A glass vessel has a mass of 53.8718 g when evacuated (no air). When filled with a liquid of density 1.319 g mL-1 it has a mass of 255.7390 g and when filled with an unknown gas at 752.3 torr and 16.12°C it has a mass of 54.2483 g. What is the molar mass of the gas, express your answer in scientific notation.?
...i'm confused about the three masses given. from the equation P=d(RT/MM), you don't need mass at all. please help?
You don't have the density, do you? The density given is that of a liquid.
how is liquid or the inital mass relevant to the question, if we're only concerned with the gas?
The liquid and mass and density of the liquid gives you a way of determining the volume of the container. Then the volume of the container and the mass of the gas gives you the density of the gas and from that the molar mass of the gas.
You are correct that the ideal gas law equation, PV = nRT, does not directly require the mass of the gas. However, in this problem, the given masses are used to indirectly calculate the molar mass of the gas. Allow me to explain the steps to solve the problem:
1. Determine the volume of the glass vessel:
Since the glass vessel is filled with liquid, the filled volume is equal to the difference in mass between the empty vessel and the vessel filled with liquid, divided by the density of the liquid.
Filled volume = (mass of liquid-filled vessel - mass of empty vessel) / density of liquid
2. Convert the filled volume from mL to the standard unit, which is cubic meters (m^3), since the ideal gas law uses SI units.
3. Convert the given temperature from Celsius to Kelvin:
Kelvin temperature = Celsius temperature + 273.15
4. Convert the given pressure from torr to Pascal (Pa), since the ideal gas law uses SI units.
5. Apply the ideal gas law equation, PV = nRT, to find the number of moles of the gas (n).
n = PV / (RT)
6. Calculate the molar mass of the gas (MM) using the equation:
molar mass = mass of gas / number of moles
Note: The mass of the gas is given in grams, so the resulting molar mass will also be in g/mol.
7. Express the molar mass of the gas in scientific notation if necessary.
By following these steps, you should be able to find the molar mass of the gas in scientific notation.