Question

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

Short answer

When 2.70 g of hydrogen (H₂) reacts with an excess of nitrogen (N₂) in the balanced chemical equation \(\mathrm{N}_{2}(\mathrm{g}) + 3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{g})\), approximately 15.2 g of ammonia (NH₃) is formed.

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation for the reaction given is: \[ \mathrm{N}_{2}(\mathrm{g}) + 3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{g}) \]

Determine the mole-to-mole relationship between hydrogen and ammonia

In the balanced chemical equation, we can see that 3 moles of hydrogen (H₂) react to produce 2 moles of ammonia (NH₃). Therefore, the mole-to-mole relationship between hydrogen and ammonia is \( \frac{2}{3} \) or 2:3.

Calculate the number of moles of hydrogen

We're given that 2.70 g of hydrogen reacts. To determine the number of moles of hydrogen in 2.70 g, we can use the molar mass of hydrogen: \[ \text{moles of hydrogen} = \frac{\text{mass of hydrogen}}{\text{molar mass of hydrogen}} \] The molar mass of hydrogen (H₂) is \(2 \times 1.008\ \text{g/mol} \approx 2.02\, \text{g/mol}\), since there are two hydrogen atoms in each hydrogen molecule and each atom has a molar mass of 1.008 g/mol. \[ \text{moles of hydrogen} = \frac{2.70\, \text{g}}{2.02 \,\text{g/mol}} \approx 1.34\, \text{moles} \]

Determine the number of moles of ammonia produced

To find the number of moles of ammonia produced, we can use the mole-to-mole ratio between hydrogen and ammonia from Step 2: \[ \text{moles of ammonia} = \text{moles of hydrogen} \times \frac{\text{moles of ammonia}}{\text{moles of hydrogen}} = 1.34\, \text{moles} \times \frac{2}{3} \approx 0.893\, \text{moles} \]

Calculate the mass of ammonia formed

Now that we know the number of moles of ammonia produced, we can determine the mass of ammonia formed by multiplying the number of moles by the molar mass of ammonia: \[ \text{mass of ammonia} = \text{moles of ammonia} \times \text{molar mass of ammonia} \] The molar mass of ammonia (NH₃) is approximately \(14.007 + 3 \times 1.008 = 17.031\, \text{g/mol}\) (1 nitrogen atom with a molar mass of 14.007 g/mol and 3 hydrogen atoms with 1.008 g/mol each). \[ \text{mass of ammonia} = 0.893\, \text{moles} \times 17.031\, \text{g/mol} \approx 15.2\, \text{g} \] Hence, 15.2 g of ammonia (NH₃) is formed when 2.70 g of hydrogen (H₂) reacts with an excess of nitrogen (N₂).

Key concepts

Mole Concept

The mole concept is a fundamental idea in chemistry that provides a bridge between the atomic world and the macroscopic world. A mole is a unit used to count particles, such as atoms or molecules, in a given substance. It's comparable to the concept of a dozen but significantly larger, with one mole defined as exactly 6.022 x 10²³ particles, thanks to Avogadro's number.

In chemical reactions, the mole concept allows us to convert between the mass of a substance and the number of moles, facilitating calculations. For example, when determining how many moles of hydrogen gas are in 2.70 grams, as in the exercise, one computes the moles by dividing the given mass by the molar mass of hydrogen. This gives students the ability to work out how much of a substance is involved in chemical reactions.

Chemical Reactions

Chemical reactions describe processes where substances, known as reactants, transform into new substances called products. This exercise showcases a specific chemical reaction where hydrogen gas reacts with nitrogen gas to form ammonia.

Understanding chemical reactions is crucial since they explain how substances interact, change, and form new compounds. Key elements of understanding include identifying reactants and products, knowing the conditions under which the reactions occur, and determining the quantitative relationships between reactants and products, which involves stoichiometry.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is a crucial concept in converting mass to moles, which is essential for stoichiometric calculations in chemistry. To determine the molar mass of a compound, sum the molar masses of its constituent atoms. For instance, the molar mass of hydrogen gas (H₂) is roughly 2.02 g/mol, derived from multiplying the atomic mass of hydrogen (1.008 g/mol) by two.

Understanding molar mass allows one to convert between the mass of a substance and its amount in moles. This conversion is vital for determining the proportions of reactants and products in a chemical reaction, ensuring accurate stoichiometry.

Balanced Chemical Equations

A balanced chemical equation precisely represents a chemical reaction, showing the reactants and products in their correct proportions. Balancing the equation ensures that the law of conservation of mass is obeyed, indicating that matter is neither created nor destroyed. Each element on the reactant side must appear in the same amount on the product side.

In the given exercise, the balanced equation for the reaction is \( \mathrm{N}_{2}(\mathrm{g}) + 3 \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{g}) \). This states that one molecule of nitrogen gas reacts with three molecules of hydrogen gas to produce two molecules of ammonia. Balancing equations is crucial for correctly understanding the stoichiometric coefficients, which define the ratio of moles needed or produced in a reaction.