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How do you balance $C a + P \to C a_{2} P_{3}$ $Ca + P -> Ca_2P_3$ ?

1 Answer

Dec 25, 2015

$2 C a + 3 P \to 1 C a_{2} P_{3}$ $color(red)(2)Ca+color(red)(3)P rarr color(red)(1)Ca_2P_3$

Explanation:

Assume:
$XXX x C a + y P \to z C a_{2} P_{3}$ $color(white)("XXX")color(red)(x)Ca+color(red)(y)P rarr color(red)(z)Ca_2P_3$

Based on $C a$ $Ca$
[1] $XXX x - 2 z = 0$ $color(white)("XXX")x-2z=0$
Based on $P$ $P$
[2] $XXX y - 3 z = 0$ $color(white)("XXX")y-3z=0$

In order to find the ratio of $(x : y : z)$ $(x:y:z)$ we will arbitrarily set one of our variables to $1$ $1$ ; later we may need to adjust our ratios to get integer results.

In order to see how this works in the general case I have chosen to use $x = 1$ $x=1$

From [1] with $x = 1$ $x=1$
[3] $XXX z = \frac{1}{2}$ $color(white)("XXX")z=1/2$
From [2] with $z = \frac{1}{2}$ $z=1/2$
[4] $XXX y = \frac{3}{2}$ $color(white)("XXX")y=3/2$

So the ratio of components is
$XXX (1, \frac{3}{2}, \frac{1}{2})$ $color(white)("XXX")(1,3/2,1/2)$

Since we want integer factors we will multiply all terms by $2$ $2$ to clear all fractions, giving:
$XXX (x : y : z) = (2 : 3 : 1)$ $color(white)("XXX")(x:y:z) = (2:3:1)$

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