For the gaseous compound C3H8, calculate the density of the gas in g L–1 at 0 °C and 1 atm.
I'm pretty sure I have to us PV=nRT, but I don't know what how to figure out the density with the given information. Any help is very much appreciated. Thanks
You are expected to remember that 1 mol of a gas occupies a volume of 22.4 L @ STP. Also the molar mass pf C3H8 is, then density = grams/L = 44/22.4 = ? g/L
Oh ok. Thanks
To calculate the density of a gas using the ideal gas law equation (PV = nRT), we need to rearrange the equation to solve for density.
The ideal gas law equation is:
PV = nRT
Where:
P = Pressure (in atmospheres)
V = Volume (in liters)
n = Number of moles of gas
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin. We can do this by adding 273.15 to the zero Celsius temperature:
0 °C + 273.15 = 273.15 K
Next, we can substitute the given values into the equation. In this case, the pressure (P) is 1 atm, the temperature (T) is 273.15 K, and the volume (V) is unknown.
Since we want to calculate the density of the gas, we need to express the number of moles (n) in terms of density, mass, and molar mass.
The molar mass of the gas C3H8 (propane) is:
C: 12 g/mol (atomic mass of carbon)
H: 1 g/mol (atomic mass of hydrogen)
Three carbon atoms and eight hydrogen atoms make up propane:
(3 × 12 g/mol) + (8 × 1 g/mol) = 44 g/mol
Now, let's assume we have 1 mole of C3H8 gas. The mass of 1 mole of C3H8 gas is 44 g.
Dividing the mass of the gas by its volume (in liters) will give us the density in g/L.
So, the equation becomes:
Density = mass of gas (g) / volume (L)
Let's proceed with these calculations:
Density = (mass of gas) / volume
Density = (44 g/mol) / volume
Now, we can substitute this expression for density back into the ideal gas law equation:
P * V = (mass / molar mass) * R * T
Rearranging the equation to solve for volume (V):
V = (mass / molar mass) * R * T / P
Finally, substitute the known values into the equation and solve for volume:
V = (44 g/mol) * (0.0821 L·atm/mol·K) * (273.15 K) / (1 atm)
After performing the calculations, you should obtain the volume (V) in liters.
To find the density, substitute the calculated volume (V) and the given mass (44 g) into the density equation:
Density = 44 g / Volume (L) = Answer (g/L)