Question

A \(248-\mathrm{mL}\) gas sample has a mass of 0.433 \(\mathrm{g}\) at a pressure of 745 \(\mathrm{mmHg}\) and a temperature of \(28^{\circ} \mathrm{C} .\) What is the molar mass of the gas?

Short answer

The molar mass of the gas is approximately 43.3 g/mol.

Step-by-step solution

Convert temperature to Kelvin

Convert the temperature from Celsius to Kelvin using the formula: Kelvin = Celsius + 273.15. In this case, we have: Kelvin = 28 + 273.15 = 301.15 K.

Convert volume to liters

Convert the volume from milliliters to liters by dividing the volume in milliliters by 1000. Thus, we have: Liters = 248 mL / 1000 = 0.248 L.

Convert pressure to atmospheres

Convert the pressure from mmHg to atmospheres using the conversion factor 1 atm = 760 mmHg. Hence, Pressure in atm = 745 mmHg / 760 mmHg/atm ≈ 0.98026 atm.

Applying the Ideal Gas Law

Use the Ideal Gas Law equation PV = nRT, where P = pressure, V = volume, n = number of moles, R = ideal gas constant, and T = temperature in Kelvin. R has a value of 0.0821 L*atm/(mol*K).

Calculate moles of the gas (n)

Rearrange the Ideal Gas Law to solve for n (moles of the gas): n = PV / (RT). Plug in the known values: n = (0.98026 atm × 0.248 L) / (0.0821 L*atm/(mol*K) × 301.15 K) ≈ 0.0100 moles.

Calculate the molar mass of the gas

Use the formula for molar mass: Molar mass = mass / moles. The mass of the gas sample is 0.433 g. So, Molar mass = 0.433 g / 0.0100 moles ≈ 43.3 g/mol.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and amount of an ideal gas. It is represented as PV = nRT, where P stands for pressure, V for volume, n for moles of gas, R is the gas constant, and T is the temperature in Kelvin.

Understanding the Ideal Gas Law is crucial for calculating properties of gases under different conditions. In the given exercise, the student applies the Ideal Gas Law to determine the number of moles of a gas sample. By rearranging the equation to n = PV / RT, they can plug in the known values after converting them into the appropriate units, such as atm for pressure, liters for volume, and Kelvin for temperature.

When introducing the Ideal Gas Law to students, it's vital to explain the importance of using the right units. Consistency in units throughout calculations ensures accuracy, as the gas constant R has specific units that must align with those used for pressure, volume, and temperature.

It's also helpful to provide real-world examples where the Ideal Gas Law can be applied, such as in predicting the behavior of air in car tires or balloons under various temperatures and pressures. These examples can make the abstract concept more relatable and easier to grasp.

Converting Units in Chemistry

Converting units is an essential skill in chemistry, as different measurements may be required for various chemical calculations. In the presented problem, it is necessary to convert the temperature from Celsius to Kelvin, the volume from milliliters to liters, and the pressure from mmHg to atmospheres before applying the Ideal Gas Law.

To help students with unit conversion, one can introduce them to common conversion factors in chemistry. For example, the given exercise uses the conversions 1 L = 1000 mL and 1 atm = 760 mmHg. Practicing these conversions with diverse exercises can aid students in remembering and applying them fluidly.

Common Conversion Factors

• Volume: 1 L = 1000 mL
• Pressure: 1 atm = 760 mmHg
• Temperature: Kelvin = Celsius + 273.15

Students might also benefit from understanding the reasons behind these conversions, such as why pressure is often expressed in atmospheres in the Ideal Gas Law, or the significance of the absolute temperature scale (Kelvin) for gas calculations. Physical chemistry contexts, like weather systems or the behavior of gases at different altitudes, can provide tangible examples to consolidate their understanding of unit conversions in gas laws.

Molar Mass

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is a critical property that bridges the microscopic world of atoms and molecules with macroscopic quantities used in laboratory practice. In the example problem, the molar mass of a gas is computed using the mass of the gas sample and the amount of the substance measured in moles (derived from the Ideal Gas Law).

The formula for molar mass is simple: Molar mass = mass of sample / number of moles. With a clear understanding of how to find the number of moles using the Ideal Gas Law, students can then easily determine the molar mass by dividing the mass of the sample by the number of moles calculated.

Applications of Molar Mass

• Converting mass to moles for balanced chemical equations
• Calculating the mass of reactants required for a reaction
• Determining the mass of a product formed from a known amount of reactants

To enhance students' ability to work with molar mass, exercises involving the use of periodic tables to find atomic or molecular weights are highly beneficial. This allows them to perform molar mass calculations for various compounds. The trick is to ensure they understand the need to convert between masses and moles, especially when relating to gas measurements, as this is a frequent requirement for problems involving the Ideal Gas Law.