Alright, so we are going to use the ideal gas law to solve this one. That law simply states that
PV=nRT
In this equation, P is pressure in atm
V is volume in liters
n is the amount of gas in moles
R is a constant equal to (0.08206L*atm)/(K*mol)
And finally, T is temperature in kelvin
So we are trying to solve for P, so we need that on one side of the equation. We can do that by just dividing by V
(PcancelV)/cancelV=(nRT)/V
P=(nRT)/V
Ok, at this point lets start plugging variables in.
V=10.0L
P=(nRT)/(10.0L)
To convert C^o to K we just add 273
K=C^o +273
K=200^oC+273
T=473K
P=(n*R*473K)/(10.0L)
Now for the tricky part. We need to convert 32g of C_2H_6 into moles. To do this we must first find the molar mass of C_2H_6, then convert 32g to moles.
The molar mass is going to equal (30.07g)/(mol) because we simply add the atomic mass of both elements:
C=12.0107*2
H=1.00794 *6
....................................
(30.07g)/(mol)
So now we need to find out how much moles 32g is
n=(mol)/(30.07g)*32g
n=(mol)/(30.07cancelg)*32cancelg
n=(32mol)/(30.07)
n=1.1mol
Ok, lets plug that in and the constant (R). I'd like to note that I like to put the constant outside the equations as it makes it a lot easier.
P=(n*R*473K)/(10.0L)
P=(1.1mol*473K)/(10.0L)(0.08206L*atm)/(K*mol)
This is the fun part, were you cancel out all the conversion names. NOTE: since you are looking to P, we should have atm left over at the end
P=(1.1cancel(mol)*473cancelK)/(10.0cancelL)(0.08206cancelL*atm)/(cancelK*cancel(mol))
Now, finally, we just solve! Notice that atm is all that left....
P=(1.1*473*0.08206*atm)/(10.0)
P=4.70atm
Hope this helped! If you have any more questions feel free to ask them!
~Chandler Dowd