Question

Ammonia burns in oxygen gas to form nitric oxide (NO) and water vapor. How many volumes of \(\mathrm{NO}\) are obtained from one volume of ammonia at the same temperature and pressure?

Short answer

1 volume of NO is obtained from 1 volume of NH₃.

Step-by-step solution

Write the Balanced Chemical Equation

The balanced chemical equation for the combustion of ammonia (NH₃) in oxygen (O₂) to produce nitric oxide (NO) and water (H₂O) is: \[4\text{NH}_3 (g) + 5\text{O}_2 (g) \rightarrow 4\text{NO} (g) + 6\text{H}_2\text{O} (g)\] This means 4 volumes of NH₃ react with 5 volumes of O₂ to produce 4 volumes of NO and 6 volumes of H₂O.

Apply Gay-Lussac's Law of Combining Volumes

According to Gay-Lussac’s Law of Combining Volumes, at constant temperature and pressure, the ratio between the volumes of reactant gases and the products can be expressed in simple whole numbers. From the balanced equation, 4 volumes of NH₃ react to produce 4 volumes of NO.

Calculate the Volume Ratio

From the balanced equation, the volume ratio of NH₃ to NO is 4:4 or 1:1. This implies that for every 1 volume of NH₃ burned, 1 volume of NO is produced, assuming the same temperature and pressure conditions.

Key concepts

Balanced Chemical Equation

A balanced chemical equation is essential in understanding chemical reactions, as it shows the ratio of molecules or moles of each reactant and product involved. In the combustion of ammonia, the balanced equation is: \[4\text{NH}_3 (g) + 5\text{O}_2 (g) \rightarrow 4\text{NO} (g) + 6\text{H}_2\text{O} (g)\]This equation demonstrates that 4 molecules of ammonia (NH₃) react with 5 molecules of oxygen gas (O₂) to produce 4 molecules of nitric oxide (NO) and 6 molecules of water vapor (H₂O). Balancing equations is crucial because it ensures that the same number of each element's atoms are present on both sides of the equation, obeying the Law of Conservation of Mass.

• Start by counting the number of each type of atom on both reactant and product sides.
• Adjust coefficients to balance the atoms, maintaining the smallest whole number ratio.

This process mirrors mathematical balancing and is pivotal in predicting the volumes of gases produced and required in reactions.

Gay-Lussac's Law of Combining Volumes

Gay-Lussac's Law states that when gases react together under constant temperature and pressure, the ratio of their volumes is always whole numbers. This is often referred to as the Law of Combining Volumes.In the balanced equation for ammonia combustion, \[4\text{NH}_3 (g) + 5\text{O}_2 (g) \rightarrow 4\text{NO} (g) + 6\text{H}_2\text{O} (g)\]the volumes of NH₃, O₂, NO, and H₂O conform to simple ratios: 4:5:4:6. With the law, we can predict the volume relationships between any gas in the equation, assuming constant conditions.

• Provides a way to determine the volume of products if the reactant volumes are known.
• Helps in converting volume ratios into mole ratios for stoichiometric calculations.

This is useful in many practical applications like industrial chemical production, as it simplifies calculations immensely.

Volume Ratio

Understanding the volume ratio in a reaction helps us predict the quantities of gases involved. The volume ratio is derived directly from the coefficients in a balanced chemical equation. For the combustion of ammonia, the relevant ratio is the following: \[\text{Volume ratio of NH}_3 \text{ to NO} = 4:4 = 1:1\]This indicates that if you have one volume of ammonia gas, an equal volume of nitric oxide gas will be produced. Important points to remember include:

• Volume ratios are directly applicable only to gases.
• At constant temperature and pressure, volume ratios can be used interchangeably with mole ratios.

Understanding volume ratios is vital for a range of chemical engineering practices, including the planning and scaling of reactions to produce desired quantities of chemicals.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the calculation of reactants and products in chemical reactions. Using stoichiometry, we quantify the exact amounts required or produced in a reaction based on the balanced chemical equation. For ammonia combustion: \[4\text{NH}_3 (g) + 5\text{O}_2 (g) \rightarrow 4\text{NO} (g) + 6\text{H}_2\text{O} (g)\]we can determine the following:

• The amount of oxygen needed to completely react with a given quantity of ammonia.
• The quantity of nitric oxide and water produced from a specific amount of ammonia.

Stoichiometry relies on the coefficients from the balanced equation to calculate these relationships and ensures that no reactant is wasted. It is an indispensable tool in laboratory and industrial chemical processes, enabling efficient resource use.