Question

What mass of solid aluminium is needed to react with excess H2SO4(aq) to produced 20.0 L of H2(g) at 1.0 atm and 298 K?

Answer 1

The mass of aluminium is 15 g.

Explanation:

Calculate the moles of `"H"_2`

We can use the Ideal Gas Law:#.

`color(blue)(bar(ul(|color(white)(a/a)pV = nRTcolor(white)(a/a)|)))" "`

We can rearrange this formula to get

`n = (pV)/(RT)`

`p = "1.0 atm"`
`V = "20.0 L"`
`R = "0.082 06 L·atm· K"^"-1""mol"^"-1"`
`T = "298 K"`

∴ `n = (1.0 color(red)(cancel(color(black)("atm"))) × 20.0 color(red)(cancel(color(black)("L"))))/("0.082 06" color(red)(cancel(color(black)("L·atm· K"^"-1")))"mol"^"-1" × 298 color(red)(cancel(color(black)("K")))) = "0.818 mol"`

Calculate the mass of `"Al"`

`"2Al"+"3H"_2"SO"_4 → "Al"_2("SO"_4)_3 +"3H"_2`

`"Mass of Al" = 0.818 color(red)(cancel(color(black)("mol H"_2))) × (2 color(red)(cancel(color(black)("mol Al"))))/(3 color(red)(cancel(color(black)("mol H"_2)))) × "26.98 g Al"/(1 color(red)(cancel(color(black)("mol Al")))) = "15 g Al"`

Note: The answer can have only two significant figures, because that is all you gave for the pressure of the hydrogen..