Respuesta :
Answer: The mass or zinc reacted is 0.624 grams.
Explanation:
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:
[tex]p_{H_2}=p_T-p_{H_2O}\\\\p_{H_2}=1.032-0.042=0.99atm[/tex]
To calculate the number of moles of hydrogen gas, we use the equation given by ideal gas follows:
[tex]PV=nRT[/tex]
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 = [tex]30^oC=[30+273]K=303K[/tex]
R = Gas constant = [tex]0.0821\text{ L. atm }mol^{-1}K^{-1}[/tex]
n = number of moles of hydrogen gas = ?
Putting values in above equation, we get:
[tex]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[/tex]
The chemical equation for the reaction of zinc and hydrochloric acid follows:
[tex]Zn+2HCl\rightarrow ZnCl_2+H_2[/tex]
By Stoichiometry of the reaction:
1 mole of hydrogen gas is produced from 1 mole of zinc metal
So, [tex]9.55\times 10^{-3}mol[/tex] of hydrogen gas is produced from = [tex]\frac{1}{1}\times 9.55\times 10^{-3}=9.55\times 10^{-3}mol[/tex] of zinc metal
To calculate the mass of zinc metal, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Molar mass of zinc = 65.38 g/mol
Moles of zinc = [tex]9.55\times 10^{-3}[/tex] moles
Putting values in above equation, we get:
[tex]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[/tex]
Hence, the mass or zinc reacted is 0.624 grams.
