# 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?

May 7, 2017

The mass of aluminium is 15 g.

#### Explanation:

Calculate the moles of ${\text{H}}_{2}$

We can use the Ideal Gas Law:.

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} p V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange this formula to get

$n = \frac{p V}{R T}$

$p = \text{1.0 atm}$
$V = \text{20.0 L}$
$R = \text{0.082 06 L·atm· K"^"-1""mol"^"-1}$
$T = \text{298 K}$

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 $\text{Al}$

${\text{2Al"+"3H"_2"SO"_4 → "Al"_2("SO"_4)_3 +"3H}}_{2}$

$\text{Mass of Al" = 0.818 color(red)(cancel(color(black)("mol H"_2))) × (2 color(red)(cancel(color(black)("mol Al"))))/(3 color(red)(cancel(color(black)("mol H"_2)))) × "26.98 g Al"/(1 color(red)(cancel(color(black)("mol Al")))) = "15 g Al}$

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