Question

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

Short answer

57.3 mL of 0.105 M NaOH are required to neutralize 14.2 mL of 0.141 M H3PO4.

Step-by-step solution

Write the balanced chemical equation

First, we need to write the balanced chemical equation for the reaction between sodium hydroxide (NaOH) and phosphoric acid (H3PO4). This reaction is an acid-base reaction, and the products are sodium phosphate and water. The balanced equation is: \(H_{3}PO_{4} + 3 NaOH \longrightarrow Na_{3}PO_{4} + 3 H_{2}O\)

Determine the moles of H3PO4

Next, use the given quantities and the balanced chemical equation to find the moles of H3PO4. We know there are 14.2 mL of 0.141 M phosphoric acid, so we can use the equation: moles of H3PO4 = volume of H3PO4 × molarity of H3PO4 moles of H3PO4 = 14.2 mL × 0.141 mol/L Convert mL to L: moles of H3PO4 = 0.0142 L × 0.141 mol/L = 0.0020042 mol

Use stoichiometry to find moles of NaOH

Now, use the balanced chemical equation and stoichiometry to find the moles of NaOH required to react with H3PO4: \(3 mol ~ NaOH \over 1 mol ~ H_{3}PO_{4}\) × 0.0020042 mol H3PO4 = 0.0060126 mol NaOH

Determine the volume of NaOH

Finally, use the molarity of NaOH to determine the volume needed to neutralize H3PO4: moles of NaOH = volume of NaOH × molarity of NaOH 0.0060126 mol NaOH = volume of NaOH × 0.105 mol/L Let x be the volume of NaOH in liters: x = \(0.0060126 \over 0.105\) L x = 0.057269 L Now, convert liters to milliliters: x = 57.269 mL So, 57.3 mL (rounded to one decimal place) of 0.105 M NaOH are required to neutralize 14.2 mL of 0.141 M H3PO4.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. It is based on the conservation of mass, which states that matter cannot be created or destroyed. When conducting a chemical reaction, chemists use stoichiometry to predict how much of each substance is consumed and produced, allowing for accurate preparation and analysis of reactions.

To understand stoichiometry:

• Begin by writing the balanced chemical equation, which shows the proportion of reactants and products.
• Use molar ratios from the balanced equation to convert between moles of different substances.
• This concept helps in calculating the amount required or produced in a reaction, such as how many mL of one solution are needed to completely react with another solution, as seen in titrations.

Stoichiometry ensures that we understand and predict the outcomes of chemical reactions efficiently.

Balanced Chemical Equation

A balanced chemical equation is essential in stoichiometry as it indicates the exact proportions of reactants and products involved in a chemical reaction. This balance ensures that the law of conservation of mass is obeyed, meaning the same number of each type of atom occurs on both sides of the equation.

Take the example of the reaction between sodium hydroxide (NaOH) and phosphoric acid (H3PO4):

• The balanced equation is: \[ H_{3}PO_{4} + 3 NaOH \longrightarrow Na_{3}PO_{4} + 3 H_{2}O \]
• This equation tells us that 1 mole of H3PO4 reacts with 3 moles of NaOH to produce 1 mole of Na3PO4 and 3 moles of water.

Balancing equations involves making sure that the number of atoms of each element is the same on both sides, which is critical when calculating quantities needed in reactions.

Molarity

Molarity is a key concept in solution chemistry that refers to the concentration of a solution, specifically the number of moles of solute per liter of solution. It is denoted by the symbol "M" and is used to express how concentrated or dilute a solution is.

Understanding molarity involves:

• Calculating the number of moles of solute present in a certain volume of solution. For example, the molarity of sodium hydroxide (NaOH) in our problem is 0.105 M.
• The formula used is: \[ ext{Molarity} (M) = rac{ ext{moles of solute}}{ ext{liters of solution}} \]

Using molarity allows chemists to prepare solutions of precise concentrations and to perform calculations such as finding the volume needed to reach a specific reactant amount. This is crucial in lab settings and industrial applications.

Neutralization Reaction

A neutralization reaction is a type of chemical reaction where an acid and a base react to form water and a salt. This reaction is fundamental in titration experiments, where the objective is to determine the concentration of an unknown acid or base solution.

Key characteristics of neutralization reactions include:

• The production of water (H2O) and a salt, such as sodium phosphate (Na3PO4 in our example) as products.
• In the given problem, phosphoric acid reacts with sodium hydroxide, a strong base, to reach a neutralization point.
• The balanced equation represents this interaction effectively, as it shows the precise mole ratio required for neutralization.

Neutralization is used in various applications, such as buffering solutions in biological systems and managing pH levels in soil and water treatment processes. Understanding this concept is vital for grasping how acidic and basic substances counteract each other in chemical reactions.