The gaseous product of a reaction is collected in a 25.0-L container at 27 C. The pressure in the container is 216 kPa, and the gas has a mass of 96.0g. What is the molar mass of the gas?
To determine the molar mass of the gas, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure (in Pa)
V = volume (in m^3)
n = number of moles
R = ideal gas constant (8.31 J/(mol*K))
T = temperature (in Kelvin)
First, we need to convert the given values into appropriate units:
Pressure: 216 kPa = 216,000 Pa
Volume: 25.0 L = 0.025 m^3
Temperature: 27°C = 300 K (convert Celsius to Kelvin by adding 273)
Next, let's rearrange the equation to solve for the number of moles (n):
n = PV / RT
Substituting the given values:
n = (216,000 Pa) * (0.025 m^3) / [(8.31 J/(mol*K)) * (300 K)]
Now, calculate the number of moles:
n = (216,000 * 0.025) / (8.31 * 300) mol
n ≈ 33.72 mol (rounded to two decimal places)
We are also given the mass of the gas as 96.0 g. Now we can calculate the molar mass by dividing the mass by the number of moles:
Molar mass = mass / moles
Molar mass = 96.0 g / 33.72 mol
Molar mass ≈ 2.85 g/mol (rounded to two decimal places)
Therefore, the molar mass of the gas is approximately 2.85 g/mol.
To find the molar mass of the gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in Pa)
V = Volume (in m³)
n = Number of moles
R = Gas constant (8.314 J/(mol·K))
T = Temperature (in Kelvin)
We have the pressure (216 kPa) and the volume (25.0 L), but we need to convert them to SI units (Pascal and cubic meters) and Kelvin, respectively.
1 kPa = 1000 Pa
1 L = 0.001 m³
So, the pressure in Pascal would be:
216 kPa × 1000 Pa/kPa = 216,000 Pa
And the volume in cubic meters would be:
25.0 L × 0.001 m³/L = 0.025 m³
Now, with the given pressure, volume, and temperature (27 degrees Celsius), we need to convert the temperature to Kelvin by adding 273.15.
T = 27 + 273.15 = 300.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / (RT)
Substituting the values we calculated:
n = (216,000 Pa) × (0.025 m³) / (8.314 J/(mol·K)) × (300.15 K)
Now we have the number of moles of the gas. Next, we can use the mass of the gas (96.0 g) to calculate the molar mass.
Molar mass (g/mol) = Mass (g) / Moles (mol)
Molar mass = 96.0 g / (PV / (RT))
Substituting the values we calculated:
Molar mass = 96.0 g / [(216,000 Pa × 0.025 m³) / (8.314 J/(mol·K) × 300.15 K)]
After canceling units and calculating the expression, you should get the molar mass of the gas.
Use PV = nRT and solve for n. Remember T must be in Kelvin.
Tnen n = grams/molar mass. Solve for molar mass. Be careful with units for R and P. I would convert kPa to atmospheres and use 0.08206 for R.