In a 25.8 liter vessel of nitrogen gas that is heated from 10 degrees Celsius to 110 degrees Celsius to reach a final pressure of 17450 mm Hg; how many grams of N2 do you have in the vessel?
PV=nRT
you have volume, final pressure, final temp. Calculate moles n.
then convert n to grams.
To calculate the mass of nitrogen gas (N2) in the vessel, we can use the ideal gas law formula:
PV = nRT
Where:
P = pressure (in atmospheres)
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 degrees Celsius to Kelvin:
T(K) = T(C) + 273.15
Initial temperature (T1) = 10°C + 273.15 = 283.15 K
Final temperature (T2) = 110°C + 273.15 = 383.15 K
We are given the final pressure (P2) as 17,450 mm Hg. To convert this to atmospheres, we divide by the conversion factor:
Conversion factor: 1 atm = 760 mm Hg
P2(atm) = P2(mm Hg) / 760
P2(atm) = 17,450 mm Hg / 760 = 22.98 atm
Now we can set up the equation using the initial and final conditions:
P1V1 / T1 = P2V2 / T2
Since n (number of moles) is the same for both conditions:
n1 = n2
We can simplify the equation:
P1V1 / T1 = P2V / T2
Now we can solve for the number of moles (n) using the equation:
n = (P2V2 / R) / T2
Substituting the given values:
n = (22.98 atm * 25.8 L) / (0.0821 L.atm/mol.K * 383.15 K)
Calculating this equation gives us the number of moles (n) of nitrogen gas in the vessel.
Finally, to calculate the mass (m) of nitrogen gas in grams, we can use the molar mass of nitrogen gas:
Molar mass of N2 = 28.02 g/mol
m = n * M
Calculating this equation gives us the mass of N2 in grams in the vessel.