the molecular weight

Question

What is the molecular weight of a hypothetical compound in the following experiment, assuming ideal gas behavior?

The mass of a 250 mL flask under vacuum weighs 105.000 grams. The flask is filled to 500 torr with the unknown gas, and the flask weighs 105.958 grams afterward. The reaction was completed under isothermal conditions at 22.3 degrees celsius.

Answer 1

Using the Ideal Gas Law equation PV=nRT

We must keep in mind that the units must match what we use for our universal gas constant which is "R" in the equation above. I am using 0.08314 L Bar K^-1 mol^-1 which means my units must match these.

Pressure (P) = 500Torr = 0.667 Bar

Volume (V) = 250ml = 0.250L

Temperature (T) = 22.3C = 295.45K

Now lets plug in:

PV=nRT Solving for n

0.667 * 0.250 = n * 0.08314 * 295.45

n = 0.00679 moles

to achieve molecular weight, the formula is M=m/n

We need the mass of the gas which can be achieved from the details given in the question: before the gas entered, the flask weighed 105g, when the gas entered the weight became 105.958g. The difference of these two values is the weight of the gas.

105.958-105= 0.958g

M=m/n = 0.958g/0.00679moles = 141.09g/mol is the molecular weight.

Answer 2

This problem can be solved using the ideal gas equation, PV = nRT where P is the pressure in torr, V is the volume in liters, n is the number of moles (weight of gas in grams divided by the molecular weight), R is the gas constant in torr-liters (62.36 Ltorr/°Kmol), T is the temperature in °K (295.46). Solve the equation for M to get M = gRT/PV. Numerically this is (105.958 - 105.000)g x 62.36Ltorr/°Kmol x 295.46°K/(500torr x 0.25L). I got a result of 141 g/mol to 3 figures.

Answer 3

Since the mass of the flask before filling was 105.000 and the mass after filling was 105.958 then the gas has a mass of 0.958 grams.

PV = nRT or, dividing by R and T, n = (PV)/(RT)

P = 500 torr

V = 0.250 L

T = 22.3 + 273.15 = 295.45 K

R = 62.36367 L Torr K^-1 mol^-1

n = (500)(0.250)/(62.36367•295.45) = 0.0067841 moles

Molecular weight is grams/mole so 0.958/0.0067841 = 141 g/mol

Note that there is only 1 sig fig in 500 torr so in reality, the answer should be given in 1 sig fig.

Answer 4

The first part of the video is spent explaining the problem, and the last half is the calculations involved.

Hope this was helpful!