Pennies that are currently being minted are composed of zinc...

Pennies that are currently being minted are composed of zinc coated with copper. A student determines the mass of a penny to be 2.482 $\mathrm{g}$ and then makes several scratches in the copper coating (to expose the underlying zinc). The student puts the scratched penny in hydrochloric acid, where the following reaction occurs between the zinc and the HCl (the copper remains undissolved): $$\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{ZnCl}_{2}(a q)$$ The student collects the hydrogen produced over water at $25^{\circ} \mathrm{C}$ . The collected gas occupies a volume of 0.899 $\mathrm{L}$ at a total pressure of 791 mmHg. Calculate the percent zinc (by mass) in the penny. (Assume that all the Zn in the penny dissolves.)

Pennies that are currently being minted are composed of zinc coated
with copper. A student determines the mass of a penny to be 2.482 $\mathrm{g}$
and then makes several scratches in the copper coating (to expose the underlying zinc). The student puts the scratched penny in hydrochloric acid, where the following reaction occurs between the zinc and the HCl (the copper remains undissolved):
$$\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{ZnCl}_{2}(a q)$$
The student collects the hydrogen produced over water at $25^{\circ} \mathrm{C}$ . The
collected gas occupies a volume of 0.899 $\mathrm{L}$ at a total pressure of 791
mmHg. Calculate the percent zinc (by mass) in the penny. (Assume that all the Zn in the penny dissolves.)

Key Concepts

Percent Composition

Percent composition is the calculation of the mass fraction of a component in a compound or mixture expressed as a percentage. In this context, it is used to determine the proportion of zinc by mass in the penny, based on the mass determined through stoichiometric calculations.

Ideal Gas Law

The ideal gas law (PV = nRT) is used to calculate the number of moles of gas collected under given conditions of volume, temperature, and pressure. This law allows one to relate these measurable quantities to the amount of substance present in a gaseous reaction product.

Stoichiometry

This concept involves using balanced chemical equations to relate the quantitative amounts of reactants and products in a chemical reaction. In this case, the stoichiometry of the reaction between zinc and hydrochloric acid is used to determine the moles of zinc based on the moles of hydrogen gas produced.

Vapor Pressure Correction

When collecting gases over water, the measured total pressure includes contributions from both the gas of interest and water vapor. Correcting for the water vapor pressure is essential for obtaining the true partial pressure of the gas being analyzed, which is necessary for accurate calculations using the ideal gas law.

Transcript

00:01 So in this question, we're reacting zinc and impending with hydrochloric acid to produce hydrogen gas.

00:07 We're bubbling that over water.

00:10 So since we're bubbling over water, the first thing we need to do is find the pressure of only the hydrogen gas, kind of without the pressure of the water also there.

00:19 So how we can you do that is by starting with dalton's law of partial pressures.

00:24 So we can say that the total pressure is equal to the pressure, from water plus the pressure from the hydrogen gas.

00:36 All right.

00:39 So we are told the total pressure, which is 791, is equal to the partial pressure from water at 25 degrees, which is going to be 23 .78 plus the pressure of hydrogen gas.

00:56 So with that, we can say the pressure of hydrogen gas, and all of the units in this is going to be millimeters from mercury.

01:01 I just kind of forgot to write them.

01:03 Is going to be 767 .22 millimeters of mercury.

01:14 Okay, so from there what we can do is we can calculate the number of moles of hydrogen gas produced.

01:21 So using the ideal gas law, we can say, obviously, pv equals nrt, or n is equal to pv over rt.

01:32 So i can say n of h2 is then going to be equal to the pressure, which we just solved for, of 767 .22 millimeters of mercury times the volume, which it tells us is 0 .89 -leaders over r, which is going to be 62 .36 millimeters of mercury times liters over moles, times kelvin...

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