Chemistry Problem Solving: Determining Molecular Weight of a Gas

Understanding the Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a fundamental equation in chemistry that relates the pressure (P), volume (V), number of moles of gas (n), ideal gas constant (R), and temperature (T) of a gas. By rearranging this equation, we can solve for different variables to determine specific properties of a gas.

Given Data

Mass of gas = 7.46 mg
Volume = 2899 mL
Pressure = 849 mm Hg = 1.117 atm
Temperature = 27.63°C = 300.78 K

Calculating the Number of Moles

First, we need to convert the temperature to Kelvin by adding 273.15 to the Celsius temperature. This gives us T = 27.63°C + 273.15 = 300.78 K.

Next, we convert the pressure from mm Hg to atm by dividing by 760. Therefore, 849 mm Hg / 760 mm Hg/atm = 1.117 atm.

Using the Ideal Gas Law formula to solve for the number of moles (n), we have n = (1.117 atm * 2899 mL / 1000 mL/L) / (0.0821 L atm mol⁻¹ K⁻¹ * 300.78 K).

Determining the Molecular Weight

Now that we have calculated the number of moles of the gas, we can proceed to find the molecular weight (MW) using the equation MW = mass (in grams) / moles. This translates to MW = 7.46 mg / 1000 mg/g / calculated moles.

By performing the necessary calculations, we will arrive at the molecular weight of the gas in grams per mole (g/mol).

By applying the principles of the Ideal Gas Law and understanding the relationships between different properties of gases, we can successfully determine the molecular weight of a gas based on experimental data. This problem-solving approach in chemistry not only strengthens our grasp of gas behavior but also enhances our analytical and critical thinking skills.