Answer : The moles of hydrogen gas will be, 201.9 moles
Solution :
First we have to calculate the molar mass of hydrogen gas.
using ideal gas equation,
![PV=nRT\\\\P=\frac{w}{V}\times \frac{RT}{M}\\\\P=D\times \frac{RT}{M}](https://tex.z-dn.net/?f=PV%3DnRT%5C%5C%5C%5CP%3D%5Cfrac%7Bw%7D%7BV%7D%5Ctimes%20%5Cfrac%7BRT%7D%7BM%7D%5C%5C%5C%5CP%3DD%5Ctimes%20%5Cfrac%7BRT%7D%7BM%7D)
where,
n = number of moles of gas
w = mass of gas
P = pressure of the gas = 1 atm
T = temperature of the gas = ![2.57^oC=273+2.57=275.57K](https://tex.z-dn.net/?f=2.57%5EoC%3D273%2B2.57%3D275.57K)
M = molar mass of hydrogen gas = ?
R = gas constant = 0.0821 Latm/moleK
D = density of gas = 0.090 g/L
Now put all the given values in the above equation, we get the molar mass of hydrogen gas.
![1atm=0.090g/L\times \frac{(0.0821L.atm/mole.K)\times (275.57K)}{M}](https://tex.z-dn.net/?f=1atm%3D0.090g%2FL%5Ctimes%20%5Cfrac%7B%280.0821L.atm%2Fmole.K%29%5Ctimes%20%28275.57K%29%7D%7BM%7D)
![M=2.03g/mole](https://tex.z-dn.net/?f=M%3D2.03g%2Fmole)
Now we have to calculate the moles of hydrogen gas.
![\text{Moles of }H_2=\frac{\text{Mass of }H_2}{\text{Molar mass of }H_2}=\frac{410g}{2.03g/mole}=201.9mole](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DH_2%3D%5Cfrac%7B%5Ctext%7BMass%20of%20%7DH_2%7D%7B%5Ctext%7BMolar%20mass%20of%20%7DH_2%7D%3D%5Cfrac%7B410g%7D%7B2.03g%2Fmole%7D%3D201.9mole)
Therefore, the moles of hydrogen gas is, 201.9 moles