Respuesta :
Answer : The the partial pressure of the nitrogen gas is 0.981 atm.
The total pressure in the tank is 2.94 atm.
Explanation :
The balanced chemical reaction will be:
[tex](CH_3)_2N_2H_2(l)+2N_4O_4(l)\rightarrow 3N_2(g)+4H_2O(g)+2CO_2(g)[/tex]
First we have to calculate the moles of dimethylhydrazine.
Mass of dimethylhydrazine = 150 g
Molar mass of dimethylhydrazine =60.104 g/mole
[tex]\text{Moles of dimethylhydrazine}=\frac{\text{Mass of dimethylhydrazine}}{\text{Molar mass of dimethylhydrazine}}[/tex]
[tex]\text{Moles of dimethylhydrazine}=\frac{150g}{60.104g/mole}=2.49mole[/tex]
Now we have to calculate the moles of [tex]N_2[/tex] gas.
From the balanced chemical reaction we conclude that,
As, 1 mole of [tex](CH_3)_2N_2H_2[/tex] react to give 3 moles of [tex]N_2[/tex] gas
So, 2.49 mole of [tex](CH_3)_2N_2H_2[/tex] react to give [tex]2.49\times 3=7.47[/tex] moles of [tex]N_2[/tex] gas
Now we have to calculate the partial pressure of nitrogen gas.
Using ideal gas equation :
[tex]PV=nRT\\\\P_{N_2}=\frac{nRT}{V}[/tex]
where,
P = Pressure of [tex]N_2[/tex] gas = ?
V = Volume of [tex]N_2[/tex] gas = 250 L
n = number of moles  [tex]N_2[/tex] gas = 7.47 mole
R = Gas constant = [tex]0.0821L.atm/mol.K[/tex]
T = Temperature of [tex]N_2[/tex] gas = [tex]127^oC=273+127=400K[/tex]
Putting values in above equation, we get:
[tex]P_{N_2}=\frac{(7.47mole)\times (0.0821L.atm/mol.K)\times 400K}{250L}=0.981atm[/tex]
Thus, the partial pressure of the nitrogen gas is 0.981 atm.
Now we have to calculate the total pressure in the tank.
Formula used :
[tex]P_{N_2}=X_{N_2}\times P_T[/tex]
[tex]P_T=\frac{1}{X_{N_2}}\times P_{N_2}[/tex]
[tex]P_T=\frac{1}{(\frac{n_{N_2}}{n_T})}\times P_{N_2}[/tex]
[tex]P_T=\frac{n_{T}}{n_{N_2}}\times P_{N_2}[/tex]
where,
[tex]P_T[/tex] = total pressure = ?
[tex]P_{N_2}[/tex] = partial pressure of nitrogen gas = 0.981 atm
[tex]n_{N_2}[/tex] = moles of nitrogen gas = 3 mole  (from the reaction)
[tex]n_{T}[/tex] = total moles of gas = (3+4+2) = 9 mole  (from the reaction)
Now put all the given values in the above formula, we get:
[tex]P_T=\frac{9mole}{3mole}\times 0.981atm=2.94atm[/tex]
Thus, the total pressure in the tank is 2.94 atm.
