Question

`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.

Answer 1

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`