Final answer:
Using the Ideal Gas Law, we convert given values to the appropriate units, calculate the number of moles, and divide the mass of the gas by the number of moles to determine the molecular weight.
Step-by-step explanation:
To calculate the molecular weight of the gas given its mass, pressure, volume, and temperature, we can use the Ideal Gas Law (PV = nRT), where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin.
First, we convert the temperature to Kelvin (K = °C + 273.15), which gives us 27.63°C + 273.15 = 300.78 K. Next, we convert the pressure from mm Hg to atm by dividing by 760, which gives us 849 mm Hg / 760 mm Hg/atm = 1.117 atm.
With the values converted, we rearrange the Ideal Gas Law to solve for n (the number of moles): n = PV / RT. Substituting the values in, we get n = (1.117 atm * 2899 mL / 1000 mL/L) / (0.0821 L atm mol⁻¹ K⁻¹ * 300.78 K), which calculates the moles of gas.
Finally, to find the molecular weight (MW), we use the equation MW = mass (in grams) / moles, consequently MW = 7.46 mg / 1000 mg/g / calculated moles. After these calculations, the resulting value will be the molecular weight of the gas in grams per mole (g/mol).