A materials scientist has created an alloy containing aluminum, copper, and zinc

Question

A materials scientist has created an alloy containing aluminum, copper, and zinc, and wants to determine the percent composition of the alloy. Thé scientist takes a 11.684 g sample of the alloy and reacts it with concentrated HCI. The reaction converts all of the aluminum and zinc in the alloy to aluminum chloride and zinc chloride in addition to producing hydrogen gas. The copper does not react with the HCI. Upon completion of the reaction, a total of 9.92 L of hydrogen gas was collected at a pressure of 735 torr and a temperature of 27.0 . Additionally, 2.273 g of unreacted copper is recovered. Calculate the mass of hydrogen gas formed from the reaction. Number Calculate the mass of aluminum in the alloy sample. Number What is the mass percent composition of the alloy? Number Number Number %Cu %Al

Explanation / Answer

the involved balanced chemical equation would be:

.. x Al + y Zn + z Cu + (3x + 2y) HCl ---> x AlCl3 + y ZnCl2 + z Cu(s) + (3/2x + y) H2

then moles of H2
.. PV = nRT
.. n = (735 torr x 1atm/760torr)*(9.92 L) / ((0.08206 Latm/molK)*(300.15K))
.. n = 0.389 mol H2
.. mass = 0.389 mol x (2.016g / 1 mol) = 0.785 g H2 .

So, 0.785 g of H2 formed from the reaction.

NOW, from the mass ratio of Cl to H in HCl, we can calc how much Cl was used
.. 0.785 g H2 x (35.45g Cl / 1.008g H) = 27.60 g Cl

then.. using the coefficients of that balanced equation
we know that the Cl ended up in AlCl3 and ZnCl2 and that mass = 27. 60 g so that
.. (3x + 2y) * 35.45 = 27. 60

now we have 1 equation and 2 unknowns.. we need another equation

we know that..

mass Al + Zn = 11.684 g - 2.273 g = 9.411 g

then from a mass balance
.. x * (26.98g / mol) + y * (65.38g / mol) = 9.411 g
simplifying
.. 26.98x + 65.38y = 9.411

now we have 2 equations and 2 unknowns
.. 26.98x + 65.38y = 9.411
.. 106.4x + 70.9y = 27.60

divide the first by 26.98
.. .... .1x +. 2.423y = 0.348
.. 106.4x + . 70.9y = 27.60

multiply the first by -106.4
..-106.4x - .257.8y = -37.11
.. 106.4x + . 70.9y = 27.60

add the 2 equations together
.. -186.9y = -9.51
then
.. .y = 0.050
then
.. .x =0.348 - 2.423 * 0.050= 0.226

and now we know
.. mass Al = 0.226 mol x (26.98g / mol) = 6.097 g
.. mass Zn = 0.050 mol x(65.38g / mol) = 3.269 g
.. mass Cu = 2.273 g

and
.. mass percent Al = 6.097 g / 11.684 g x 100= 52.1
.. mass percent Zn = 3.269 / 11.684g x 100 = 27.9
.. mass percent Cu = 2.273 / 11.684g x 100= 19.4

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