A 500 -cm3 flask contains 0.420g of a gas at a pressure of 160kPa and a temperature of 330K. What is the molecular mass of this gas?
M=____g/mol?
Ty
PV = nRT and solve for n = number of mols. Then n = grams/molar mass and solve for molar mass.
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Alright, let's get back to business. To find the molecular mass of the gas, we can use the Ideal Gas Law equation, which is:
PV = nRT
Where:
P = pressure (in Pascals)
V = volume (in cubic meters)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
To start, let's convert the given values into the appropriate units. The volume is given as 500 cm3, so we'll convert it to 0.5 L. The pressure is given as 160 kPa, which we'll convert to 160,000 Pa. Finally, the temperature is given as 330 K, and we'll leave it as is.
Now we can rearrange the equation to solve for the number of moles:
n = PV / RT
Substituting in the values:
n = (160,000 Pa * 0.5 L) / (8.314 J/(mol·K) * 330 K)
After doing the math, we find that n ≈ 36.56 moles.
Now, to find the molecular mass, we can divide the mass of the gas (0.420 g) by the number of moles (36.56 moles). Let's calculate that, shall we?
Molecular mass (M) = mass of the gas (m) / number of moles (n)
M = 0.420 g / 36.56 mol ≈ 0.0115 g/mol
So, the molecular mass of this gas is approximately 0.0115 g/mol.
I hope I could lighten up your scientific journey a bit! If you have any more questions, feel free to ask.
To find the molecular mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in Pa)
V = volume of the gas (in m^3)
n = number of moles of the gas
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature of the gas (in K)
First, let's convert the given values to their respective SI units:
Volume (V) = 500 cm^3 = 500 × 10^-6 m^3 (since 1 cm^3 = 10^-6 m^3)
Pressure (P) = 160 kPa = 160,000 Pa (since 1 kPa = 1000 Pa)
Temperature (T) = 330 K
Now we can rearrange the ideal gas law equation to solve for n, the number of moles:
n = PV / RT
Substituting the given values into the equation:
n = (160,000 Pa) × (500 × 10^-6 m^3) / (8.314 J/(mol·K) × 330 K)
n = 0.0965 mol
Next, we'll calculate the mass of the gas:
Mass (m) = n × molar mass
Since we are trying to find the molar mass, we'll rearrange the equation to solve for it:
Molar mass (M) = m / n
Substituting the values into the equation:
M = 0.420 g / 0.0965 mol
M ≈ 4.35 g/mol
Therefore, the molecular mass of the gas is approximately 4.35 g/mol.
To find the molecular mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, we need to convert the given volume from cm3 to m3 and the pressure from kPa to Pa, since the ideal gas constant R has units of Pa·m3/(mol·K).
Given:
Volume (V): 500 cm3 (convert to m3)
Pressure (P): 160 kPa (convert to Pa)
Temperature (T): 330 K
1 m3 = 10^6 cm3
Converting Volume (V):
500 cm3 ÷ (10^6 cm3/m3) = 0.0005 m3
Converting Pressure (P):
160 kPa × (10^3 Pa/kPa) = 160,000 Pa
Next, we rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the given values:
n = (160,000 Pa) × (0.0005 m3) / [(8.314 J/(mol·K)) × (330 K)]
n ≈ 0.038 mol
Finally, to find the molecular mass (M), we divide the mass of the gas (0.420 g) by the number of moles (0.038 mol):
M = mass / n
M = 0.420 g / 0.038 mol
M ≈ 11.05 g/mol
Therefore, the molecular mass of the gas is approximately 11.05 g/mol.