Answer : The mass of chlorine reacted with the phosphorus is, 53.25 grams.
Explanation :
First we have to calculate the moles of phosphorus.
[tex]\text{Moles of phosphorus}=\frac{\text{Mass of phosphorus}}{\text{Molar mass of phosphorus}}[/tex]
[tex]\text{Moles of phosphorus}=\frac{15.5g}{31g/mol}=0.5mol[/tex]
Now we have to calculate the moles of [tex]Cl_2[/tex]
The balanced chemical reaction is:
[tex]2P+3Cl_2\rightarrow 2PCl_3[/tex]
From the balanced chemical reaction, we conclude that
As, 2 moles of phosphorous react with 3 moles of [tex]Cl_2[/tex]
So, 0.5 moles of phosphorous react with [tex]\frac{3}{2}\times 0.5=0.75[/tex] moles of [tex]Cl_2[/tex]
Now we have to calculate the mass of [tex]Cl_2[/tex]
[tex]\text{Mass of }Cl_2=\text{Moles of }Cl_2\times \text{Molar mass of }Cl_2[/tex]
Molar mass of [tex]Cl_2[/tex] = 71 g/mol
[tex]\text{Mass of }Cl_2=0.75mol\times 71g/mol=53.25g[/tex]
Therefore, the mass of chlorine reacted with the phosphorus is, 53.25 grams.
