<u>Answer:</u> The mass or zinc reacted is 0.624 grams.
<u>Explanation:</u>
We are given:
Total pressure = 1.032 atm
Vapor pressure of water = 32 torr = 0.042 atm (Conversion factor: 1 atm = 760 torr)
To calculate partial pressure of hydrogen gas, we use the equation:
![p_{H_2}=p_T-p_{H_2O}\\\\p_{H_2}=1.032-0.042=0.99atm](https://tex.z-dn.net/?f=p_%7BH_2%7D%3Dp_T-p_%7BH_2O%7D%5C%5C%5C%5Cp_%7BH_2%7D%3D1.032-0.042%3D0.99atm)
To calculate the number of moles of hydrogen gas, we use the equation given by ideal gas follows:
![PV=nRT](https://tex.z-dn.net/?f=PV%3DnRT)
where,
P = pressure of hydrogen gas = 0.99 atm
V = Volume of hydrogen gas = 240. mL = 0.240 L (Conversion factor: 1 L = 1000 mL)
T = Temperature of hydrogen gas = ![30^oC=[30+273]K=303K](https://tex.z-dn.net/?f=30%5EoC%3D%5B30%2B273%5DK%3D303K)
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 hydrogen gas = ?
Putting values in above equation, we get:
![0.99atm\times 0.240L=n\times 0.0821\text{ L atm }mol^{-1}K^{-1}\times 303K\\n=\frac{0.99\times 0.240}{0.0821\times 303}=9.55\times 10^{-3}mol](https://tex.z-dn.net/?f=0.99atm%5Ctimes%200.240L%3Dn%5Ctimes%200.0821%5Ctext%7B%20L%20atm%20%7Dmol%5E%7B-1%7DK%5E%7B-1%7D%5Ctimes%20303K%5C%5Cn%3D%5Cfrac%7B0.99%5Ctimes%200.240%7D%7B0.0821%5Ctimes%20303%7D%3D9.55%5Ctimes%2010%5E%7B-3%7Dmol)
The chemical equation for the reaction of zinc and hydrochloric acid follows:
![Zn+2HCl\rightarrow ZnCl_2+H_2](https://tex.z-dn.net/?f=Zn%2B2HCl%5Crightarrow%20ZnCl_2%2BH_2)
By Stoichiometry of the reaction:
1 mole of hydrogen gas is produced from 1 mole of zinc metal
So,
of hydrogen gas is produced from =
of zinc metal
To calculate the mass of zinc metal, we use 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)
Molar mass of zinc = 65.38 g/mol
Moles of zinc =
moles
Putting values in above equation, we get:
![9.55\times 10^{-3}mol=\frac{\text{Mass of zinc}}{65.38g/mol}\\\\\text{Mass of zinc}=(9.55\times 10^{-3}mol\times 65.38g/mol)=0.624g](https://tex.z-dn.net/?f=9.55%5Ctimes%2010%5E%7B-3%7Dmol%3D%5Cfrac%7B%5Ctext%7BMass%20of%20zinc%7D%7D%7B65.38g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20zinc%7D%3D%289.55%5Ctimes%2010%5E%7B-3%7Dmol%5Ctimes%2065.38g%2Fmol%29%3D0.624g)
Hence, the mass or zinc reacted is 0.624 grams.