<u>Answer:</u> The percent gallium in gallium bromide is 30.30 %.
<u>Explanation:</u>
To calculate the number of moles, we use the equation:
.....(1)
Given mass of gallium bromide = 0.165 g
Molar mass of titanium gallium bromide = 229.53 g/mol
Putting values in equation 1, we get:
![\text{Moles of gallium bromide}=\frac{0.165g}{229.53g/mol}=0.00072mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20gallium%20bromide%7D%3D%5Cfrac%7B0.165g%7D%7B229.53g%2Fmol%7D%3D0.00072mol)
- The chemical equation for the reaction of gallium bromide and silver nitrate follows:
![GaBr_2+2AgNO_3\rightarrow 2AgBr(s)+Ga(NO_3)_2](https://tex.z-dn.net/?f=GaBr_2%2B2AgNO_3%5Crightarrow%202AgBr%28s%29%2BGa%28NO_3%29_2)
By Stoichiometry of the reaction:
1 moles of gallium bromide produces 1 mole of gallium nitrate
So, 0.00072 moles of gallium bromide will produce =
of gallium nitrate
- Now, calculating the mass of gallium nitrate from equation 1, we get:
Molar mass of gallium nitrate = 193.73 g/mol
Moles of gallium nitrate = 0.00072 moles
Putting values in equation 1, we get:
![0.00072mol=\frac{\text{Mass of gallium nitrate}}{193.73g/mol}\\\\\text{Mass of gallium nitrate}=0.139g](https://tex.z-dn.net/?f=0.00072mol%3D%5Cfrac%7B%5Ctext%7BMass%20of%20gallium%20nitrate%7D%7D%7B193.73g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20gallium%20nitrate%7D%3D0.139g)
Calculating the mass of gallium in the reaction, we use unitary method:
In 1 mole of gallium nitrate, 1 mole of gallium atom is present.
In 193.73 grams of gallium nitrate, 69.72 g of gallium atom is present.
So, in 0.139 grams of gallium nitrate, the mass of gallium present will be = ![\frac{69.72}{193.73}\times 0.139=g](https://tex.z-dn.net/?f=%5Cfrac%7B69.72%7D%7B193.73%7D%5Ctimes%200.139%3Dg)
- To calculate the percentage composition of gallium in gallium bromide, we use the equation:
![\%\text{ composition of gallium}=\frac{\text{Mass of gallium}}{\text{Mass of gallium bromide}}\times 100](https://tex.z-dn.net/?f=%5C%25%5Ctext%7B%20composition%20of%20gallium%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20gallium%7D%7D%7B%5Ctext%7BMass%20of%20gallium%20bromide%7D%7D%5Ctimes%20100)
Mass of gallium bromide = 0.165 g
Mass of gallium = 0.050 g
Putting values in above equation, we get:
![\%\text{ composition of gallium}=\frac{0.050g}{0.165g}\times 100=30.30\%](https://tex.z-dn.net/?f=%5C%25%5Ctext%7B%20composition%20of%20gallium%7D%3D%5Cfrac%7B0.050g%7D%7B0.165g%7D%5Ctimes%20100%3D30.30%5C%25)
Hence, the percent gallium in gallium bromide is 30.30 %.