<u>Answer:</u> The mass of calcium hydride needed is 35.8 grams
<u>Explanation:</u>
To calculate the moles of hydrogen gas, we use the equation given by ideal gas, which follows:
![PV=nRT](https://tex.z-dn.net/?f=PV%3DnRT)
where,
P = pressure of the hydrogen gas = 0.888 atm
V = Volume of the hydrogen gas = 48.0 L
T = Temperature of the hydrogen gas = ![32^oC=[32+273]K=305K](https://tex.z-dn.net/?f=32%5EoC%3D%5B32%2B273%5DK%3D305K)
R = Gas constant = ![0.0821\text{ L. atm }mol^{-1}K^{-1}](https://tex.z-dn.net/?f=0.0821%5Ctext%7B%20L.%20atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D)
n = number of moles of the hydrogen gas = ?
Putting values in above equation, we get:
![0.888atm\times 48.0L=n_{H_2}\times 0.0821\text{ L atm }mol^{-1}K^{-1}\times 305K\\\\n_{H_2}=\frac{0.888\times 48.0}{0.0821\times 305}=1.702mol](https://tex.z-dn.net/?f=0.888atm%5Ctimes%2048.0L%3Dn_%7BH_2%7D%5Ctimes%200.0821%5Ctext%7B%20L%20atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20305K%5C%5C%5C%5Cn_%7BH_2%7D%3D%5Cfrac%7B0.888%5Ctimes%2048.0%7D%7B0.0821%5Ctimes%20305%7D%3D1.702mol)
The given chemical equation follows:
![CaH_2(s)+2H_2O(l)\rightarrow Ca(OH)_2(aq.)+2H_2](https://tex.z-dn.net/?f=CaH_2%28s%29%2B2H_2O%28l%29%5Crightarrow%20Ca%28OH%29_2%28aq.%29%2B2H_2)
By Stoichiometry of the reaction:
2 moles of hydrogen gas is produced by 1 mole of calcium hydride
So, 1.702 moles of hydrogen gas will be produced from =
of calcium hydride
Now, calculating the mass of calcium hydride by using the equation:
![\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20moles%7D%3D%5Cfrac%7B%5Ctext%7BGiven%20mass%7D%7D%7B%5Ctext%7BMolar%20mass%7D%7D)
Moles of calcium hydride = 0.851 moles
Molar mass of calcium hydride = 42 g/mol
Putting values in above equation, we get:
![0.851mol=\frac{\text{Mass of calcium hydride}}{42g/mol}\\\\\text{Mass of calcium hydride}=(0.851mol\times 42g/mol)=35.8g](https://tex.z-dn.net/?f=0.851mol%3D%5Cfrac%7B%5Ctext%7BMass%20of%20calcium%20hydride%7D%7D%7B42g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20calcium%20hydride%7D%3D%280.851mol%5Ctimes%2042g%2Fmol%29%3D35.8g)
Hence, the mass of calcium hydride needed is 35.8 grams