# Question 91e81

Feb 12, 2016

${\text{0.27 g H}}_{2}$

#### Explanation:

The first thing to do here is write a balanced chemical equation for this single replacement reaction

$\textcolor{red}{2} {\text{Al"_text((s]) + 6"HCl"_text((aq]) -> 2"AlCl"_text(3(aq]) + color(blue)(3)"H}}_{\textrm{2 \left(g\right]}} \uparrow$

You're interested in finding out how much hydrogen gas will be produced by your sample of aluminium, so the $\textcolor{red}{2} : \textcolor{b l u e}{3}$ mole ratio that exists between the two chemical species is important here,

Now, focus on using the **percent composition of the alloy to figure out how much aluminium you have in your $\text{2.6-g}$ sample.

Since you know that the alloy is 93.7% aluminium by mass, which is equivalent to saying that out of every $\text{100 g}$ of alloy, $\text{93.7 g}$ will be aluminium, you will have

2.6 color(red)(cancel(color(black)("g alloy"))) * "93.7 g Al"/(100color(red)(cancel(color(black)("g alloy")))) = "2.436 g Al"

Next, use aluminium's molar mass to find how many moles of aluminium you have in that sample

2.436 color(red)(cancel(color(black)("g"))) * "1 mole Al"/(26.98color(red)(cancel(color(black)("g")))) = "0.09029 moles Al"

Since you know that every $\textcolor{red}{2}$ moles of aluminium will produce $\textcolor{b l u e}{3}$ moles of hydrogen gas, you will have

0.09029color(red)(cancel(color(black)("moles Al"))) * (color(blue)(3)" moles H"_2)/(color(red)(2)color(red)(cancel(color(black)("moles Al")))) = "0.1354 moles H"_2

Finally, use the molar mass of hydrogen gas to find you many grams would contain this many moles

0.1354 color(red)(cancel(color(black)("moles H"_2))) * "2.0159 g"/(1color(red)(cancel(color(black)("mole H"_2)))) = color(green)("0.27 g H"_2)#

The answer is rounded to two sig figs, the number of sig figs you have for the mass of the alloy.