A gas occupies a volume of .350 L at a temperature of 18.0 degrees Celsius and a pressure of 980.0 torr. What will be the volume of this gas at standard conditions? Please explain how to do it.
p v = n R T
n and R the same
so
P1 V1/T1 = P2 V2/T2
T1 = 18 + 273
T2 = 273
P1 = 980 Torr
P2 = 760 Torr
V1 = .35
V2 = ?
Why are n and R the same? Isn't n the mol's and R the ideal gas constant?
Damon used PV = nRT. n isn't known at the conditions listed. Using those conditions allows the evaluation of n. Then that value of n is used in another PV = nRT calculation to solve for the volume at the new conditions.
You can avoid that problem if you use
(P1V1/T1) = (P2V2/T2) and just one calculation.
To answer your question, yes, n is mols and R is constant. The P1V1/T1 = P2V2/T2 avoids the use of both n and R although they are used inherently (perhaps intrinsically is a better word).
Okay, I understand that part, but if I use P1V1=P2V2, what happens to the temperature that they gave me? What do I do with it?
I don't see a P1V1 = P2V2.
I see a (P1V1/T1) = (P2V2/T2) so the T is taken into account.
Oh okay, my bad, and thank you for your help
To find the volume of a gas at standard conditions, we can use the Combined Gas Law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 is the initial pressure of the gas
V1 is the initial volume of the gas
T1 is the initial temperature of the gas
P2 is the standard pressure (which is typically 1 atmosphere or 760 torr)
V2 is the volume of the gas at standard conditions (what we are trying to find)
T2 is the standard temperature (which is typically 0 degrees Celsius or 273.15 Kelvin)
In this case, we are given:
P1 = 980.0 torr
V1 = 0.350 L
T1 = 18.0 degrees Celsius
We need to convert the temperature from Celsius to Kelvin:
T1(K) = T1(°C) + 273.15
T1(K) = 18.0 + 273.15
T1(K) = 291.15 K
We also know:
P2 = 760 torr (standard pressure)
T2 = 273.15 K (standard temperature)
Now, we can plug in the values into the equation and solve for V2:
(980.0 torr * 0.350 L) / (291.15 K) = (760 torr * V2) / (273.15 K)
Simplifying the equation:
((980.0 torr * 0.350 L) * (273.15 K)) / (291.15 K) = 760 torr * V2
Solving for V2:
V2 = ((980.0 torr * 0.350 L * 273.15 K) / (291.15 K)) / (760 torr)
V2 ≈ 0.320 L (rounded to three significant figures)
Therefore, the volume of the gas at standard conditions will be approximately 0.320 L.