Respuesta :
Answer : The mass of [tex]Mg[/tex] required is 30.38 mg.
Explanation :
To calculate the moles of hydrogen gas, we use the equation given by ideal gas :
PV = nRT
where,
P = Pressure of hydrogen gas = 754 torr
V = Volume of the hydrogen gas = 31.2 mL = 0.0312 L
n = number of moles of hydrogen gas = ?
R = Gas constant = [tex]62.364\text{ L.torr }mol^{-1}K^{-1}[/tex]
T = Temperature of hydrogen gas = [tex]25^oC=273+25=298K[/tex]
Putting values in above equation, we get:
[tex]754torr\times 0.0312L=n\times 62.364\text{ L.torr }mol^{-1}K^{-1}\times 298K\\\\n=1.266\times 10^{-3}mole[/tex]
Now we have to calculate the moles of [tex]Mg[/tex].
The balanced chemical reaction is:
[tex]Mg(s)+2HCl(aq)\rightarrow MgCl_2(aq)+H_2(g)[/tex]
From the balanced chemical reaction, we conclude that
As, 1 mole of [tex]H_2[/tex] produced from 1 mole [tex]Mg[/tex]
As, [tex]1.266\times 10^{-3}[/tex] mole of [tex]H_2[/tex] produced from [tex]1.266\times 10^{-3}[/tex] mole [tex]Mg[/tex]
Now we have to calculate the mass of [tex]Mg[/tex].
Molar mass of [tex]Mg[/tex] = 24 g/mol
[tex]\text{Mass of }Mg=\text{Moles of }Mg\times \text{Molar mass of }Mg[/tex]
[tex]\text{Mass of }Mg=1.266\times 10^{-3}mole\times 24g/mole=30.38\times 10^{-3}g=30.38mg[/tex]
conversion used : (1 g = 1000 mg)
Therefore, the mass of [tex]Mg[/tex] required is 30.38 mg
