# Question 3932d

Sep 24, 2015

Here's how you can solve this problem.

#### Explanation:

Since you didn't get to finish the question, I will assume that you are asked to find either

• the total mass of the initial mixture, or
• the total mass of the final mixture.

I'll show you how to find both, just for good measure.

So, let's say that the mass of solid silicon is $x$ and the mass of solid phosphorus is $y$.

You know that this mixture contain 28.2% by mass silicon, so you can say that

$\frac{x}{x + y} \times 100 = 28.2 \text{ } \textcolor{b l u e}{\left(1\right)}$

Keep this in mind.

Now, focus on the final mixture. You know that this mixture will contain silicon tetrachloride, ${\text{SiCl}}_{4}$, and phosphorus trichloride, ${\text{PCl}}_{3}$.

Moreover, you know that this mixture contains 48.2 g of phosphorus trichloride. The balanced chemical equation for the reaction that takes place between solid phosphorus and chlorine gas looks like this

${\text{P"_text(4(s]) + 6"Cl"_text(2(g]) -> color(red)(4)"PCl}}_{\textrm{3 \left(l\right]}}$

Notice that you have a $1 : \textcolor{red}{4}$ mole ratio between solid phosphorus and phosphorus trichloride. This means that evey mole of the former that reacts will produce 4 moles of the latter.

Use the compound's molar mass to find the number of moles of ${\text{PCl}}_{3}$ formed by the reaction

48.2color(red)(cancel(color(black)("g"))) * ("1 mole PCl"""_3)/(137.33color(red)(cancel(color(black)("g")))) = "0.351 moles PCl"""_3

This means that you started with

0.351color(red)(cancel(color(black)("moles PCl"""_3))) * ("1 mole P"""_4)/(color(red)(4)color(red)(cancel(color(black)("moles PCl"""_3)))) = "0.08775 moles P"""_4

Now you can work backward from this value to find the mass of silicon that the initial mixture contained.

The mass of solid phosphorus that contains that many moles is

0.08775color(red)(cancel(color(black)("moles P"""_4))) * "123.90 g"/(1color(red)(cancel(color(black)("mole P"""_4)))) = "10.87 g P"""_4

Rember that this is equal to $y$. Use equation $\textcolor{b l u e}{\left(1\right)}$ to find $x$

$\frac{x}{x + 10.87} \times 100 = 28.2$

$100 x = 28.2 + 306.6 \implies x = \frac{306.6}{71.8} = \text{4.27 g}$

The initial mixture had a total mass of - rounded to three sig figs

m_"initial" = "4.27 g" + "10.87 g" = color(green)("15.1 g")

Now use the mass of solid silicon to find the mass of silicon tetrachloride produced by the reaction

${\text{Si"_text((s]) + 2"Cl"_text(2(g]) -> "SiCl}}_{\textrm{4 \left(l\right]}}$

The number of moles of silicon that react is

4.27color(red)(cancel(color(black)("g"))) * "1 mole Si"/(28.09color(red)(cancel(color(black)("g")))) = "0.152 moles"

The $1 : 1$ mole ratio that exists between solid silicon and silicon tetrachloride tells you that the reaction will produce 0.152 moles of silicon tetrachloride.

Finally, use the compound's molar mass to determine how many grams would contain that many moles

0.152color(red)(cancel(color(black)("moles SiCl"""_4))) * "169.90 g"/(1color(red)(cancel(color(black)("mole SiCl"""_4)))) = "25.8 g SiCl"""_4

The total mass of the final mixture is - rounded to three sig figs

m_"final" = "48.2 g" + "25.8 g" = color(green)("74.0 g")#