Problem 37 - Chemistry The Molecular Nature of Matter

Question

A \(345 \mathrm{~mL}\) vessel contains \(\mathrm{NH}_{3}\) at a pressure of 745 torr and a temperature of \(45^{\circ} \mathrm{C}\). What is the molar concentration of ammonia in the container?

Step-by-Step Solution

Answer

First convert 745 torr to 0.9803 atm and 45C to 318.15 K. Then use Ideal Gas Law with R = 0.0821 L*atm/mol*K to find moles of NH3. Finally, divide moles by volume in liters (0.345 L) to obtain the molarity.

Step 1: Convert the pressure from torr to atm

To use the ideal gas law, pressure must be in atmospheric units. Convert the given pressure from torr to atm by using the conversion factor 1 atm = 760 torr.

Step 2: Convert the temperature from Celsius to Kelvin

Temperature must be in Kelvin for gas law calculations. Use the conversion formula: Kelvin = Celsius + 273.15.

Step 3: Use the Ideal Gas Law to calculate moles of NH3

Apply the Ideal Gas Law, PV = nRT, where P is the pressure in atm, V is the volume in liters, n is the number of moles, R is the ideal gas constant (0.0821 L*atm/mol*K), and T is the temperature in Kelvin. Solve for 'n' to find the moles of NH3.

Step 4: Convert the volume from mL to L

The volume must be in liters for use in the Ideal Gas Law. Convert volume from milliliters to liters using the conversion factor 1 L = 1000 mL.

Step 5: Calculate the molar concentration of NH3

Molar concentration (Molarity, M) is defined as moles of solute per liter of solution. Use the calculated moles of NH3 from Step 3 and volume in liters from Step 4 to find the molarity of NH3.

Key Concepts

Understanding the Ideal Gas Law

The Ideal Gas Law is a crucial concept in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

To apply this law, it's important to ensure that all units are consistent. In the context of our exercise, it's used to find the amount of ammonia in a container. Understanding how to manipulate this equation is essential for gas law calculations and predicting how a gas will behave under different conditions.

The Importance of Unit Conversion

Unit conversion is a fundamental skill in science, especially in chemistry where measurements need to be precise. To perform accurate calculations, you must be able to convert units such as volume from milliliters to liters or pressure from torr to atmospheres. This is because equations like the Ideal Gas Law require specific units to work with the gas constant R.

For example, R is often given in terms of liters, atmospheres, moles, and Kelvin. If your input values are in different units, such as milliliters or Celsius, you need to convert them before proceeding with calculations. Mistakes in conversion can lead to incorrect results, making it a crucial step in problem-solving.

Navigating Gas Law Calculations

Successfully navigating gas law calculations often involves a multi-step process that includes unit conversion and application of the gas laws. It begins by ensuring that all measurements are in the correct units for the particular gas equation you are using, such as the Ideal Gas Law in our example.

Once units are correct, you then plug the values into the equation and solve for the unknown variable, which, in our exercise, is the number of moles of ammonia. The calculated moles can then be related to other quantities, such as molar mass or volume, to find the desired concentration or other properties of the gas.

Calculating Molarity

Molarity is a measure of the concentration of a solute in a solution and is defined as the number of moles of solute per liter of solution. It's a critical concept when dealing with solutions in chemistry. Molarity allows chemists to quantify the concentration of a substance and to perform stoichiometric calculations for reactions in solution.

In our textbook problem, after finding the moles of ammonia (NH3) using the Ideal Gas Law, the molarity is determined by dividing the moles of NH3 by the volume of the container in liters. This gives us the molar concentration of ammonia in the container, allowing us to understand its concentration and to predict how it might react in chemical processes.