Question

a 0.200 gram sample of an unknown metal is dropped into hydrochloric acid and reacts to produce 88.9 ml of dry hydrogen gas at 20 C and 736mmHg.what is the unknown metal, X?

Answer 1

First, we have to find out the mass of hydrogen gas.

Given that 88.9 ml of dry hydrogen gas at 20 C and 736mmHg is produced.

Hence,

Volume of H2, V = 88.9 mL = 0.0889 L

Pressure of H2, P = 736 mmHg = 736/760 atm = 0.97 atm

Temperature T = 20∘C = 20 +273 K= 293 K

molar mass of H2 gas M = 2 g/mol

mass of H2 gas m= ? g

Ideal gas equation , PV = n R T , R = 0.0821 L.atm/mol/K

Then, PV = (m/M) RT [ n = moles = mass (m)/ molar mass (M) ]

m = PVM/ RT

= (0.97 atm) (0.0889 L) (2 g/mol) / (0.0821 L.atm/mol/K x 293 K )

= 0.0072 g

Mass of H2 gas= 0.0072 g

Let us assume unknown metal as X.

X + 2HCl -----------> XCl₂ + H₂

1 mol 1 mol

? g 2 g

0.2 g 0.0072 g

Then,

? = 0.2 g x (2g / 0.0072 g)

= 55.5 g

This is the molar mass of unknown metal.

55.5 g is refers to Fe.

We know that molar mass of Fe = 55.5 g

Therefore, the unknown metal = Fe