A container of volume V = 103 cm3 has a mass of 30.0042 g when evacuated. When the container is filed with an unknown gas of pressure p = 4.72 atm at temperature T = 20oC, the mass of the system increases to 30.9508 g. Assuming that the unknown gas behaves like an ideal gas, calculate from these data the average molar mass of the unknown gas.
use the difference in the masses to find the mass of gas in the container.
use PV=nRT to find the number of moles
n=mass of gas/molar mass
hence find the molar mass
HOBKNOCKER
To calculate the average molar mass of the unknown gas, we will use the ideal gas law equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, we need to determine the change in mass of the gas when it is introduced into the container. We can calculate this by subtracting the mass of the evacuated container from the mass of the system filled with gas:
change in mass = mass of system with gas - mass of evacuated container
= 30.9508 g - 30.0042 g
= 0.9466 g
Next, we need to convert the change in mass into moles of the unknown gas. We do this by dividing the change in mass by the molar mass of the gas:
moles of gas = change in mass / molar mass
Since we want to calculate the average molar mass, we rearrange the equation to solve for the molar mass:
molar mass = change in mass / moles of gas
Now, let's calculate the moles of gas. We need to convert the pressure from atm to Pascals (Pa) and the temperature from Celsius to Kelvin (K) since the ideal gas law requires these units:
Pressure (P) = 4.72 atm = 4.72 * 101325 Pa (1 atm = 101325 Pa)
Temperature (T) = 20°C = 20 + 273.15 K (Celsius to Kelvin conversion)
Now, we can substitute the values into the ideal gas law equation to solve for the moles of gas:
PV = nRT
(4.72 * 101325) * V = n * (0.0821) * (20 + 273.15)
Since the volume (V) is given as 103 cm^3, we need to convert it into m^3 for the units to match with the value of R (0.0821):
V = (103 cm^3) * (1 m^3 / 1000000 cm^3)
= 0.000103 m^3
Substituting the values into the equation:
(4.72 * 101325) * 0.000103 = n * (0.0821) * (20 + 273.15)
Now, solve for n (moles of gas):
n = [(4.72 * 101325) * 0.000103] / [(0.0821) * (20 + 273.15)]
Calculate the value of n using a calculator:
n ≈ 0.004896 moles
Now, we can calculate the average molar mass by substituting the values into the rearranged equation:
molar mass = change in mass / moles of gas
molar mass = 0.9466 g / 0.004896 moles
Calculate the value:
molar mass ≈ 193.58 g/mol
Therefore, the average molar mass of the unknown gas is approximately 193.58 g/mol.