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

Jul 17, 2017

The mass of the element is 1.7 g.

#### Explanation:

The equivalent mass of a metal $\text{M}$ is the mass that will displace 1.008 g of $\text{H}$
(one-half mole of ${\text{H}}_{2}$).

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

${\text{Moles of H"_2 = 0.7 color(red)(cancel(color(black)("L H"_2))) × "1 mol H"_2/(22.7 color(red)(cancel(color(black)("L H"_2)))) = "0.031 mol H}}_{2}$

${\text{Equivalents of H"_2 = 0.031 color(red)(cancel(color(black)("mol H"_2))) × "2 eq H"_2/(1 color(red)(cancel(color(black)("mol H"_2)))) = "0.062 eq H}}_{2}$

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

$\text{1 eq of H"_2 = "1 eq of M}$ and

$\text{0.062 eq of H"_2 = "0.062 eq of M}$

$\text{Mass of M" = 0.062 color(red)(cancel(color(black)("eq M"))) × "28 g M"/(1 color(red)(cancel(color(black)("eq M")))) = "1.7 g M}$

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.