A sample of 0.50 moles of gas is placed in a container of volume of 2.5 L. What is the pressure of the gas in torr if the gas is at 25 degrees C ? Show work ?
To find the pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in torr)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L•atm/mol•K)
T = Temperature (in Kelvin)
First, we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature:
T(K) = T(°C) + 273.15
In this case, the temperature is 25°C, so:
T(K) = 25 + 273.15 = 298.15 K
Now, we can substitute the given values into the equation:
(2.5 L)(P) = (0.50 moles)(0.0821 L•atm/mol•K)(298.15 K)
By rearranging the equation to solve for P, we can find the pressure:
P = (0.50 moles)(0.0821 L•atm/mol•K)(298.15 K) / (2.5 L)
P ≈ 4.939 atm
Now, let's convert the pressure from atm to torr. 1 atm is approximately equal to 760 torr:
P(torr) = P(atm) * 760
P(torr) ≈ 4.939 atm * 760 torr/atm
P(torr) ≈ 3750.64 torr
Therefore, the pressure of the gas in torr, when the sample of 0.50 moles of gas is in a container of volume 2.5 L at 25°C, is approximately 3750.64 torr.