Respuesta :
A sample of rutile, an ore of titanium consisting principally of TiO2(s), was found to be 65.2% TiO2(s) by mass, with the remainder being sand impurities. what is the minimum number of metric tons of the ore that must be processed to obtain 10.0 metric tons of titanium
Explanation:
Ore contains ---- 65.2% [tex]TiO_2[/tex]
Mass% of titanium in TiO2 can be calculated as shown below:
[tex]mass percentage of Ti in TiO2=\frac{mass of Ti}{mass of TiO_2} *100\\=(47.86g/79.866g)* 100\\=59.9[/tex]
Given 10.0 metric tons of titanium is required.
The mass of ore that should be processed can be calculated as shown below:
Mass of Ti = ore x TiO2 % x Ti mass %
10.0 x 1000 kg = M (mass of ore) x (65.2/100) x (59.9/100) Ti
=>M=(10.0 metric tons) / (0.652 x 0.599)
=>M=25.6 metric tons
Hence, the mass of ore required is 25.6 metric tons.
The minimum amount of rutile ore to be processed is 25.6 metric tons.
Explanation:
Given :
The sample of rutile, 65.2% [tex]TiO_2[/tex] (s) by mass.
To find:
The minimum number of metric tons of the ore that must be processed to obtain 10.0 metric tons of titanium
Solution:
The atomic mass of titanium = 47.867 g/mol
The atomic mass of oxygen = 15.999 g/mol
The molar mass of [tex]TiO_2[/tex] [tex]= 47.867 g/mol+2\times 15.999 g/mol=79.865 g/mol[/tex]
Percentage of the titanium in [tex]TiO_2[/tex] :
[tex]Ti(\%)=\frac{1\times 47.867 g/mol}{79.865 g/mol}\times 100\\=59.935\%[/tex]
Quantity of titanium required = 10.0 metric ton
Quantity of [tex]TiO_2[/tex] from rutile ore = x
[tex]59.935\%=\frac{10.0 \text{metric ton}}{x}\times 100\\x=\frac{10.0 \text{metric ton}}{59.935}\times 100=16.7 \text{metric ton}[/tex]
Mass of [tex]TiO_2[/tex] form rutile ore= 16.7 metric ton
The percentage of [tex]TiO_2[/tex] in rutile = 65.2 %
The quantity of rutile ore to be processed = M
[tex]65.2\%=\frac{16.7 \text{metric ton}}{M}\times 100\\M=\frac{16.7 \text{metric ton}}{65.2}\times 100=25.6 \text{metric ton}[/tex]
The minimum amount of rutile ore to be processed is 25.6 metric tons.
Learn more about the percent of an element in the compound here:
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