# Question 56d2c

Feb 2, 2016

$\text{48% Cu}$

#### Explanation:

Since copper does not react with hydrochloric acid, you can conclude that all the hydrogen collected will come from zinc's reaction with the acid.

This means that you can write

${\text{Zn"_text((s]) + 2"HCl"_text((aq]) -> "ZnCl"_text(2(aq]) + "H}}_{\textrm{2 \left(g\right]}} \uparrow$

and

"Cu"_text((s]) + "HCl"_text((aq]) -> color(purple)("N.R.")

Here $\text{N.R.}$ means no reaction.

Your strategy now will be to use the molar volume of a gas at STP to find how many moles of hydrogen were produced by zinc's reaction with hydrochloric acid.

This will allow you top find the number of moles of zinc present in the initial sample.

So, STP conditions are defined as a pressure of $\text{100 kPa}$ and a temperature of ${0}^{\circ} \text{C}$. Under these specific conditions for pressure and temperature, one mole of any ideal gas will occupy a volume of $\text{22.7 L}$.

Your reaction produced a volume of $\text{4.48 L}$ of hydrogen gas at STP, which means that a total of

4.48 color(red)(cancel(color(black)("L H"_2))) * "1 mole H"_2/(22.7color(red)(cancel(color(black)("L H"_2)))) = "0.1974 moles H"_2

were produced by this reaction.

The balanced chemical equation tells you that one mole of zinc metal will produce one mole of hydrogen gas $\to$ you have a $1 : 1$ mole ratio between the two.

This means that the initial sample contained $0.1974$ moles of zinc. Use zinc's molar mass to find how many grams would contain this many moles of zinc

0.1974 color(red)(cancel(color(black)("moles Zn"))) * "65.38 g"/(1color(red)(cancel(color(black)("mole Zn")))) = "12.91 g"

The mass of copper present in the initial sample will be

${m}_{\text{sample}} = {m}_{Z n} + {m}_{C u}$

${m}_{C u} = \text{25 g" - "12.91 g" = "12.09 g}$

The mass percentage of copper can be found by dividing the mass of copper by the total mass of the sample, and multiplying the result by $100$.

$\textcolor{b l u e}{\text{% Cu" = "mass of copper"/"mass of sample} \times 100}$

In your case, this will amount to

"% Cu" = (12.09 color(red)(cancel(color(black)("g"))))/(25color(red)(cancel(color(black)("g")))) xx 100 = color(green)("48%")#

The answer is rounded to two sig figs.

Here's a very cool image showing the two metals immersed in hydrochloric acid.

Zinc, shown here on the right, produces hydrogen gas which as you can see bubbles out of the solution. Copper, on the other hand, is unreactive.

SIDE NOTE If you want to use the molar volume of a gas as being $\text{22.4 L}$, you will get a mass percent of copper equal to $\text{47.696%}$.

Rounding this off to two sig figs will once again get you $\text{48%}$, so the result is the same regardless of the value you pick for the molar volume of a gas at STP.