Answer :
Answer: 10.2 grams
Explanation:
The balanced chemical reaction is :
[tex]CaH_2(s)+2H_2O(l)\rightarrow Ca(OH)_2(aq)+2H_2(g)[/tex]
According to the ideal gas equation:
[tex]PV=nRT[/tex]
P = Pressure of the gas = 740 torr = 0.97 atm (760torr=1atm)
V= Volume of the gas = 12.0 L
T= Temperature of the gas = 19°C = 292 K [tex]0^0C=273K[/tex]
R= Gas constant = 0.0821 atmL/K mol
n= moles of gas
[tex]n=\frac{PV}{RT}=\frac{0.97\times 12.0}{0.0821\times 292}[/tex]
[tex]n=0.48[/tex]
According to stoichiometry:
2 moles of hydrogen are generated by = 1 mole of [tex]CaH_2[/tex]
Thus 0.48 moles of hydrogen are generated by =[tex]\frac{1}{2}\times 0.48=0.24[/tex] moles of [tex]CaH_2[/tex]
Mass of [tex]CaH_2=moles\times {\text {Molar mass}}=0.24mol\times 42g/mol=10.2g[/tex]
Thus 10.2 grams of [tex]CaH_2[/tex] are needed to generate 12.0 L of hydrogen gas if the pressure of hydrogen is 740. torr at 19°C
The grams of CaH₂ are needed to generate 12.0 L of H₂ gas if the pressure of H₂ is 740. torr at 19°C is 10.2 grams.
How do we calclate mass from moles?
Mass of any substance will be calculated by using the moles as:
n = W/M, where
W = required mass
M = molar mass
Moles will be calculated by using the ideal gas equation as:
PV = nRT, where
P = pressure of H₂ = 740torr = 0.97 atm
V = volume of H₂ = 12 L
R = universal gas constant = 0.0821 atmL/K mol
T = temperature of H₂ = 19°C = 292 K
n = moles of H₂ = ?
On putting these values on the above equation, we get
n = (0.97)(12) / (0.0821)(292) = 0.48
Chemical reaction will be represented as:
CaH₂(s) + 2H₂O(l) → Ca(OH)₂(aq) + 2H₂(g)
From the stoichiometry of the reaction, we know that
2 moles of H₂ = produced by 1 mole of CaH₂
0.48 moles of H₂ = produced by 0.48/2=0.24 mole of CaH₂
Mass of 0.24 moles of CaH₂ = (0.24mol)(42g/mol) = 10.2g
Hence required mass of CaH₂ is 10.2g.
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