Nutritional biochemists have known for decades that acidic foods cooked in cast-iron cookware can supply significant amounts of dietary iron (ferrous ion).

(a) Write a balanced net ionic equation, with oxidation numbers, that supports this fact.

(b) Measurements show an increase from 3.3 mg of iron to 49 mg of iron per$\frac{\mathbf{1}}{\mathbf{2}}$ -cup (125-g) serving during the slow preparation of tomato sauce in a cast-iron pot. How many ferrous ions are present in a 26-oz (737-g) jar of the tomato sauce?

The balanced net ionic equation can be written as

$\mathbf{Fe}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{H}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\to }{\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

Oxidation no of element free iron is 0.

Oxidation no of element free hydrogen is 0.

Oxidation no of Fe²⁺ is +2.

Oxidation no of H⁺ is +1.

Answer of subpart (b):

Answer: You need to calculate how many ferrous ions are present in a 26-oz (737-g) jar of the tomato sauce.

According to the question,

Mass of tomato sauce = 737g

Increase mass of iron = 49mg = 0.049g

Mass of tomato sauce added for increase = 125g

Now, you can write

Mass of Fe

$\begin{array}{l}\mathbf{=}\left(737\times \frac{0.049}{125}\right)\mathbf{\left(}\mathbf{g}\mathbf{\right)}\\ \mathbf{=}\mathbf{0}\mathbf{.2889}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\end{array}$

Hence, mass of iron is 0.2889g.

Mass of Fe = 0.2889g

Molecular mass of Fe = 55.85g/mol

Again you know,

$\mathbf{moles}\mathbf{=}\frac{\mathbf{mass}\mathbf{}\mathbf{\left(}\mathbf{given}\mathbf{\right)}}{\mathbf{mass}\mathbf{}\mathbf{\left(}\mathbf{molar}\mathbf{\right)}}$

Moles of Fe

$\begin{array}{l}\mathbf{=}\frac{\mathbf{0}\mathbf{.2889}}{\mathbf{55}\mathbf{.85}}\mathbf{\left(}\mathbf{mol}\mathbf{\right)}\\ \mathbf{=}\mathbf{0}\mathbf{.00517}\mathbf{\left(}\mathbf{mol}\mathbf{\right)}\end{array}$

Hence, moles of Fe are 0.00517mol.

According to the balanced equation

$\mathbf{Fe}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{H}}^{\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\to }{\mathbf{Fe}}^{\mathbf{2}\mathbf{+}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

1 mole of Fe produces 1 moles Fe²⁺

Now, moles of Fe²⁺

$\begin{array}{l}\mathbf{=}\mathbf{0}\mathbf{.00517}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{1}}\mathbf{\left(}\mathbf{mol}\mathbf{\right)}\\ \mathbf{=}\mathbf{0}\mathbf{.00517}\mathbf{\left(}\mathbf{mol}\mathbf{\right)}\end{array}$

Hence, moles of Fe²⁺ are 0.00517mol.

Number of Fe²⁺ ions

$\begin{array}{l}\mathbf{=}\mathbf{0}\mathbf{.00517}\mathbf{\times }\mathbf{(}\mathbf{6}\mathbf{.023}\mathbf{\times }{\mathbf{10}}^{\mathbf{23}}\mathbf{)}\\ \mathbf{=}\mathbf{0}\mathbf{.0311}\mathbf{\times }{\mathbf{10}}^{\mathbf{23}}\end{array}$

Hence, 0.0311 X 10²³ moles ferrous ions are present in a 26-oz (737-g) jar of the tomato sauce.