A 0.642 g sample of an unknown gas was collected over water at 25 C and 1.04 atm. The collection cylinder contained 151.3 mL of gas after the sample was released. Find the molar mass of the unknown gas?
Convert the volume to V at 1 atm.
At 25°C, the molar volume is 24.465 L.
Use proportion to find the molar mass, M
0.642/V = M/24.465
Since this gas was collected over H2O, I think we should correct for the vapor pressure of H2O at 25C which is 23.8 mm Hg. That makes the pressure of the gas 1.0086 atm which is too many s.f. but I just leave that in my calculator. That makes a difference of 3 or 4 in the molar mass of the gas vs the problem as solved above.
If you want to work the problem with chemistry, use PV = nRT and solve for n.
1.0086 x 0.1513 = n*0.08206*298
Then molar mass = 0.642/n
To find the molar mass of the unknown gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L.atm / mol.K)
T = temperature in Kelvin
First, we need to convert the given numbers to the appropriate units:
Pressure: 1.04 atm
Volume: 151.3 mL = 0.1513 L
Temperature: 25°C = 298 K
Let's substitute these values into the equation and solve for n:
(1.04 atm) * (0.1513 L) = n * (0.0821 L.atm / mol.K) * (298 K)
Calculating:
0.1575352 = n * 24.4378
We can now solve for n:
n ≈ 0.1575352 / 24.4378
n ≈ 0.006437 mol
Next, we need to find the mass of the gas:
Mass = moles * molar mass
In this case, the mass is given as 0.642 g, so we can rearrange the equation to solve for the molar mass:
Molar mass = mass / moles
Plugging in the known values:
Molar mass ≈ 0.642 g / 0.006437 mol
Calculating:
Molar mass ≈ 99.849 g/mol
Therefore, the approximate molar mass of the unknown gas is 99.849 g/mol.
To find the molar mass of the unknown gas, we can 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 in Kelvin.
First, we need to determine the number of moles of the unknown gas using the ideal gas law. Rearranging the equation, we have n = (PV) / (RT).
Given:
P = 1.04 atm
V = 151.3 mL = 0.1513 L
T = 25 degrees Celsius = 25 + 273.15 = 298.15 K
Rearranging the units of pressure and volume to match the units of R (0.0821 L * atm / (mol * K)), we have:
P = 1.04 atm * (1.01325 J / (1 L * atm))
V = 0.1513 L
Plugging in the values into the equation, we get:
n = (1.04 atm * (1.01325 J / (1 L * atm)) * 0.1513 L) / ((0.0821 L * atm / (mol * K)) * 298.15 K)
Calculating this will give us the number of moles (n). Once we have the number of moles, we can calculate the molar mass by dividing the mass by the number of moles.
Given that the sample had a mass of 0.642 g, we can calculate the molar mass of the unknown gas using the equation: molar mass = mass / moles.
Plugging in the values, we have:
molar mass = 0.642 g / moles
By following these steps and performing the calculations, you can find the molar mass of the unknown gas.