Question

A steel cylinder with nitrogen, hydrogen, and ammonia gases is at \(500^{\circ} \mathrm{C}\) and \(5.00 \mathrm{~atm}\). If the partial pressure of nitrogen is \(1850 \mathrm{~mm} \mathrm{Hg}\) and hydrogen is \(1150 \mathrm{~mm} \mathrm{Hg}\), what is the partial pressure of ammonia in \(\mathrm{mm}\) Hg?

Short answer

The partial pressure of ammonia is 800 mm Hg.

Step-by-step solution

Convert Total Pressure to mm Hg

The total pressure in the cylinder is given in atm. We convert it to mm Hg using the conversion: \[ 1 ext{ atm} = 760 ext{ mm Hg} \] The total pressure in mm Hg is: \[ 5.00 ext{ atm} \times 760 ext{ mm Hg/atm} = 3800 ext{ mm Hg} \]

Use Dalton's Law of Partial Pressures

According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. \[ P_{ ext{total}} = P_{ ext{N}_2} + P_{ ext{H}_2} + P_{ ext{NH}_3} \] Here, \(P_{\text{total}} = 3800\) mm Hg, \(P_{\text{N}_2} = 1850\) mm Hg, and \(P_{\text{H}_2} = 1150\) mm Hg.

Calculate Partial Pressure of Ammonia

Rearrange Dalton's Law to find the partial pressure of ammonia (\(P_{\text{NH}_3}\)): \[ P_{\text{NH}_3} = P_{\text{total}} - P_{\text{N}_2} - P_{\text{H}_2} \] Substitute the known values: \[ P_{\text{NH}_3} = 3800 \text{ mm Hg} - 1850 \text{ mm Hg} - 1150 \text{ mm Hg} = 800 \text{ mm Hg} \]

Key concepts

Understanding Partial Pressure

In a gas mixture, each gas exerts its own pressure, known as the partial pressure. Think of it like each gas having its little slice of the total pressure pie.
When gases like nitrogen (N₂), hydrogen (H₂), and ammonia (NH₃) are mixed, each one pushes against the walls of the container. This is their partial pressure. The beauty of partial pressures is that they add up to the total pressure of the gas mixture. Hence, it's the sum of the partial pressures of all the gases present in a container, like a party where each gas contributes to the fun!
It's important to measure these pressures accurately, as they are crucial in many chemical calculations and reactions. By breaking down the total pressure into partial pressures, we can better understand and control gas behavior in constant volume containers at a fixed temperature.

Exploring Gas Mixtures

Gas mixtures are fascinating because they involve combinations of different gases, each behaving according to its own properties. In our exercise, a steel cylinder contains a mix of nitrogen, hydrogen, and ammonia gases.
With gas mixtures, it's essential to recognize that each gas in the mixture retains its original properties. It's like bringing together a mixed group of friends; they interact, yet each maintains individuality.
This unique behavior can be attributed to the fact that gas molecules are so spread out that they rarely collide, allowing them to act independently. Therefore, gases in a mixture will not react, unless under specific chemical conditions, and will preserve their own pressure contributions.
By understanding each component within a gas mixture, we can make more accurate predictions in chemical reactions and control environmental conditions.

The Essentials of Chemistry Problem-Solving

Solving chemistry problems requires a systematic approach. Let’s see how we handle them step-by-step using Dalton’s Law of Partial Pressures.
First, convert units consistently. For example, converting pressures from atm to mm Hg ensures uniformity in your calculations, preventing errors.
Second, apply relevant laws or theories. With gas mixtures, Dalton’s Law is crucial. This law helps you add up or break down pressures efficiently.
Lastly, substitute known values and solve for the unknowns. Take your time to fill in the values you know and carefully calculate the rest. In our exercise, substituting the partial pressures of nitrogen and hydrogen into Dalton's equation allows us to isolate and figure out the unknown, which is the partial pressure of ammonia.
These steps provide a clear path in chemistry problem-solving, boosting confidence and understanding.