#CaH_2(s) + 2 H_2O(l)= Ca(OH)_2(aq) + 2 H_2(g)# How many grams of CaH2 are needed to generate 10.0 L of H2 gas if the pressure of H2 is 720. torr at 16°C?

This reaction is sometimes used to inflate life rafts, weather balloons, and the like, where a simple, compact means of generating H2 is desired.

1 Answer
Aug 14, 2016

You need 8.40 g of #"CaH"_2#.

Step 1. Use the Ideal Gas Law to calculate the moles of hydrogen.

The Ideal Gas Law is

#color(blue)(|bar(ul(PV = nRT)|)#,

where

  • #P# is the pressure
  • #V# is the volume
  • #n# is the number of moles
  • #R# is the gas constant
  • #T# is the temperature

We can rearrange the Ideal Gas Law to get

#n = (PV)/(RT)#

#P = 720. color(red)(cancel(color(black)("torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("torr")))) = "0.9474 atm"#
#V = "10.0 L"#
#R = "0.082 06 L·atm·K"^"-1""mol"^"-1"#
#T = "(16 + 273.15) K" = "289.15 K"#

#n = (PV)/(RT) = (0.9474 color(red)(cancel(color(black)("atm"))) × 10.0 color(red)(cancel(color(black)("L"))))/( "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1"))) "mol"^"-1" × 289.15 color(red)(cancel(color(black)("K")))) = "0.3993 mol"#

Step 2. Calculate the moles of #"CaH"_2#.

The balanced equation is:

#"CaH"_2 + "2H"_2"O" → "Ca(OH)"_2 + "2H"_2"#

#"Moles of CaH"_2 = 0.3993 cancel("mol H"_2) × ("1 mol CaH"_2)/(2 cancel("mol H"_2)) = "0.1996 mol CaH"_2#

Step 3. Calculate the mass of #"CaH"_2#

#"Mass of CaH"_2 = 0.1996 color(red)(cancel(color(black)("mol CaH"_2))) × ("42.09 g CaH"_2)/(1 color(red)(cancel(color(black)("mol CaH"_2)))) = "8.40 g CaH"_2#