Questions: Balance the following chemical equation (if necessary): Ca(OH)2(s) + H3PO4(aq) → H2O(l) + Ca3(PO4)2(aq)

Balance the following chemical equation (if necessary): Ca(OH)2(s) + H3PO4(aq) → H2O(l) + Ca3(PO4)2(aq)
Transcript text: Balance the following chemical equation (if necessary): \[ \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{~s})+\mathrm{H}_{3} \mathrm{PO}_{4}(\mathrm{aq}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{I})+\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{aq}) \]
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Solution

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Solution Steps

Step 1: Set Up the Chemical Equation

We start with the unbalanced chemical equation: \[ \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s}) + \mathrm{H}_{3} \mathrm{PO}_{4}(\mathrm{aq}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) + \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(\mathrm{aq}) \]

Step 2: Define the Coefficients

Let:

  • \( a \) = coefficient of \( \mathrm{Ca(OH)}_{2} \)
  • \( b \) = coefficient of \( \mathrm{H}_{3} \mathrm{PO}_{4} \)
  • \( c \) = coefficient of \( \mathrm{H}_{2} \mathrm{O} \)
  • \( d \) = coefficient of \( \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2} \)
Step 3: Write the Element Balance Equations

From the equation, we can derive the following balance equations for each element:

  1. For Calcium (Ca): \[ a = 3d \]
  2. For Oxygen (O): \[ 2a = 2c \]
  3. For Hydrogen (H): \[ 2a = 3b + 8d \]
  4. For Phosphorus (P): \[ b = 2d \]
Step 4: Solve the System of Equations

Solving the above equations leads to the coefficients: \[ a = 0, \quad b = 0, \quad c = 0, \quad d = 0 \]

Step 5: Interpret the Results

The solution indicates that the coefficients are all zero, which means that the equation is not balanced as written. This suggests that the original equation may need to be re-evaluated or that the compounds do not react in the manner described.

Final Answer

Since the coefficients are all zero, the equation cannot be balanced as given. Thus, we conclude that the chemical equation is not valid in its current form. Therefore, the final answer is: \[ \boxed{\text{The equation cannot be balanced.}} \]

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