the gaseous product of a reaction is collected in a 25.0-L container at 27degree celcious. the pressure in the container is 300 kPa and the gas has a mass of 96.0g. what is the molar mass
Use PV = nRT and solve for n = number of moles. Then n = grams/molar mass and solve for molar mass.
For PV = nRT, don't forget T must be in kelvin (note the correct spelling of celsius) and R must be 8.314 if you use kPa for P or R = 0.08206 if P is in atmospheres. To convert to atmospheres 300 kPa/101.325.
22.3
To find the molar mass of the gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure in Pascal (Pa)
V = volume in liters (L)
n = number of moles of the gas
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature in Kelvin (K)
First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 27°C + 273.15
T(K) = 300.15 K
Now, let's convert the given pressure from kilopascals (kPa) to Pascals (Pa):
P(Pa) = P(kPa) * 1000
P(Pa) = 300 kPa * 1000
P(Pa) = 300,000 Pa
Next, we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the given values:
n = (300,000 Pa * 25.0 L) / (8.314 J/(mol·K) * 300.15 K)
Now, let's calculate the number of moles of the gas:
n = 300,000 * 25.0 / (8.314 * 300.15)
n ≈ 30.19 mol
The molar mass (M) can be calculated by dividing the mass of the gas (m) by the number of moles (n):
M = m / n
Substituting the given mass:
M = 96.0 g / 30.19 mol
Now, let's calculate the molar mass:
M ≈ 3.18 g/mol
Therefore, the molar mass of the gas is approximately 3.18 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 m^3)
n = Number of moles
R = Universal gas constant (8.314 J/(mol⋅K))
T = Temperature (in Kelvin)
First, we need to convert the given values to the appropriate units.
Pressure: 300 kPa = 300,000 Pa
Volume: 25.0 L = 0.025 m^3
Temperature: 27 degrees Celsius = 27 + 273 = 300 K
Now, let's rearrange the Ideal Gas Law equation to solve for the number of moles (n):
n = PV / RT
Substituting the known values:
n = (300,000 Pa) * (0.025 m^3) / ((8.314 J/(mol⋅K)) * 300 K)
Calculating:
n ≈ 0.30176 mol
Next, we'll calculate the molar mass (M) using the formula:
M = mass / n
Substituting the given mass:
M = 96.0 g / 0.30176 mol
Calculating:
M ≈ 318.27 g/mol
Therefore, the molar mass of the gas is approximately 318.27 g/mol.