How many grams of phosphoric acid would be needed to neutralise `100 g` of magnesium hydroxide? (The molecular weight are: `H_(3)PO_(4) = 98` and `Mg(OH)_(2) = 58.3)`

Options

A. `66.7 g`
B. `252 g`
C. `112 g`
D. `168 g`

Explanation

To determine how many grams of phosphoric acid (H₃PO₄) are needed to neutralize 100 grams of magnesium hydroxide (Mg(OH)₂), we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced chemical reaction between magnesium hydroxide and phosphoric acid is:

\[ 3 \, \text{Mg(OH)}_2 + 2 \, \text{H}_3\text{PO}_4 \rightarrow \text{Mg}_3\text{(PO}_4\text{)}_2 + 6 \, \text{H}_2\text{O} \]

This shows that 3 moles of magnesium hydroxide react with 2 moles of phosphoric acid.

### Step 2: Calculate the number of moles of magnesium hydroxide
To find the number of moles of magnesium hydroxide in 100 grams, we use its molar mass:

- Molar mass of Mg(OH)₂ = 58.3 g/mol

Using the formula:

\[ \text{Number of moles of Mg(OH)}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{100 \, \text{g}}{58.3 \, \text{g/mol}} \approx 1.71 \, \text{moles} \]

### Step 3: Use the stoichiometry of the reaction
From the balanced equation, we see that 3 moles of Mg(OH)₂ react with 2 moles of H₃PO₄. Therefore, the number of moles of H₃PO₄ required can be calculated using the ratio:

\[ \text{Moles of H}_3\text{PO}_4 = \frac{2}{3} \times \text{Moles of Mg(OH)}_2 \]

Substituting the value we calculated:

\[ \text{Moles of H}_3\text{PO}_4 = \frac{2}{3} \times 1.71 \approx 1.14 \, \text{moles} \]

### Step 4: Calculate the mass of phosphoric acid required
Now, we can find the mass of phosphoric acid needed using its molar mass:

- Molar mass of H₃PO₄ = 98 g/mol

Using the formula:

\[ \text{Mass of H}_3\text{PO}_4 = \text{Number of moles} \times \text{Molar mass} = 1.14 \, \text{moles} \times 98 \, \text{g/mol} \approx 111.72 \, \text{g} \]

### Step 5: Round the answer
Rounding this to the nearest whole number, we find that approximately 112 grams of phosphoric acid are needed to neutralize 100 grams of magnesium hydroxide.

### Final Answer
112 grams of phosphoric acid (H₃PO₄) are needed to neutralize 100 grams of magnesium hydroxide (Mg(OH)₂).

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