Problem 21 - Chemistry Matter and Change

Question

Calculate Hydrogen reacts with excess nitrogen as follows: \begin{equation} \mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{g}) \end{equation} If 2.70 gof \(H_{2}\) reacts, how many grams of \(\mathrm{NH}_{3}\) is formed?

Step-by-Step Solution

Answer

15.21 grams of \( \mathrm{NH}_{3} \) is formed.

Step 1: Determine the molar mass of hydrogen and ammonia

First, calculate the molar mass of hydrogen \( H_2 \) which is 2.02 g/mol \( (1.01 \, \text{g/mol} \times 2) \) and ammonia \( NH_3 \), which is 17.03 g/mol \( (14.01 \, \text{g/mol} + 3 \times 1.01 \, \text{g/mol}) \).

Step 2: Convert grams of hydrogen to moles

Using the calculated molar mass of \( H_2 \), convert 2.70 g of hydrogen to moles: \( \text{moles of } H_2 = \frac{2.70 \, \text{g}}{2.02 \, \text{g/mol}} \approx 1.34 \, \text{mol}. \)

Step 3: Use stoichiometry to find moles of ammonia

From the balanced equation \( \mathrm{N}_{2} + 3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3} \), three moles of hydrogen make two moles of ammonia. Therefore, \( \text{moles of } NH_3 = \frac{2}{3} \times 1.34 \, \text{mol} \approx 0.893 \, \text{mol}. \)

Step 4: Convert moles of ammonia to grams

Use the molar mass of ammonia to convert moles to grams: \( \text{grams of } NH_3 = 0.893 \, \text{mol} \times 17.03 \, \text{g/mol} \approx 15.21 \, \text{g}. \)

Key Concepts

Molar Mass

To fully understand chemical reactions, we begin with the concept of molar mass. Molar mass is the weight of one mole of a substance and is usually expressed in grams per mole (g/mol). It acts like a conversion factor between mass and amount of substance, which is essential in stoichiometry.
For instance, in the reaction given, we calculated the molar mass of hydrogen (\( H_2 \)) and ammonia (\( NH_3 \)).

• The molar mass for hydrogen (\( H_2 \)) is found by multiplying the atomic mass of hydrogen (1.01 g/mol) by 2, resulting in 2.02 g/mol.
• For ammonia (\( NH_3 \)), we sum the atomic masses of nitrogen (14.01 g/mol) and three hydrogen atoms (3 x 1.01 g/mol), which equals 17.03 g/mol.

Understanding molar mass allows us to convert between grams and moles and is fundamental in predicting the amounts of reactants and products in a reaction, making it an indispensable concept in chemistry.

Balanced Chemical Equation

In stoichiometry, balanced chemical equations offer a map of how substances react. They ensure that the same number of each type of atom appears on both sides of the equation, respecting the Law of Conservation of Mass.
The given equation, \[\mathrm{N}_{2} + 3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3}\], indicates that nitrogen (\( \mathrm{N}_2 \)) and hydrogen (\( \mathrm{H}_2 \)) react in specific proportions to form ammonia (\( \mathrm{NH}_3 \)).

• One molecule of nitrogen reacts with three molecules of hydrogen.
• The reaction produces two molecules of ammonia.

This equation helps us understand the stoichiometric relationships between the reactants and products. In practice, it means for every three moles of hydrogen used, two moles of ammonia are produced. Such balanced equations are crucial for any stoichiometric calculation.

Conversion Between Grams and Moles

Converting between grams and moles is a vital skill in chemistry, allowing us to quantify the amount of substance involved in a reaction. This conversion uses the molar mass as a bridge.
To solve the problem of how many grams of ammonia (\( \mathrm{NH}_3 \)) are formed, from the initial amount of hydrogen (\( \mathrm{H}_2 \)):

• First, convert the grams of hydrogen to moles using its molar mass: \[\text{moles of } H_2 = \frac{2.70 \, \text{g}}{2.02 \, \text{g/mol}} \approx 1.34 \, \text{mol}\].
• Next, apply stoichiometry, using the balanced equation to find the moles of ammonia formed. Since 3 moles of \( H_2 \) produce 2 moles of \( NH_3 \), we compute: \[\text{moles of } NH_3 = \frac{2}{3} \times 1.34 \, \text{mol} \approx 0.893 \, \text{mol}\].
• Finally, convert moles of ammonia back to grams using its molar mass: \[\text{grams of } NH_3 = 0.893 \, \text{mol} \times 17.03 \, \text{g/mol} \approx 15.21 \, \text{g}\].

These steps illustrate how to convert mass to moles and back, crucial techniques for predicting the amount of a substance produced in any chemical reaction.