A sample of 2.0 moles of dihydrogen gas is placed in a container with a volume of 10.4 L. What is the pressure of of the gas in torr if the gas is at 25 degrees Celsius.
R = 62.4 L Torr K−1 mol−1
T = 273 + 25 = 298 K
n = 2 mol
V = 10.4 L
and
P = n R T/V = 2 * 62.4 * 298 / 10.4
To find the pressure of the gas, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure of the gas
V = volume of the container
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the given temperature from Celsius to Kelvin by adding 273.15:
T = 25 + 273.15 = 298.15 K
Next, we can rearrange the equation to solve for pressure:
P = nRT / V
Substituting the given values:
P = (2.0 mol) * (0.0821 L·atm/mol·K) * (298.15 K) / (10.4 L)
Now, let's simplify the equation:
P = (2.0 * 0.0821 * 298.15) / 10.4
P = 4.478301 / 10.4
P ≈ 0.431 atm
To convert the pressure from atm to torr, we can use the conversion factor:
1 atm = 760 torr
So, to convert the pressure to torr:
P = 0.431 atm * 760 torr/atm
P ≈ 327.76 torr
Therefore, the pressure of the gas is approximately 327.76 torr when the gas is at 25 degrees Celsius in a container with a volume of 10.4 L.