A container with a one-liter capacity at 27 degree C is filled with helium to a pressure of 2 atm. how many moles of helium does it hold?
PV=nRT
n=PV/RT use for R, units atm*liters/Kelvins
change C to Kelvins
To calculate the number of moles of helium in the container, you can use the ideal gas law equation: PV = nRT, where:
- P is the pressure (in atm),
- V is the volume (in liters),
- n is the number of moles,
- R is the ideal gas constant (0.0821 L∙atm/(mol∙K)),
- T is the temperature (in Kelvin).
First, we need to convert the temperature from Celsius to Kelvin. The relationship between Celsius and Kelvin is given by:
T(°C) = T(K) - 273.15
So, 27°C = T(K) - 273.15
T(K) = 27 + 273.15 = 300.15 K
Next, we can rearrange the ideal gas law equation to solve for n:
n = (PV) / (RT)
Substituting the given values:
P = 2 atm
V = 1 L
R = 0.0821 L∙atm/(mol∙K)
T = 300.15 K
n = (2 atm * 1 L) / (0.0821 L∙atm/(mol∙K) * 300.15 K)
Simplifying:
n ≈ 0.0813 moles
Therefore, the container holds approximately 0.0813 moles of helium.
To determine the number of moles of helium in the container, we can use the Ideal Gas Law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperature from degrees Celsius to Kelvin. The Kelvin scale is obtained by adding 273 to the temperature in degrees Celsius. So, 27 degrees Celsius is equal to 27 + 273 = 300 Kelvin.
Given:
Pressure (P) = 2 atm
Volume (V) = 1 liter
Temperature (T) = 300 K
Ideal gas constant (R) = 0.0821 L.atm/(mol.K) (assuming we are using atm as the unit for pressure)
Now, rearranging the Ideal Gas Law equation, we can solve for the number of moles (n):
n = PV / RT
Substituting the given values:
n = (2 atm) x (1 liter) / (0.0821 L.atm/(mol.K) x 300 K)
Using the unit cancellation method, we can simplify the equation:
n = 2 / 0.0821
n ≈ 24.33 moles of helium
Therefore, the container holds approximately 24.33 moles of helium.