Answer : The volume of [tex]H_[/tex] gas produced is, 305.8 L
Explanation :
First we have to calculate the moles of Ca.
[tex]\text{Moles of Ca}=\frac{\text{Mass of Ca}}{\text{Molar mass of Ca}}[/tex]
Molar mass of Ca = 40 g/mol
[tex]\text{Moles of Ca}=\frac{500.0g}{40g/mol}=12.5mol[/tex]
Now we have to calculate the moles of [tex]H_2[/tex] gas.
The balanced chemical reaction is:
[tex]Ca(s)+2HCl(aq)\rightarrow CaCl_2(aq)+H_2(g)[/tex]
From the balanced chemical reaction we conclude that,
As, 1 mole of Ca react to give 1 mole of [tex]H_2[/tex] gas
So, 12.5 mole of Ca react to give 12.5 mole of [tex]H_2[/tex] gas
Now we have to calculate the volume of [tex]H_[/tex] gas.
Using ideal gas equation:
[tex]PV=nRT[/tex]
where,
P = Pressure of [tex]H_2[/tex] gas = 1.0 atm
V = Volume of [tex]H_2[/tex] gas = ?
n = number of moles [tex]H_2[/tex] = 12.5 mole
R = Gas constant = [tex]0.0821L.atm/mol.K[/tex]
T = Temperature of [tex]H_2[/tex] gas = [tex]25^oC=273+25=298K[/tex]
Putting values in above equation, we get:
[tex]1.0atm\times V=12.5mole\times (0.0821L.atm/mol.K)\times 298K[/tex]
[tex]V=305.8L[/tex]
Thus, the volume of [tex]H_[/tex] gas produced is, 305.8 L