Question

How many milliliters of \(0.105 M\) NaOH are required to neutralize exactly \(14.2 \mathrm{mL}\) of \(0.141 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4} ?\)

Short answer

57.17 mL of \(0.105 M\) NaOH is required to neutralize exactly \(14.2 mL\) of \(0.141 M H_{3}PO_{4}\).

Step-by-step solution

Write down the balanced chemical equation for the neutralization reaction

The balanced chemical equation for the neutralization of phosphoric acid (H₃PO₄) and sodium hydroxide (NaOH) is: \[ H_{3}PO_{4} + 3NaOH \rightarrow Na_{3}PO_{4} + 3H_{2}O \]

Calculate the moles of H₃PO₄

Given the volume and molarity of the phosphoric acid solution, calculate the moles by multiplying them: \[ moles \ of \ H_{3}PO_{4} = Molarity \times Volume \] \[ moles \ of \ H_{3}PO_{4} = 0.141 \mathrm{M} \times 14.2\mathrm{mL} \times \frac{1L}{1000\mathrm{mL}} = 0.002001\mathrm{mol} \]

Determine the stoichiometric ratio between H₃PO₄ and NaOH

According to the balanced chemical equation: \[H_{3}PO_{4} + 3NaOH \rightarrow Na_{3}PO_{4} + 3H_{2}O\] The stoichiometric ratio of H₃PO₄ to NaOH required is 1:3.

Calculate the moles of NaOH required

Using the stoichiometric ratio from Step 3, calculate the moles of NaOH required to neutralize the given moles of H₃PO₄. \[moles \ of \ NaOH = \frac{3 \ moles \ of \ NaOH}{1 \ mole \ of \ H_{3}PO_{4}} \times 0.002001\mathrm{mol} \ of \ H_{3}PO_{4} = 0.006003\mathrm{mol} \ of \ NaOH\]

Determine the volume of NaOH solution required

Use the moles of NaOH and the given molarity to find the required volume of NaOH solution: \[ Volume \ of \ NaOH = \frac{moles \ of \ NaOH}{Molarity \ of \ NaOH} \] \[ Volume \ of \ NaOH = \frac{0.006003\mathrm{mol}}{0.105 \mathrm{M}} = 0.05717 \mathrm{L} \] Finally, convert the volume to milliliters: \[ Volume \ of \ NaOH = 0.05717\mathrm{L} \times \frac{1000\mathrm{mL}}{1\mathrm{L}} = 57.17\mathrm{mL} \] Therefore, 57.17 mL of 0.105 M NaOH is required to neutralize exactly 14.2 mL of 0.141 M H₃PO₄.

Key concepts

Stoichiometry

Stoichiometry is the key to understanding chemical reactions. It tells us the relationship between the quantities of reactants and products. In a chemical equation, stoichiometry helps balance how much of each substance is involved.

Think of it as a recipe. If you know you need 3 eggs for a cake, you can easily adjust if you want to make 2 cakes. Similarly, in the equation \[ H_{3}PO_{4} + 3NaOH \rightarrow Na_{3}PO_{4} + 3H_{2}O \]we see the stoichiometric ratio is 1:3 between H₃PO₄ and NaOH.

This means 1 mole of phosphoric acid reacts with 3 moles of sodium hydroxide. By using stoichiometry, we ensure the reaction consumes the correct amount of each reactant for complete neutralization. This is why you multiply the moles of H₃PO₄ by 3 to find the moles of NaOH needed. It's like adjusting a recipe to match the available ingredients.

Molarity Calculations

Molarity is a measure of concentration. It tells us how many moles of a substance are present in 1 liter of solution. This calculation is crucial when you're dealing with reactions in a liquid form.

To find the moles in a solution, use the formula:\[\text{Moles} = \text{Molarity} \times \text{Volume}\]Always convert the volume to liters by dividing milliliters by 1000.

• For H₃PO₄: \[0.141 \text{ M} \times 14.2 \text{ mL} \times \frac{1\text{ L}}{1000\text{ mL}} = 0.002001 \text{ mol}\]
• For NaOH: the moles required were calculated as \[0.006003 \text{ mol}\]

This information helps us determine how much sodium hydroxide solution is needed to react precisely with phosphoric acid in the neutralization process. It's like making sure you have the right amount of each ingredient for your dish.

Balanced Chemical Equations

A balanced chemical equation is essential for understanding how reactions occur. It ensures that atoms are conserved and the same number appear on both sides of the equation.

In our neutralization reaction, the equation:\[ H_{3}PO_{4} + 3NaOH \rightarrow Na_{3}PO_{4} + 3H_{2}O \]is balanced because it has the same number of H, Na, P, and O atoms on each side.

• One phosphoric acid molecule reacts with three sodium hydroxide molecules.
• This produces one sodium phosphate molecule and three water molecules.

Balancing this equation allows us to accurately use stoichiometry to calculate quantities of reactants and products. It's like ensuring your scale is equal before measuring ingredients. This guarantees that the reaction can proceed smoothly and completely, without leaving excess reactants or products.