What is the atomic mass of an element if 1 gram of an element is converted into 1.08 grams of oxide? (specific heat capacity=0.06 cal per degree centigrade per gram)

1 Answer
Mar 25, 2018

The atomic mass of the element is 100 u.

Explanation:

Let #"X"# represent the element.

Step 1. Calculate the mass of #"O"# that reacts with 1 g of #"X"#

The equation is

#color(white)(mmmmm)"X +O"_2 → "X"_text(m)"O"_text(n)#
#"Mass/g": color(white)(m)1color(white)(ml)xcolor(white)(mmm)1.08#

From the data,

#1 + x = 1.08#

#x = "1.08 - 1 = 0.08"#

1 g of #"X"# reacts with 0.08 g of #"O"#.

Step 2. Calculate the equivalent mass of #"X"#

#"Eq. mass" = 8 color(red)(cancel(color(black)("g O"))) × "1 g X"/(0.08 color(red)(cancel(color(black)("g O")))) = "100 g X"#

Step 3. Identify #"X"#

The relative atomic mass of #"X"# must be a multiple of 100.

Possible candidates are

#ulbb("Element"color(white)(m)A_text(r)color(white)(m)C_text(s)"/J·°C"^"-1""g"^"-1")#
#color(white)(mll)"Tc"color(white)(mmml)98color(white)(mmll)0.063#
#color(white)(mll)"Ru"color(white)(mmll)101color(white)(mmll)0.238#
#color(white)(mll)"Au"color(white)(mmll)197color(white)(mmll)0.1291#
#color(white)(mll)"Hg"color(white)(mmll)201color(white)(mmll)0.1395#

The specific heat capacity of #"X" = "0.06 cal·°C"^"-1""g"^"-1" = "0.25 J·°C"^"-1""g"^"-1"#

Element #"X"# is ruthenium, and #A_text(r) = 100#