# Rust is a reddish brown solid with the chemical formula Fe2O3 · nH2O. To determine the number of molecules of water of crystallization in a formula unit of a rust sample, 40.0 cm3 of 1.5M hydrochloric acid was added to 1.89 g of.... (Details below)?

Aug 25, 2017

#### Answer:

$\textsf{0.0424}$

$\textsf{n = 5.97}$

#### Explanation:

The iron(III) oxide in the rust reacts with the acid which is INXS:

$\textsf{F {e}_{2} {O}_{3 \left(s\right)} + 6 H C {l}_{\left(a q\right)} \rightarrow 2 F e C {l}_{3 \left(a q\right)} + 3 {H}_{2} {O}_{\left(l\right)}}$

The initial no. of moles of HCl added is given by:

$\textsf{n H C {l}_{\text{init}} = c \times v = 1.5 \times \frac{40.0}{1000} = 60.0 \times {10}^{- 3}}$

The unreacted HCl is titrated against 1.20 M NaOH:

$\textsf{H C {l}_{\left(a q\right)} + N a O {H}_{\left(a q\right)} \rightarrow N a C {l}_{\left(a q\right)} + {H}_{2} {O}_{\left(l\right)}}$

$\textsf{n O {H}^{-} = c \times v = 1.20 \times \frac{14.65}{1000} = 17.58 \times {10}^{- 3}}$

From the equation we can say that:

$\textsf{n H C {l}_{\text{rem}} = 17.58 \times {10}^{- 3}}$

$\therefore$ the no. of moles of HCl consumed is given by:

$\textsf{n H C l = \left(60.0 - 17.58\right) \times {10}^{- 3} = 42.42 \times {10}^{- 3}}$

This is the answer to the 1st part of the question.

From the equation we can say that:

$\textsf{n F {e}_{2} {O}_{3} = \frac{42.42 \times {10}^{- 3}}{6} = 7.07 \times {10}^{- 3}}$

Mass $\textsf{F {e}_{2} {O}_{3} = n \times {M}_{r} = 7.07 \times {10}^{- 3} \times 159.688 = 1.12899 \textcolor{w h i t e}{x} g}$

$\therefore$Mass $\textsf{{H}_{2} O = 1.89 - 1.12899 = 0.76101 \textcolor{w h i t e}{x} g}$

The no. moles of $\textsf{{H}_{2} O}$ is given by:

$\textsf{n {H}_{2} O = \frac{m}{M} _ r = \frac{0.76101}{18.0153} = 0.04224}$

Ratio by moles $\textsf{F {e}_{2} {O}_{3} : {H}_{2} O \Rightarrow}$

$\textsf{0.00707 : 0.04224}$

=$\textsf{1 : 5.97}$

So we can write the formula:

$\textsf{F {e}_{2} {O}_{3.} {\left({H}_{2} O\right)}_{5.97}}$

I'll leave it unrounded as rust is not a stoichiometric compound with regard to the water present.