Final answer:
To find the molecular weight of an unknown gas under non-STP conditions, use the Ideal Gas Law PV=nRT, converting units to atm and Kelvin first. Then, calculate moles (n) and divide the mass of the gas sample by n to find the molecular weight.
Step-by-step explanation:
To calculate the molecular weight of an unknown gas given certain conditions, we can apply the Ideal Gas Law formula, which is PV = nRT. Here, P stands for pressure, V for volume, n for the number of moles, R for the Universal Gas Constant, and T for temperature. To find the molecular weight (MW) of the gas, we should first convert the pressure from mmHg to atm, and the temperature from degrees Celsius to Kelvin:
Pressure in atm = 420 mmHg / 760 mmHg/atm = 0.5526 atm
Temperature in Kelvin = 32°C + 273.15 = 305.15 K
Now we use the Ideal Gas Law formula rearranged to solve for n (moles of gas):
n = PV / RT = (0.5526 atm × 1.81 L) / (0.0821 Latm/mol·K × 305.15 K
After calculating n, we can find the molecular weight (MW) of the gas using the formula:
MW = Mass of gas sample / Moles of gas
Your mass is 2.60 grams, so you would divide this by the number of moles calculated previously. Once you have the MW, you can then compare it to known values to determine the identity of the gas.
The strategy suggests using a value from STP conditions, which is not applicable here as the conditions provided are not at STP. Always use the actual conditions given in the problem.