Answer : The volume of reactant measured at STP left over is 409.9 L
Explanation :
First we have to calculate the moles of
and
by using ideal gas equation.
<u>For
:</u>
![PV_{N_2}=n_{N_2}RT](https://tex.z-dn.net/?f=PV_%7BN_2%7D%3Dn_%7BN_2%7DRT)
where,
P = Pressure of gas at STP = 1 atm
V = Volume of
gas = 1580 L
n = number of moles
= ?
R = Gas constant = ![0.0821L.atm/mol.K](https://tex.z-dn.net/?f=0.0821L.atm%2Fmol.K)
T = Temperature of gas at STP = 273 K
Putting values in above equation, we get:
![1atm\times 1580L=n_{N_2}\times (0.0821L.atm/mol.K)\times 273K](https://tex.z-dn.net/?f=1atm%5Ctimes%201580L%3Dn_%7BN_2%7D%5Ctimes%20%280.0821L.atm%2Fmol.K%29%5Ctimes%20273K)
![n_{N_2}=70.49mole](https://tex.z-dn.net/?f=n_%7BN_2%7D%3D70.49mole)
<u>For
:</u>
![PV_{H_2}=n_{H_2}RT](https://tex.z-dn.net/?f=PV_%7BH_2%7D%3Dn_%7BH_2%7DRT)
where,
P = Pressure of gas at STP = 1 atm
V = Volume of
gas = 3510 L
n = number of moles
= ?
R = Gas constant = ![0.0821L.atm/mol.K](https://tex.z-dn.net/?f=0.0821L.atm%2Fmol.K)
T = Temperature of gas at STP = 273 K
Putting values in above equation, we get:
![1atm\times 3510L=n_{H_2}\times (0.0821L.atm/mol.K)\times 273K](https://tex.z-dn.net/?f=1atm%5Ctimes%203510L%3Dn_%7BH_2%7D%5Ctimes%20%280.0821L.atm%2Fmol.K%29%5Ctimes%20273K)
![n_{H_2}=156.6mole](https://tex.z-dn.net/?f=n_%7BH_2%7D%3D156.6mole)
Now we have to calculate the limiting and excess reagent.
The balanced chemical reaction is,
![N_2(g)+3H_2(g)\rightarrow 2NH_3(g)](https://tex.z-dn.net/?f=N_2%28g%29%2B3H_2%28g%29%5Crightarrow%202NH_3%28g%29)
From the balanced reaction we conclude that
As, 3 mole of
react with 1 mole of ![N_2](https://tex.z-dn.net/?f=N_2)
So, 156.6 moles of
react with
moles of ![N_2](https://tex.z-dn.net/?f=N_2)
From this we conclude that,
is an excess reagent because the given moles are greater than the required moles and
is a limiting reagent and it limits the formation of product.
Now we have to calculate the excess moles of
reactant (unreacted gas).
Excess moles of
reactant = 70.49 - 52.2 = 18.29 moles
Now we have to calculate the volume of reactant, measured at STP, is left over.
![PV=nRT](https://tex.z-dn.net/?f=PV%3DnRT)
where,
P = Pressure of gas at STP = 1 atm
V = Volume of gas = ?
n = number of moles of unreacted gas = 18.29 moles
R = Gas constant = ![0.0821L.atm/mol.K](https://tex.z-dn.net/?f=0.0821L.atm%2Fmol.K)
T = Temperature of gas at STP = 273 K
Putting values in above equation, we get:
![1atm\times V=18.29mole\times (0.0821L.atm/mol.K)\times 273K](https://tex.z-dn.net/?f=1atm%5Ctimes%20V%3D18.29mole%5Ctimes%20%280.0821L.atm%2Fmol.K%29%5Ctimes%20273K)
![V=409.9L](https://tex.z-dn.net/?f=V%3D409.9L)
Therefore, the volume of reactant measured at STP left over is 409.9 L