To determine the cost of the mercury per cubic inch, we need to divide the total cost with the total volume in units of cubic inches. To do this, we first determine the volume of the mercury given the mass and the density. In any operation, it is important to remember that the units of the values involved should be homogeneous so that we can cancel them. We do as follows:
mass of mercury = 76 lb ( 1 kg / 2.2 lbs ) ( 1000 g / 1 kg ) = 34545.45 g
volume of mercury in cm^3 = 34545.45 g / 13.534 g / cm^3 = 2552.49 cm^3
We need to convert this to units of cubic inches since it is what is asked.
volume of mercury in in^3 = 2552.49 cm^3 ( 1 in / 2.54 cm )^3 = 155.76 in^3
cost per in^3 = $126 / 155.76 in^3 = $ 0.809 / in^3
The atomic mass of the metal.(M) = 51 g/mol
<h3>Further explanation</h3>
Given
32% of oxygen
Required
the atomic mass of the metal.
Solution
An oxide of trivalent metal : M₂O₃(Ar O = 16 g/mol)
The molar mass of metal oxide = 2M+16.3=2M+48
32% of oxygen, then :
32% x 2M+48 = 48
0.32(2M+48)=48
0.64M+15.36=48
0.64M=32.64
M=51
