To solve this problem, we need to use stoichiometry.
From the balanced chemical equation, we can see that 1 mole of PCl3 produces 3 moles of HCl. Therefore, we need to first calculate the number of moles of PCl3 in 15.0 g:
moles of PCl3 = mass / molar mass
moles of PCl3 = 15.0 g / 137.33 g/mol
moles of PCl3 = 0.109 mol
Now, we can use the mole ratio from the balanced chemical equation to find the number of moles of HCl produced:
moles of HCl = moles of PCl3 x (3 moles of HCl / 1 mole of PCl3)
moles of HCl = 0.109 mol x 3
moles of HCl = 0.327 mol
Finally, we can use the molar mass of HCl to convert the number of moles to mass:
mass of HCl = moles of HCl x molar mass
mass of HCl = 0.327 mol x 36.46 g/mol
mass of HCl = 11.9 g
Therefore, 15.0 g of PCl3 can produce 11.9 g of HCl.