calculate the densities of each of the following gases in g/L at STP:
a. F2
b. CH4
c. Ne
d. SO2
One (1) mole of a gas occupies 22.4 L at STP. For example, F2 = 19x2=38 grams and 38/22.4 L = ??g/L which is density.
To calculate the densities of gases at STP (Standard Temperature and Pressure), we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (atmospheres)
V = volume (liters)
n = number of moles
R = ideal gas constant (0.0821 L⋅atm/mole⋅K)
T = temperature (Kelvin)
At STP, the pressure is 1 atm and the temperature is 273 K.
To find the density in g/L, we need to convert the number of moles (n) into grams and divide by the volume (V).
Let's calculate the densities of each gas one by one:
a. F2:
The molar mass of F2 is 2.01588 g/mol.
Using PV = nRT, we can calculate n:
1 atm * V = (1 mol * 0.0821 L⋅atm/mole⋅K * 273 K)
V = 0.0821 L⋅atm/mole⋅K * 273 K
V ≈ 22.414 L (approximately equal to the molar volume of an ideal gas at STP)
n = 1 mol
Density = (n * molar mass) / V
Density = (1 mol * 2.01588 g/mol) / 22.414 L
Density ≈ 0.0900 g/L
b. CH4:
The molar mass of CH4 is 16.04 g/mol.
Using PV = nRT, we can calculate n:
1 atm * V = (1 mol * 0.0821 L⋅atm/mole⋅K * 273 K)
V ≈ 22.414 L (approximately equal to the molar volume of an ideal gas at STP)
n = 1 mol
Density = (n * molar mass) / V
Density = (1 mol * 16.04 g/mol) / 22.414 L
Density ≈ 0.717 g/L
c. Ne:
The molar mass of Ne is 20.18 g/mol.
Using PV = nRT, we can calculate n:
1 atm * V = (1 mol * 0.0821 L⋅atm/mole⋅K * 273 K)
V ≈ 22.414 L (approximately equal to the molar volume of an ideal gas at STP)
n = 1 mol
Density = (n * molar mass) / V
Density = (1 mol * 20.18 g/mol) / 22.414 L
Density ≈ 0.901 g/L
d. SO2:
The molar mass of SO2 is 64.06 g/mol.
Using PV = nRT, we can calculate n:
1 atm * V = (1 mol * 0.0821 L⋅atm/mole⋅K * 273 K)
V ≈ 22.414 L (approximately equal to the molar volume of an ideal gas at STP)
n = 1 mol
Density = (n * molar mass) / V
Density = (1 mol * 64.06 g/mol) / 22.414 L
Density ≈ 2.86 g/L
Therefore, the densities of the given gases at STP are:
a. F2: 0.0900 g/L
b. CH4: 0.717 g/L
c. Ne: 0.901 g/L
d. SO2: 2.86 g/L
To calculate the density of a gas at STP (Standard Temperature and Pressure), you need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
At STP, the pressure is 1 atm, the volume is 22.4 L (which is the molar volume at STP), and the temperature is 273 K.
Now, let's calculate the density of each gas.
a. F2:
Atomic mass of fluorine (F) = 19 g/mol
Number of moles (n) = mass / molar mass = 1 mol / 19 g/mol = 0.0526 moles
Volume (V) = 22.4 L
Pressure (P) = 1 atm
Temperature (T) = 273 K
Using the ideal gas law equation: PV = nRT, we can rearrange it to find density.
Density (d) = (n * molar mass) / V = (0.0526 mol * 38 g/mol) / 22.4 L = 0.089 g/L
So, the density of F2 gas at STP is 0.089 g/L.
b. CH4:
Molar mass of methane (CH4) = 16 g/mol
Using the same steps as above, we can calculate the number of moles.
Number of moles (n) = 1 mol / 16 g/mol = 0.0625 moles
Density (d) = (n * molar mass) / V = (0.0625 mol * 16 g/mol) / 22.4 L = 0.0443 g/L
So, the density of CH4 gas at STP is 0.0443 g/L.
c. Ne:
Molar mass of neon (Ne) = 20 g/mol
Number of moles (n) = 1 mol / 20 g/mol = 0.05 moles
Density (d) = (n * molar mass) / V = (0.05 mol * 20 g/mol) / 22.4 L = 0.0446 g/L
So, the density of Ne gas at STP is 0.0446 g/L.
d. SO2:
Molar mass of sulfur dioxide (SO2) = 64 g/mol
Number of moles (n) = 1 mol / 64 g/mol = 0.01563 moles
Density (d) = (n * molar mass) / V = (0.01563 mol * 64 g/mol) / 22.4 L = 0.0441 g/L
So, the density of SO2 gas at STP is 0.0441 g/L.