Question

${P_4}(s) + 6C{l_2}(g) \to 4PC{l_3}(l)$ A reaction mixture initially contains $45.13g$ ${P_4}$ and $132.0g$ $C{l_2}$ . Once the reaction has occurred as completely as possible, what mass (in g) of the excess reactant is left?

Answer 1

To solve this problem, we will first observe the number of moles of each reactant reacting with each other. Then we will convert the given mass of reactants into their number of moles. Therefore, using the stoichiometric calculations, we will see which reactant is left after the completion of the reaction.

Complete Step By Step Answer:
We are given with a balanced chemical equation which is written as:
${P_4}(s) + 6C{l_2}(g) \to 4PC{l_3}(l)$
We can see that one mole of ${P_4}$ reacts with six moles of $C{l_2}$ . Now, we will find out the number of moles of each reactant using their given masses and molecular masses.
Given mass of ${P_4}$ is $45.13g$ .
Given mass of $C{l_2}$ is $132.0g$ .
Molecular mass of ${P_4}$ is $123.89g$ .
Molecular mass of $C{l_2}$ is $71g$ .
Now, the formula to calculate number of moles (n) in terms of given mass (m) and molecular mass (M.M.) is given as:
$n = \dfrac{m}{{M.M.}}$
No. of moles of ${P_4}$ are:
${n_{{P_4}}} = \dfrac{{45.13}}{{123.89}}$
${n_{{P_4}}} = 0.3642$
No. of moles of $C{l_2}$ are:
${n_{C{l_2}}} = \dfrac{{132.0}}{{71}}$
${n_{C{l_2}}} = 1.8591$
Six of $C{l_2}$ reacts with one mole of ${P_4}$ . Therefore, Chlorine is the limiting reactant.
Therefore, $1.8591$ of $C{l_2}$ reacts with:
$= \dfrac{1}{6} \times 1.8591$
$= 0.30985$ moles of ${P_4}$
Therefore, number of moles of ${P_4}$ left after complete reaction is:
$= 0.3642 - 0.30985$
$= 0.05435$
Hence, the mass of ${P_4}$ left after complete reaction is:
$= 0.05435 \times 123.89$
$= 6.7334g$
Therefore, the mass of ${P_4}$ left after complete reaction is $6.7334g$ .

Note:
The product $PC{l_3}$ is known as Phosphorus trichloride. It has many applications such as it is used in the making of phosphorus oxychloride and this happens when Phosphorus trichloride is oxidized with oxygen. It is also used to make many chlorinated products such as Phosphoryl chloride, Phosphorus pentachloride and many more.