Question

What mass of a metal `"M"` displaces 0.7 L of hydrogen at STP if the equivalent mass of the metal is 28 g?

Answer 1

The mass of the element is 1.7 g.

Explanation:

The equivalent mass of a metal `"M"` is the mass that will displace 1.008 g of `"H"`
(one-half mole of `"H"_2`).

At STP, (0 °C and 1 bar) the molar volume of a gas is 22.7 L.

`"Moles of H"_2 = 0.7 color(red)(cancel(color(black)("L H"_2))) × "1 mol H"_2/(22.7 color(red)(cancel(color(black)("L H"_2)))) = "0.031 mol H"_2`

`"Equivalents of H"_2 = 0.031 color(red)(cancel(color(black)("mol H"_2))) × "2 eq H"_2/(1 color(red)(cancel(color(black)("mol H"_2)))) = "0.062 eq H"_2`

1 eq of anything reacts with 1 eq of anything else, so

`"1 eq of H"_2 = "1 eq of M"` and

`"0.062 eq of H"_2 = "0.062 eq of M"`

`"Mass of M" = 0.062 color(red)(cancel(color(black)("eq M"))) × "28 g M"/(1 color(red)(cancel(color(black)("eq M")))) = "1.7 g M"`

Note: The answer should have only one significant figure, because that is all you gave for the volume of hydrogen.

However, I kept two significant figures.