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...

1 Answer
Mar 27, 2017

Answer:

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.