moles.

Calculating Molar Mass and Mass in Reactions

The molar mass is the weight of one mole of a substance, usually expressed in grams per mole (g/mol). It's a crucial factor when converting between mass and moles, especially in chemical reactions.

To find the molar mass of hydrazine \( \mathrm{N}_2\mathrm{H}_4 \), you add the atomic masses of its elements:

• Each nitrogen (N) atom has an atomic mass of approximately 14.01 g/mol, and hydrogen (H) has about 1.01 g/mol.
• For hydrazine, 2 nitrogen atoms contribute \( 2 \times 14.01 \), and 4 hydrogen atoms contribute \( 4 \times 1.01 \), resulting in a total molar mass of 32.05 g/mol.

To find the mass of hydrazine needed for a chemical reaction, you multiply the number of moles by its molar mass. With 0.073 moles of hydrazine required, and a molar mass of 32.05 g/mol, the mass of hydrazine necessary is 2.34 grams. This conversion lets us understand and measure actual quantities of hydrazine that will fully react with the given sulfuric acid, ensuring no excess is left unreacted.