Compute the approximate density of methane, CH4, at 20oC and 5.00 atm. The molecular weight of methane is 16.0.
From Ideal Gas Law PV=nRT=(mass/fwt)RT => (mass/Vol)=Density=P(fwt)/RT
P = 5 Atm
fwt = 16 g/mol
R = 0.08206 L-Atm/mol-K
T = (273+20)K = 293K
Density = [(5)(16)/(0.08206)(293)]g/L
= 3.33 g/L
assume one mole (16grams)
density=mass/volume
so volume= 22.4(273+20)/273*1atm/5atm
volume=4.81 liters
denstiy=16/4.81 g/liter
Oh, methane! The funny cousin of natural gas. Now, let's calculate its density. To do that, we need to use the ideal gas law equation: PV = nRT.
First, we convert 20°C to Kelvin because that's what thermodynamics likes. So, 20°C is 293.15 K.
Now, let's rearrange our formula and solve for density, which is mass/volume. We can approximate the molar mass of methane (CH4) as 16 g/mol.
P = 5.00 atm
R = 0.0821 L·atm/(mol·K)
T = 293.15 K
Molecular weight of methane (CH4) = 16 g/mol
Now, we can rewrite the formula as:
density = (Molecular weight * P) / (R * T)
Substituting in the values:
density = (16 g/mol * 5.00 atm) / (0.0821 L·atm/(mol·K) * 293.15 K)
Now it's time for some math fun! Drumroll, please...
Calculating...
Wait for it...
The approximate density of methane at 20°C and 5.00 atm is approximately 0.717 g/L.
Well, that's quite light, don't you think? Be careful, it might just float away!
To compute the approximate density of methane (CH4) at a given temperature and pressure, we can make use of the ideal gas law equation. The ideal gas law equation is given as:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of the gas
R = Ideal gas constant
T = Temperature
We can rearrange the equation to get the equation for density (ρ):
ρ = (PM) / (RT)
Where:
ρ = Density
P = Pressure
M = Molecular weight of the gas
R = Ideal gas constant
T = Temperature
Given:
Pressure (P) = 5.00 atm
Temperature (T) = 20oC = 293.15 K (Converted to Kelvin)
Molecular weight of methane (M) = 16.0 g/mol
The ideal gas constant (R) is typically expressed in units of L·atm/(mol·K). However, since the molecular weight is provided in grams, we will use the value for R in units of J/(mol·K), which is equal to 8.314 J/(mol·K).
Substituting the given values into the equation for density:
ρ = (P * M) / (R * T)
= (5.00 atm * 16.0 g/mol) / (8.314 J/(mol·K) * 293.15 K)
≈ 24.23 g/L
Therefore, the approximate density of methane (CH4) at 20°C and 5.00 atm is approximately 24.23 g/L.