# Question #ca262

Jan 22, 2018

It's not possible.

#### Explanation:

Let's take a look at the skeleton equation:

$L {i}_{3} P {O}_{4} + C s I \to L {i}_{3} I + C {s}_{3} P {O}_{4}$

There is no way we can get this to follow the law of conservation of matter, because cesium is the only unbalanced portion of the equation.

If we attempt to balance it, we could go on forever.
Let's try:

• Balance the cesium atoms by adding a coefficient of $3$ on $C s I$ on the reactant side. $L {i}_{3} P {O}_{4} + 3 C s I \to L {i}_{3} I + C {s}_{3} P {O}_{4}$

• Balance the iodine atoms by adding a coefficient of $3$ on $L {i}_{3} I$, making the equation $L {i}_{3} P {O}_{4} + 3 C s I \to 3 L {i}_{3} I + C {s}_{3} P {O}_{4}$

• Balance the lithium atoms by adding a coefficient of $3$ on $L {i}_{3} P {O}_{4}$, making the equation $3 L {i}_{3} P {O}_{4} + 3 C s I \to 3 L {i}_{3} I + C {s}_{3} P {O}_{4}$

• Balance the phosphate ions by adding a coefficient of $3$ on $C {s}_{3} P {O}_{4}$, making the equation $3 L {i}_{3} P {O}_{4} + 3 C s I \to 3 L {i}_{3} I + 3 C {s}_{3} P {O}_{4}$

• And we're back to cesium again!

So, no matter what we do, the equation can never be balanced. :(

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However, if the question had $L i I$ instead of $L {i}_{3} I$, we could balance it—for more details as to why this should be the case, refer to the comments made by Hendrik D., anor277, and Truong-Son N.!

The skeleton question would be:

$L {i}_{3} P {O}_{4} + C s I \to L i I + C {s}_{3} P {O}_{4}$

Which would make the equation simple to balance:

$L {i}_{3} P {O}_{4} + C s I \to \textcolor{red}{3} L i I + C {s}_{3} P {O}_{4}$

$L {i}_{3} P {O}_{4} + \textcolor{red}{3} C s I \to 3 L i I + C {s}_{3} P {O}_{4}$