Question

A materials scientist has created an alloy containing aluminum, copper, and zinc, and wants to determine the percent composition of the alloy. The scientist takes a 12.232 g sample of the alloy and reacts it with concentrated HCl. 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 HCl. Upon completion of the reaction, a total of 10.1 L of hydrogen gas was collected at a pressure of 739 torr and a temperature of 27.0°C. Additionally, 2.797 g of unreacted copper is recovered. Calculate the mass of hydrogen gas formed from the reaction. mass: g Calculate the mass of aluminum in the alloy sample. mass: g What is the mass percent composition of the alloy? Cu : % Zn : % Al : %

Answer 1

Answer:-

Given:-

total wt. of alloy sample = 12.232 g

volume of hydrogen (H2) gas (V) = 10.1 L

temperature of hydrogen (H2) gas (T) = 27.0 0C = 273 + 27 = 300 K

pressure of hydrogen (H2) gas (P) = 739 torr

wt.of hydrogen (H2) gas (w) = ?

wt. of unreacted copper (Cu) = 2.797 g

As we know that

gas constant (R) = 62.364 L.torr.K-1.mol-1

Since we know that

molar mass of hydrogen (H2) gas = 2 molar mass of H

molar mass of hydrogen (H2) gas = 2 1

molar mass of hydrogen (H2) gas = 2 g /mol

So according to the formula

PV = nRT

or

PV = wRT/M

therefore

pressure of hydrogen (H2) gas (P) volume of hydrogen (H2) gas (V) = wt.of hydrogen (H2) gas (w) gas constant (R) temperature of hydrogen (H2) gas (T) / molar mass of hydrogen (H2) gas(M)

739 torr 10.1 L = wt.of hydrogen (H2) gas (w) 62.364 L.torr.K-1.mol-1 300 K / 2 g /mol

wt.of hydrogen (H2) gas (w) = 739 torr 10.1 L 2 g /mol / 62.364 L.torr.K-1.mol-1 300 K

wt.of hydrogen (H2) gas (w) =14927.8‬ g / 18709.2

wt.of hydrogen (H2) gas (w) =0.798 g (i.e the answer)

Also we know that

molar mass of aluminium (Al) = 26.98 g /mol

and

molar mass of zinc (Zn) = 65.38 g /mol

So

total molar mass of aluminium (Al) and zinc (Zn) = 26.98 g /mol + 65.38 g /mol

total molar mass of aluminium (Al) and zinc (Zn) = 92.36 g /mol

Since we know that

wt. of unreacted copper (Cu) i.e wt. of copper (Cu) = 2.797 g

therefore

wt. of aluminium (Al) and zinc (Zn) in alloy sample = total wt. of alloy sample - wt. of unreacted copper (Cu)

wt. of aluminium (Al) and zinc (Zn) in alloy sample = 12.232 g - 2.797 g

wt. of aluminium (Al) and zinc (Zn) in alloy sample = 9.435‬ g

therefore

92.36 g wt. of aluminium (Al) and zinc (Zn) contained = 26.98 g aluminium (Al)

1 g wt. of aluminium (Al) and zinc (Zn) contained = 26.98 / 92.36 g aluminium (Al)

then

9.435‬ g wt. of aluminium (Al) and zinc (Zn) alloy sample contained = 26.98 9.435 / 92.36 g aluminium (Al)

9.435‬ g wt. of aluminium (Al) and zinc (Zn) alloy sample contained = 248.8953‬ / 92.36 g aluminium (Al)

9.435‬ g wt. of aluminium (Al) and zinc (Zn) alloy sample contained = 2.695 g aluminium (Al)

So

wt. of aluminium (Al) = 2.695 g

and

wt. of aluminium (Al) and zinc (Zn) in alloy sample = wt. of aluminium (Al) + wt. of zinc (Zn)

9.435‬ g = 2.695 g + wt. of zinc (Zn)

wt. of zinc (Zn) = 9.435‬ g - 2.695 g

wt. of zinc (Zn) = 6.74‬0 g

In tthis way we get

wt. of zinc (Zn) = 6.74‬0 g

wt. of aluminium (Al) = 2.695 g

wt. of copper (Cu) =   2.797 g

total wt. of alloy sample = 12.232 g

therefore

mass percent (%) of copper (Cu) = wt. of copper (Cu) 100 / total wt. of alloy sample

mass percent (%) of copper (Cu) = 2.797 g 100 / 12.232 g

mass percent (%) of copper (Cu) = 279.7 / 12.232

mass percent (%) of copper (Cu) = 22.87 %

similarly

mass percent (%) of   zinc (Zn)​​​​​​​ = wt. of  zinc (Zn)​​​​​​​ 100 / total wt. of alloy sample

mass percent (%) of   zinc (Zn)​​​​​​​ =   6.740 g 100 / 12.232 g

mass percent (%) of   zinc (Zn)​​​​​​​ =   674.0 / 12.232

mass percent (%) of zinc (Zn)​​​​​​​ =  55.10 %

similarly

mass percent (%) of aluminium (Al) = wt. of aluminium (Al) 100 / total wt. of alloy sample

mass percent (%) of aluminium (Al) =  2.695 g 100 / 12.232 g

mass percent (%) of aluminium (Al) =  269.5 / 12.232

mass percent (%) of aluminium (Al) =​​​​​​​  22.03 %

So

Cu : % Zn : % Al : % = 22.87 % : 55.10 % : 22.03 % (i.e the answer)