A sample of nitrogen gas (N2) kept in a container of volume 11.7 L and at a temperature of 23.3°C exerts a pressure of 2.6 atm. Calculate the number of grams of gas present.
Use PV = nRT
Then n = grams/molar mass
Solve for grams.
To calculate the number of grams of gas present, we can use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
First, let's convert the given temperature from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 23.3°C + 273.15 = 296.45 K
Now we can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
n = (2.6 atm) x (11.7 L) / (0.0821 L.atm/mol.K x 296.45 K)
n ≈ 0.45078 moles
Finally, we need to calculate the number of grams. To do this, we'll use the molar mass of nitrogen gas (N2), which is approximately 28 g/mol:
Mass (in grams) = moles x molar mass
Mass (in grams) ≈ 0.45078 moles x 28 g/mol
Mass (in grams) ≈ 12.62 grams
Thus, the number of grams of nitrogen gas present is approximately 12.62 grams.