A sample of an ideal gas consists of 2 moles, pressure = 1 atm, volume = 0.5 liters
Find the temperature
pV=nRT
T = p*V/(n*R)
T = 1 atm * 0.5 liters / (2 moles * .08206 L atm K^-1 * mol^-1)
T = 3.04 K
Did I do that problem correctly? That temperature seems unrealistically low.
Yes, that's correct. Note that
T = p*v/(n*R)
so T = 273 K when p is 1 atm, v is 22.4 L, and n = 1. So you have reduced v from 22.4 to 0.5 AND you have reduced the number even more by doubling the denominator.
Yes, you did the problem correctly. However, I think there might be an error in your calculation.
The ideal gas law equation is: PV = nRT
To find the temperature (T), you need to rearrange the equation:
T = PV / (nR)
Now, substitute the given values:
P = 1 atm (pressure)
V = 0.5 L (volume)
n = 2 moles (number of moles)
R = 0.08206 L∙atm/(mol∙K) (gas constant)
T = (1 atm * 0.5 L) / (2 moles * 0.08206 L∙atm/(mol∙K))
T = 0.025 L∙atm/(mol∙K)
Now, let's calculate the result:
T = 0.025 L∙atm/(mol∙K)
The unit of atm gets canceled out with L, resulting in 0.025 K/mol, which is a reasonable temperature. It seems like you made a mistake in the calculation, as the value you obtained, 3.04 K, is much higher than expected for the given conditions.