A 5.00 liter sample of gas measured at 27 degrees Celcius and 1.25 atm of pressure has a mass of 10.13 grams. What is the molecular weight of the gas in u?
Use PV = nRT and solve for moles = n.
Then moles = grams/molar mass. Solve for molar mass.
To find the molecular weight of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given measurements to the correct units:
Volume (V) = 5.00 L
Pressure (P) = 1.25 atm
Temperature (T) = 27 degrees Celsius + 273.15 degrees Celsius (conversion to Kelvin) = 300.15 K
Next, rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Plugging in the values:
n = (1.25 atm * 5.00 L) / (0.0821 L·atm/(mol·K) * 300.15 K)
Performing the calculation:
n = 0.02502 mol
The molecular weight of a substance is the mass of one mole of that substance. To find the molecular weight, we divide the mass of the gas sample by the number of moles:
Molecular weight = Mass of the gas sample / Number of moles
Plugging in the values:
Molecular weight = 10.13 g / 0.02502 mol
Performing the calculation:
Molecular weight ≈ 404 g/mol
Therefore, the molecular weight of the gas is approximately 404 g/mol.
To calculate the molecular weight of a gas, we can use the ideal gas law equation:
PV = nRT,
where:
P is the pressure of the gas (in atm),
V is the volume of the gas (in liters),
n is the number of moles of gas,
R is the ideal gas constant (0.0821 L.atm/(mol.K)),
T is the temperature of the gas (in Kelvin).
First, we need to convert the given temperature from degrees Celsius to Kelvin. We can do this by adding 273.15 to the Celsius temperature.
Given:
V = 5.00 L,
T = 27 + 273.15 K = 300.15 K,
P = 1.25 atm.
Now we can rearrange the ideal gas law equation to solve for the number of moles (n) of gas:
n = (PV) / (RT).
Plugging in the given values:
n = (1.25 atm * 5.00 L) / (0.0821 L.atm/(mol.K) * 300.15 K).
Now we can calculate the value of n:
n = 0.2608 mol.
Next, we need to calculate the molecular weight of the gas by dividing the mass of the gas by the number of moles:
Molecular weight = mass of gas / number of moles.
Given:
Mass of gas = 10.13 grams,
Number of moles = 0.2608 mol.
Now we can calculate the molecular weight:
Molecular weight = 10.13 g / 0.2608 mol.
The resulting value is the molecular weight of the gas in grams per mole (g/mol). However, the question specifies the molecular weight in atomic mass units (u). To convert from g/mol to u, we need to use Avogadro's number.
The conversion factor is 1 g/mol = 1 u.
So the molecular weight of the gas in atomic mass units (u) is the same as the calculated value:
Molecular weight = 10.13 u / 0.2608.
Calculating the final value gives us the molecular weight of the gas in u.