Answer : The chemical symbol for this element is, (La)
Explanation : Given,
Mass of
= 0.760 g
Mass of
= 1.610 g
The given chemical reaction is:

First we have to calculate the moles of
and
.

Molar mass of Cl = 35.5 g/mole
Let the molar mass of element 'X' be, M
![\text{Moles of }XCl_3=\frac{0.760}{[M+3(35.5)]}](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DXCl_3%3D%5Cfrac%7B0.760%7D%7B%5BM%2B3%2835.5%29%5D%7D)
and,

Molar mass of I = 126.9 g/mole
Let the molar mass of element 'X' be, M
![\text{Moles of }XI_3=\frac{1.610}{[M+3(126.9)]}](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DXI_3%3D%5Cfrac%7B1.610%7D%7B%5BM%2B3%28126.9%29%5D%7D)
From the balanced chemical reaction we conclude that,
The moles of ratio of
and
is, 1 : 1
That means,
![\frac{0.760}{[M+3(35.5)]}=\frac{1.610}{[M+3(126.9)]}](https://tex.z-dn.net/?f=%5Cfrac%7B0.760%7D%7B%5BM%2B3%2835.5%29%5D%7D%3D%5Cfrac%7B1.610%7D%7B%5BM%2B3%28126.9%29%5D%7D)
![\frac{0.760}{[M+106.5]}=\frac{1.610}{[M+380.7]}](https://tex.z-dn.net/?f=%5Cfrac%7B0.760%7D%7B%5BM%2B106.5%5D%7D%3D%5Cfrac%7B1.610%7D%7B%5BM%2B380.7%5D%7D)

From this we conclude that the element (X) is lanthanum (La) that has molecular weight, 138.667 g/mol.
Hence, the chemical symbol for this element is, (La)