Balance the following equations: (a) for the reaction to...

Balance the following equations: (a) for the reaction to produce "superphosphate" fertilizer $$\begin{aligned} \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) & \rightarrow \\ & \mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2}(\mathrm{aq})+\mathrm{CaSO}_{4}(\mathrm{s}) \end{aligned}$$ (b) for the reaction to produce diborane, $\mathrm{B}_{2} \mathrm{H}_{6}$ $\mathrm{NaBH}_{4}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \rightarrow$$$\mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{g})+\mathrm{H}_{2(\mathrm{g})+\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})$$ (c) for the reaction to produce tungsten metal from $$\begin{array}{l}\text { tungsten(VI) oxide } \\\qquad \mathrm{WO}_{3}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{g}) \rightarrow \mathrm{W}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell)\end{array}$$(d) for the decomposition of ammonium dichromate $$\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(\mathrm{s}) \rightarrow \mathrm{N}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{Cr}_{2} \mathrm{O}_{3}(\mathrm{s})$$

Balance the following equations:
(a) for the reaction to produce "superphosphate" fertilizer $$\begin{aligned}
\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) & \rightarrow \\
& \mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2}(\mathrm{aq})+\mathrm{CaSO}_{4}(\mathrm{s})
\end{aligned}$$
(b) for the reaction to produce diborane, $\mathrm{B}_{2} \mathrm{H}_{6}$
$\mathrm{NaBH}_{4}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \rightarrow$$$\mathrm{B}_{2} \mathrm{H}_{6}(\mathrm{g})+\mathrm{H}_{2(\mathrm{g})+\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})$$
(c) for the reaction to produce tungsten metal from
$$\begin{array}{l}\text { tungsten(VI) oxide } \\\qquad \mathrm{WO}_{3}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{g}) \rightarrow \mathrm{W}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\ell)\end{array}$$(d) for the decomposition of ammonium dichromate
$$\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(\mathrm{s}) \rightarrow \mathrm{N}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell)+\mathrm{Cr}_{2} \mathrm{O}_{3}(\mathrm{s})$$

Key Concepts

Stoichiometry

Stoichiometry is the quantitative study of reactants and products in a chemical reaction. It uses balanced equations to relate the amounts of substances involved, allowing for calculations of mass, moles, and volume in chemical processes.

Reaction Types

Different reaction types, such as synthesis, decomposition, acid-base, and redox reactions, have characteristic patterns that can help guide the balancing process by indicating which components might combine or break apart during the reaction.

Balancing Chemical Equations

This concept involves adjusting coefficients in a chemical equation so that the number of atoms for each element is equal on both sides, ensuring that the equation accurately represents the reaction according to the law of conservation of mass.

Conservation of Mass

The conservation of mass principle states that matter is neither created nor destroyed in a chemical reaction. This principle is the foundation for balancing chemical equations, as it requires that the total mass of the reactants equals the total mass of the products.

Redox Reactions

Redox reactions involve the transfer of electrons between species, affecting their oxidation states. Balancing these reactions requires not only accounting for atoms but also ensuring that the changes in oxidation numbers and the electron balance are properly reflected.

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