The answer is 0.13grams.
First, let's start with the balanced equation
Zn(s)+2HCl(aq)→ZnCL2(aq)+H2(g)
Now, the gas collected in t he 36.6mL tube is hydrogen mixed with water vapor. In order to get the amount of hydrogen (H2), we must get its partial pressure in the mixture by using Dalton's law.
So, the total pressure collected over the water is equal to the partial pressure of water and the partial pressure of H2.
Pcollected=PH2+Pwater, which means
PH2=Pcollected−Pwater=890.0−17.5=872.5mmHg.
Using the ideal gas law, PV=nRT, we can determine the number of moles of H2 produced in the reaction
nH2=PVRT=(872.5760)⋅36.6⋅10−30.082⋅(20+273.15)=0.002moles (notice the conversions of pressure, volume and temperature to atm, L, and K, respectively);
From the balanced equation we can see that we have a 1:1 mole ratio between Zn and H2, which means that the number of moles of Zn is equal to
nZn=0.002 moles
Therefore, the mass of Zn (knowing that its molar mass is 65.4gmol), is equal to
mZn=nZn⋅65.4gmol=0.004moles⋅65.4gmol=0.13g
Here's a helpful link to better visualize this reaction:
http://employees.oneonta.edu/viningwj/modules/CI_limiting_reactants_zinc_HCl.html
