Question #3ed00

1 Answer
Aug 8, 2017

Answer:

The relative atomic mass of the element is #48#.

Explanation:

The idea here is that the vapor density of the chloride will help you determine its molar mass.

As you know, the vapor density of a gas is defined as the ratio that exists between the molar mass of the gas and the molar mass of hydrogen gas, #"H"_2#.

In your case, you have

#"VD" = "molar mass chloride"/"molar mass H"_2 = 59.5#

To make the calculations easier, you can use the approximation

#"molar mass H"_2 ~~ "2 g mol"^(-1)#

This means that you have

#"molar mass chloride" = 59.5 * "2 g mol"^(-1)#

#"molar mass chloride" = "119 g mol"^(-1)#

Now, you know that the equivalent mass of the metal is equal to #"24 g"#. In your case, the equivalent mass of the metal, which is essentially the mass of #1# equivalent of metal, tells you the mass of metal that combines directly with #"35.5 g"# of chlorine, #"Cl"#.

So if #"24 g"# of the metal combine with #"35.5 g"# of chlorine, it follows that you have

#"24 g metal + 35.5 g Cl = 59.5 g chloride"#

#"24 g metal + 35.5 g Cl = 59.5 g chloride"#
#color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa)/color(white)(a)#
#"48 g metal + 71 g Cl = 119 g chloride"#

This means that #"48 g"# of metal combine with #"71 g"# of chlorine to form #"119 g"# of metal chloride, which tells you that the mass of #1# mole of metal, which is equal to #2# equivalents of metal, is equal to

#"molar mass metal = 48 g mol"^(-1)#

The relative atomic mass of the metal will thus be

#A_r = (48 color(red)(cancel(color(black)("g mol"^(-1)))))/(1color(red)(cancel(color(black)("g mol"^(-1))))) = 48#