Question

What volume of \(0.0200 M\) calcium hydroxide is required to neutralize \(35.00 \mathrm{~mL}\) of \(0.0500 \mathrm{M}\) nitric acid?

Short answer

The volume of \(0.0200 M\) calcium hydroxide required to neutralize \(35.00 mL\) of \(0.0500 M\) nitric acid is \(43.75 mL\).

Step-by-step solution

Write the balanced chemical equation for the reaction

The balanced chemical equation for the reaction between calcium hydroxide (Ca(OH)2) and nitric acid (HNO3) is: \(Ca(OH)_{2_(aq)} + 2 HNO_{3_(aq)} \rightarrow Ca(NO_{3})_{2_(aq)} + 2 H_{2}O_{(l)}\) This tells us that one mole of calcium hydroxide reacts with two moles of nitric acid to produce one mole of calcium nitrate and two moles of water.

Calculate the moles of nitric acid

Given information: Volume of nitric acid = 35.00 mL Molarity of nitric acid = 0.0500 M To find the moles of nitric acid, use the formula: moles = molarity × volume (in liters) First, convert the volume of nitric acid from mL to L: \(35.00\mathrm{~mL} = 35.00 \times 10^{-3} L = 0.03500 L\) Now, calculate the moles of nitric acid: moles of nitric acid = 0.0500 M × 0.03500 L = 0.00175 moles

Find the moles of calcium hydroxide required for neutralization

From the balanced chemical equation, we see that the mole ratio of calcium hydroxide to nitric acid is 1:2. Moles of calcium hydroxide = (moles of nitric acid) / 2 Moles of calcium hydroxide = 0.00175 moles / 2 = 0.000875 moles

Calculate the volume of calcium hydroxide required

Molarity of calcium hydroxide = 0.0200 M Moles of calcium hydroxide = 0.000875 moles To find the volume of calcium hydroxide, use the formula: volume (in L) = moles / molarity Volume of calcium hydroxide (in L) = 0.000875 moles / 0.0200 M = 0.04375 L Finally, convert the volume of calcium hydroxide from L to mL: Volume of calcium hydroxide = 0.04375 L × 10^3 mL/L = 43.75 mL

Conclusion

It requires 43.75 mL of 0.0200 M calcium hydroxide to neutralize 35.00 mL of 0.0500 M nitric acid.

Key concepts

Molarity Calculations

Molarity, often abbreviated as M, is an important concept in chemistry, particularly when dealing with solutions. It refers to the concentration of a solute within a solution. To calculate molarity, you use the formula: \[ \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]In our exercise, we have two solutions: calcium hydroxide and nitric acid. We need to calculate the volume of calcium hydroxide needed to perform a reaction. We know the molarity and volume of nitric acid. By using the formula mentioned above, we can calculate the moles of nitric acid present.
The key steps include:

• Converting the volume from milliliters to liters, since molarity calculations require the volume in liters.
• Using the molarity and volume to find out how many moles of nitric acid we have.

Once we have the moles of nitric acid, we can use stoichiometry to find how much calcium hydroxide is needed by applying the mole ratio from the balanced chemical equation.

Balanced Chemical Equations

A balanced chemical equation is essential in understanding chemical reactions because it shows the proportions in which reactants combine and products form. Balance is achieved by ensuring that the number of atoms of each element is the same on both sides of the equation.For the reaction between calcium hydroxide \((\text{Ca(OH)}_2)\) and nitric acid \((\text{HNO}_3)\), the balanced chemical equation is:\[\text{Ca(OH)}_{2(aq)} + 2 \text{HNO}_{3(aq)} \rightarrow \text{Ca(NO}_3)_{2(aq)} + 2 \text{H}_2\text{O}_{(l)}\]This equation tells us that one mole of calcium hydroxide reacts with two moles of nitric acid to form one mole of calcium nitrate \((\text{Ca(NO}_3)_2)\) and two moles of water \((\text{H}_2\text{O})\). Balanced chemical equations are crucial because they help us understand the stoichiometry of the reaction, allowing for accurate molarity and yield calculations.

Stoichiometry

Stoichiometry is the study of the quantitative relationships in chemical reactions. It allows us to predict the amounts of reactants needed or products formed. In essence, stoichiometry utilizes balanced chemical equations to determine the ratios of reactants and products.To solve the exercise using stoichiometry:

• From the balanced chemical equation, identify the mole ratio. In this reaction, calcium hydroxide and nitric acid have a mole ratio of 1:2.
• Use the moles of nitric acid, calculated through molarity, to find the moles of calcium hydroxide required. This involves dividing the moles of nitric acid by the ratio of 2.
• Once the moles of calcium hydroxide are known, calculate the volume needed using its known molarity by rearranging the molarity formula to solve for volume: \( \text{Volume} = \frac{\text{moles}}{\text{molarity}} \)

By correctly applying stoichiometric principles, you can determine the precise volume of calcium hydroxide required to completely neutralize a given volume of nitric acid.