Determine the density of methane (CH4) in g/L at 27.8oC and 1.1 atm.
The general gas formula of PV = nRT can be modified to
P*molar mass = density*R*T
So I have gotten 2 different answers. I used V=nRT/P to get the volume. Which was 24.7. Then I used D=M/V and divided 16.042/24.7 to get .65g/L
Is that right?
no. If you obtained two different answers why did you pick that one? You know something must be wrong. How did you get V = 24.7 L. If I plug those numbers into V =nRT/P I don't get that. But I do obtain a number that agrees with the formula I gave you.
V=nRT/P I used (1)(.0821)(300.8)/1=24.7
Two points.
If T is to 4 places I would use R as 0.08205 although that won't make much difference.
The other one makes more difference. P is 1.1 atm in the problem and not 1.
Yes, thank you for catching that. So with the corrections (except I kept R as .0821) I got (1)(.0821)(300.8)/1.1=22.45. Then 16.042/22.45=0.71g/L
Is it now correct? I appreciate all your help!!!
Yes. If that 1.1 is 1.1 and not 1.10 atm, then 0.71 is right. If it is 1.10 you should have one more place in your answer.
THANK YOU!!!
To determine the density of methane (CH4) at a specific temperature and pressure, you need to use the ideal gas law and the molar mass of methane.
The ideal gas law is given by:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given temperature of 27.8°C to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 27.8 + 273.15
T(K) = 300.95 K
Now, rearrange the ideal gas law to solve for the number of moles (n):
n = PV / RT
Next, we need to calculate the number of moles of methane. The molar mass of methane (CH4) is:
C: 12.01 g/mol
H: 1.008 g/mol
4(H): 4(1.008) g/mol = 4.032 g/mol
So, the molar mass of methane (CH4) is 16.04 g/mol.
Now, we can calculate the number of moles (n):
n = (1.1 atm) (V) / (0.0821 L·atm/(mol·K)) (300.95 K)
Since we want the density in g/L, we can rearrange the equation to solve for density (d):
d = (molar mass) (n) / V
Now, let's substitute the values:
d = (16.04 g/mol) (n) / V
To get the final density in g/L, you'll need to know the volume (V) of the methane.