Lessons · Gas stoichiometry

How much hydrogen? A metal, an acid, and a gas you can measure

Machine-checked — balanced, charge-conserved, extent-verified by ChemKernel 4 modeling assumptions (disclosed)

A 3.269 g strip of zinc metal is dropped into 120.0 mL of 1.00 M hydrochloric acid. The zinc dissolves, bubbling hydrogen gas, which is collected at 1.00 atm and 25.00 °C. Which reactant runs out first, and what volume of hydrogen forms?

Volume of

\mathrm{H_{2}}

gas ideal gas

1.22 L

at 1.00 atm, 25.00 °C

Mass of

\mathrm{H_{2}}

formed

0.101 g

Dissolved salt (

\mathrm{ZnCl_{2}}

)

6.814 g

Limiting reagent

Left over

HCl 20 mmol

Gas volume — model-exact (ideal gas) the moles are machine-checked; PV=nRT converts them to a volume at the stated conditions

0.05 mol

\mathrm{H_{2}}

from the ledger (ξ)

24.5 L/molRT/P at 1.00 atm, 298.15 K

1.22 Lvolume of

\mathrm{H_{2}}

The molar volume is RT/P = 24.5 L/mol at these conditions — not the 22.4 L/mol you memorized for STP (0 °C, 1 atm). One mole of gas only fills 22.4 L at STP; change the temperature or pressure and you must use PV=nRT.

Molecular equation — what you combine

\mathrm{Zn}\,\text{(s)} + 2\,\mathrm{HCl}\,\text{(aq)} \rightarrow \mathrm{ZnCl_{2}}\,\text{(aq)} + \mathrm{H_{2}}\,\text{(g)}

Complete ionic — every strong electrolyte shown as free ions strong-electrolyte model

\mathrm{Zn} + 2\,\mathrm{H}^{+} + 2\,\mathrm{Cl}^{-} \rightarrow \mathrm{Zn}^{2+} + 2\,\mathrm{Cl}^{-} + \mathrm{H_{2}}

Net ionic — spectators cancelled, the reaction that actually happens

\mathrm{Zn} + 2\,\mathrm{H}^{+} \rightarrow \mathrm{Zn}^{2+} + \mathrm{H_{2}}

Spectator ions (unchanged, still dissolved): Cl⁻

Verification Every claim below was proven at build time — not asserted.

✓ Atoms balance across the equation [conservation matrix]
✓ Charge balances (net ionic re-verified) [charge row]
✓ Units cancel through the dimensional chain [units engine]
✓ No amount goes negative — extent is physical [nonnegative-extent guard]

✗ Common misconception: “One mole of any gas occupies 22.4 L, so the hydrogen volume is just its moles times 22.4 L.”

22.4 L/mol is the molar volume only at STP (0 °C, 1 atm). At 1.00 atm and 25.00 °C it is RT/P = 24.5 L/mol, so $\mathrm{H_{2}}$ occupies 1.22 L — not 1.12 L. Whenever you are not at STP, use PV = nRT at the actual pressure and temperature.

Modeling assumptions — author-asserted, disclosed not discharged

model The zinc reacts completely with the acid — the single-replacement reaction goes essentially to completion.
model Hydrogen behaves as an ideal gas: PV = nRT holds exactly only for a dilute gas (low pressure, not-too-low temperature).
model HCl is a strong acid and dissociates completely in water.
model The hydrogen is collected dry at the stated pressure and temperature — no water-vapor-pressure correction (collecting a gas over water is a later refinement).

Concepts in this lesson

Linked into the Chemical Atlas where an entry exists; the rest fill in as the Atlas grows.

Practice this

The lesson goes deep on one scenario; the gym builds fluency by repetition. Drill these: