Question

What volume of dihydrogen gas will be generated by the action of excess hydrochloric acid on a `21*g` mass of zinc metal?

A temperature of `13` `""^@C`, and a pressure of `704*mm*Hg` are specified...

Answer 1

To answer this question we need (i) to know that:

`"760 mm Hg"` `-=` `1*atm`

Explanation:

That is `1*atm` of pressure will support a column of mercury that is `760*mm` high. This is a convenient laboratory measurement that I hope has been shown to you in the lab. The difference between mercury columns can thus be related to differences between absolute pressures. A mercury column is thus useful for pressures BELOW `1*atm`. IT IS NOT USED FOR PRESSURES ABOVE `1* atm`. (Why not? Because you will get mercury all over the lab, and guess who is going to clean it up.)

And of course we need (ii) a stoichiometrically balanced equation:

`Zn(s) + 2HCl(aq) rarr ZnCl_2(aq) + H_2(g)uarr`

So for each equiv metal, 1 equiv of dihydrogen gas results.

`"Moles of zinc"` `-=` `(21*g)/(65.38*g*mol^-1)=0.321*mol`.

And thus, by the stoichiometry, `0.321*mol` `H_2(g)` will result.

And so now, this is an Ideal Gas Equation, where we solve for volume:

`V=(nRT)/P=(0.321*cancel(mol)xx0.0821*(L*cancel"atm")/(cancel(K^-1*mol^-1))xx286*cancelK)/((704cancel(*mm*Hg))/(760cancel(*mm*Hg*atm^-1))`

You can do the math. I get an answer of approx. `8*L` at this pressure. And this is consistent with the known molar volume of an Ideal Gas under standard conditions, i.e. approx. `25*L`.

See here for more on the use of mercury to measure moderate pressure.