The question requires us to calculate the amount of hydrogen gas that would evolve when reacting 5 ng of lead (Pb) with hydrochloric acid (HCl).
The reaction between Pb and HCl produces lead chloride and hydrogen gas, as shown below:
Pb + 2HCl -> PbCl2 + H2(g)
With the stoichiometric coefficients from the reaction, we can now calculate the amount of gas produced when 5 ng of metal are used.
First, we need to convert the mass of Pb into its number of moles, considering the atomic mass of Pb (207.2 u):
207.2 g of Pb --------------- 1 mol of Pb
5 x 10^-9 g of Pb ----------- x
Solving for x, we have that 5 ng of Pb corresponds to 0.024 x 10^-9 moles or 0.024 moles of Pb.
(note that the unit of mass used is nanogram, which corresponds to 10^-9 g)
Now, from the reaction, we have that:
1 mol Pb ------------------------------ 1 mol H2
0.024 x 10^-9 mol Pb ----------- y
Solving for y, we have that 0.024 nmol of H2 are produced.
We can convert the amount of H2 gas calculated into volume, considering the Standard Temperature and Pressure conditions (1 mol = 22.4 L under STP):
1 mol H2 ----------------------------- 22.4 L of H2
0.024 x 10^-9 mol H2 ---------- z
Solving for z, we have that 5.38 x 10^-10 L or 53.8 nL of H2 would be produced from 5 ng of Pb.