If I contain 3 moles of gas in a container with a volume of 60 liters and at temperature of 400 K, what is the pressure inside the container?
Ideal Gas Law: PV=nRT
I know I'm given the volume, temperature, and numbers of moles of gas, but how do I know which ideal gas constant (R) to use in order to find the pressure?
R= 0.0821 if pressure is in atm
R= 8.31 if used if pressure is in kPa
It depends upon the units you want for pressure in the answer. If you want the pressure in units of kPa use 8.31. If you want the pressure in units of atm use 0.08206.
To find the pressure inside the container, you can use the Ideal Gas Law equation: PV = nRT.
Given:
Volume (V) = 60 liters
Temperature (T) = 400 K
Number of moles of gas (n) = 3 moles
To find the pressure, you need to use the appropriate value for the ideal gas constant (R) based on the unit used for pressure.
If pressure is in atmospheres (atm), you would use R = 0.0821 L•atm/(mol•K).
If pressure is in kilopascals (kPa), you would use R = 8.31 J/(mol•K).
In this case, since the unit of pressure is not mentioned, it's not clear whether the pressure is in atm or kPa. Therefore, we can calculate the pressure using both values of R and then convert the results.
Using R = 0.0821 L•atm/(mol•K):
P = (nRT) / V
P = (3 mol * 0.0821 L•atm/(mol•K) * 400 K) / 60 L
P = 16.42 atm
Using R = 8.31 J/(mol•K):
P = (nRT) / V
P = (3 mol * 8.31 J/(mol•K) * 400 K) / 60 L
P = 166.2 J/(L•mol)
Converting from J/(L•mol) to kPa:
1 J/(L•mol) = 1 kPa
Thus, the pressure is also equal to 166.2 kPa.
So, based on the information provided, the pressure inside the container is approximately 16.42 atm or 166.2 kPa.
To determine which value of the ideal gas constant (R) to use, you need to consider the unit of pressure you are given or want to calculate. In your question, the possible options are pressure in atmospheres (atm) or kilopascals (kPa).
If you want the pressure in atm, you should use the value of R = 0.0821 atm·L/mol·K.
On the other hand, if you want the pressure in kPa, you should use the value of R = 8.31 kPa·L/mol·K.
Since you didn't specify the unit of pressure you are interested in, you can assume that R = 0.0821 atm·L/mol·K is the appropriate value to use.
Now, you can substitute the given values into the ideal gas law equation and solve for pressure (P):
PV = nRT
P * 60 L = 3 mol * 0.0821 atm·L/mol·K * 400 K
P * 60 L = 98.52 atm·L
P = 98.52 atm·L / 60 L
P ≈ 1.642 atm
Therefore, the pressure inside the container is approximately 1.642 atm.