To balance a chemical reaction, we need to remember that the number of each atom in the reactant and the product side of the equation should be equal. So, from the reaction P4(s) + Cl2(g) = PCl3(l), there are 4 P atoms in the reactant, the P atoms in the prodcut side should be 4 as well. We balance as follows:
P4(s) + 6Cl2(g) = 4PCl3(l)
Therefore, the coefficient of the PCl3 should be 4.
