Aluminum reacts with excess hydrochloric acid to form aqueous aluminum chloride and 46.5 mL of hydrogen gas over water at 27 degrees Celsius and 751 mmHg. How many grams of aluminum reacted? The partial pressure of water at 27 C is 26.8 mmHg.

1 Answer
Jul 8, 2017

Answer:

#0.0324# #"g Al"#

Explanation:

We're asked to find the number of grams of #"Al"# that reacted, given some #"H"_2 (g)# product characteristics.

Let's first write the chemical equation for this reaction:

#2"Al"(s) + 6"HCl"(aq) rarr2 "AlCl"_3(aq) + 3"H"_2 (g)#

The total pressure of the gaseous system is given as #751# #"mm Hg"#, and the partial pressure of water vapor is #26.8# #"mm Hg"# at #27^"o""C"#. The pressure of hydrogen gas is thus

#P_"total" = P_ ("H"_2"O") + P_ ("H"_2)#

#P_ ("H"_2) = 751# #"mm Hg"# #- 26.8# #"mm Hg"# #= color(red)(724# #color(red)("mm Hg"#

This pressure in atmospheres is

#724cancel("mm Hg")((1color(white)(l)"atm")/(760cancel("mm Hg"))) = color(red)(0.953# #color(red)("atm"#

We'll now use the ideal gas equation to find the number of moles of #"H"_2# formed:

(#T = 27^"o""C" + 273 = 300# #"K"#)

#n = (PV)/(RT) = ((color(red)(0.953)cancel(color(red)("atm")))(0.0465cancel("L")))/((0.082057(cancel("L")•cancel("atm"))/("mol"•cancel("K")))(300cancel("K"))) = color(green)(0.00180# #color(green)("mol H"_2#

(volume converted to liters here)

Using the coefficients of the chemical equation, we'll now find the relative number of moles of #"Al"# that react:

#color(green)(0.00180)cancel(color(green)("mol H"_2))((2color(white)(l)"mol Al")/(3cancel("mol H"_2))) = color(purple)(0.00120# #color(purple)("mol Al"#

Lastly, we'll use the molar mass of aluminum (#26.98# #"g/mol"#) to find the number of grams that reacted:

#color(purple)(0.00120)cancel(color(purple)("mol Al"))((26.98color(white)(l)"g Al")/(1cancel("mol Al"))) = color(blue)(0.0324# #color(blue)("g Al"#

Thus, #color(blue)(0.0324# #sfcolor(blue)("grams of aluminum"# reacted.