Question

What volume of \(0.0521 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) is required to neutralize exactly \(14.20 \mathrm{~mL}\) of \(0.141 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}\) ? Phosphoric acid contains three acidic hydrogens.

Short answer

To neutralize 14.20 mL of 0.141 M phosphoric acid, a volume of 57.65 mL of 0.0521 M barium hydroxide solution is required.

Step-by-step solution

Determine the moles of phosphoric acid

First, let's calculate the moles of phosphoric acid in the given solution using its molarity and volume. Moles = Molarity × Volume, where Molarity = 0.141 M (given) and Volume = 14.20 mL (given). We convert mL to L by dividing by 1000: Volume = 14.20 mL × (1 L/1000 mL) = 0.0142 L Moles of \(H_3PO_4\) = 0.141 M × 0.0142 L = 0.002002 mol

Determine the moles of barium hydroxide required to neutralize

From the balanced chemical equation, we can see that the mole ratio of \(H_3PO_4\) to \(Ba(OH)_2\) is 2:3. So, let's use this ratio to find the moles of barium hydroxide required to neutralize the phosphoric acid. Moles of \(Ba(OH)_2\) = (Moles of \(H_3PO_4\)) × (Mole ratio of \(Ba(OH)_2\) to \(H_3PO_4\)) Moles of \(Ba(OH)_2\) = 0.002002 mol × (3 mol \(Ba(OH)_2\)/2 mol \(H_3PO_4\)) = 0.003003 mol

Calculate the volume of barium hydroxide solution required

Now we have the moles of barium hydroxide and the molarity of the solution (0.0521 M), we can find the required volume of barium hydroxide solution. Volume = Moles / Molarity Volume of \(Ba(OH)_2\) = 0.003003 mol / (0.0521 M) = 0.05765 L

Convert the volume to milliliters

Finally, we convert the volume of barium hydroxide solution, which is calculated in liters, to milliliters. Volume in mL = Volume in L × 1000 Volume of \(Ba(OH)_2\) = 0.05765 L × 1000 = 57.65 mL So, 57.65 mL of 0.0521 M barium hydroxide solution is required to neutralize exactly 14.20 mL of 0.141 M phosphoric acid.

Key concepts

Molarity Calculations

Molarity, often represented by the symbol 'M', is a measure of concentration in chemistry that indicates the number of moles of a solute in one liter of solution. To understand molarity calculations, let's take a dive into the units involved. A mole is a unit that represents a fixed number of particles (6.022×10²³ particles), analogous to a dozen eggs being a count of 12.

To calculate molarity, you use the formula:
\[ Molarity (M) = \frac{moles \; of \; solute}{volume \; of \; solution \; in \; liters} \].
In the exercise, we're given the volume of a phosphoric acid solution and its molarity, and we're asked to use these to find out how much of another solution (barium hydroxide) is needed to neutralize it. This brings us to another key point related to molarity: the concept of neutralization.

In neutralization reactions, an acid and a base react to form water and a salt. The amount of an acid solution needed to neutralize a base, or vice versa, can be calculated if we know the molarity of one solution and the volume of the other. Remember that the neutralization point—the point at which equivalent amounts of hydrogen ions (from the acid) and hydroxide ions (from the base) are present—depends on the stoichiometry of the reaction, which leads us to our next concept, stoichiometry.

Stoichiometry

Stoichiometry is the section of chemistry that pertains to the measurement of the quantities of substances involved in chemical reactions. It can be seen as the 'recipe' for a chemical reaction. Central to stoichiometry is the balanced chemical equation, which tells us how many moles of each reactant and product are involved.

In our exercise, the stoichiometry of the neutralization reaction is important because it dictates the relationship between the moles of phosphoric acid and barium hydroxide. In a balanced chemical equation, the ratio of the coefficients indicates the ratio of moles of reactants and products needed for the reaction to occur without any excess of either.

To apply stoichiometry to our problem, we first find the moles of phosphoric acid and then use the mole ratio from the balanced equation to determine the moles of barium hydroxide required for complete neutralization. This step is crucial because without the correct stoichiometric ratio, it's impossible to determine the correct volumes of reactants needed for the reaction. To reiterate, the mole ratio is obtained from the stoichiometry of the balanced chemical equation, and it is this ratio that allows us to calculate how much of one reactant is needed to react completely with a given quantity of another reactant.

Chemical Equation Balancing

Balancing chemical equations is a fundamental skill in chemistry because it ensures that the Law of Conservation of Mass is obeyed in chemical reactions. This law states that mass cannot be created or destroyed in a chemical reaction; thus, the mass of the reactants must equal the mass of the products. In terms of atoms, this means that the number of atoms of each element must be the same on both sides of the equation.

To balance a chemical equation, we adjust the coefficients (the numbers in front of the chemical formulas), not the subscripts (the numbers within the chemical formulas), until the number of atoms of each element is the same on both sides. In the exercise, the chemical equation for the neutralization reaction would need to be balanced to ensure that there are equal numbers of atoms for each element involved in the reactants and products. The coefficients from the balanced equation provide the stoichiometric ratios needed to relate the moles of one substance to the moles of another.

Understanding how to balance chemical equations is critical for accurate stoichiometry calculations, as it tells us exactly how much of each reactant is consumed and how much of each product is formed in a reaction. In the context of our exercise, the balanced equation indicates the stoichiometry between phosphoric acid and barium hydroxide, which is essential for performing accurate molarity calculations and ultimately solving the problem at hand.