The first step to solve this question is to convert the given masses to moles using the corresponding molecular weight:
![15.2gAl\cdot(molAl)/(27gAl)=0.56molAl](https://img.qammunity.org/2023/formulas/chemistry/college/1pqdp9sft9x6luo23u3i3zyqg1j2q0rus7.png)
![39.1gCl\cdot(molCl_2)/(35.45gCl_2)=1.1molCl_2](https://img.qammunity.org/2023/formulas/chemistry/college/b5c53vc8uwgaqdb8i0cp7mv22xfy1i7fwh.png)
Divide each of the results by the coefficient of each reactant in the equation. It means, divide the amount of Al by 2 and the amount of Cl2 by 3:
![\begin{gathered} (0.56molAl)/(2molAl)=0.28 \\ (1.1molCl_2)/(3molCl_2)=0.367 \end{gathered}](https://img.qammunity.org/2023/formulas/chemistry/college/rjdh5h4n4a4ezw0k1qtooq4yhqoa6kzmsz.png)
It means that the limiting reactant is Aluminium and we have to base our calculations on this reactant. From the equation we know than 2 moles of Al produce 2 moles of AlCl3.
![0.56molAl\cdot(2molAlCl_3)/(2molAl)=0.56molAlCl_3](https://img.qammunity.org/2023/formulas/chemistry/college/z28lavnnulksdyt51z92hpnqbq9nn2jjhe.png)
Now, convert this amount of AlCl3 to mass using its molecular weight:
![0.56molAlCl_3\cdot(133.33gAlCl_3)/(molAlCl_3)=74.66gAlCl_3](https://img.qammunity.org/2023/formulas/chemistry/college/ph1r2do24kbbsl4nvd2ik9cujlbei1hgth.png)
It means that the mass of AlCl3 formed is 74.66g.