Chapter 14: Problem 126
Calculate the volume, in milliliters, of a \(0.215 \mathrm{M} \mathrm{NaOH}\) solution that will completely neutralize each of the following: (14.8) a. \(3.80 \mathrm{~mL}\) of a \(1.25 \mathrm{M} \mathrm{HNO}_{3}\) solution b. \(8.50 \mathrm{~mL}\) of a \(0.825 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}\) solution
Short Answer
Step by step solution
- Write the Neutralization Reaction (Part a)
- Calculate the Moles of HNO\textsubscript{3} (Part a)
- Calculate the Moles of NaOH Required (Part a)
- Calculate the Volume of NaOH Solution (Part a)
- Write the Neutralization Reaction (Part b)
- Calculate the Moles of H\textsubscript{3}PO\textsubscript{4} (Part b)
- Calculate the Moles of NaOH Required (Part b)
- Calculate the Volume of NaOH Solution (Part b)
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Stoichiometry
A balanced chemical equation is the foundation for stoichiometric calculations. For example, in the reaction between NaOH and HNO\textsubscript{3}, the balanced equation is:
\( \text{NaOH} + \text{HNO}_3 \rightarrow \text{NaNO}_3 + \text{H}_2\text{O} \)
* This equation shows a 1:1 molar ratio between NaOH and HNO\textsubscript{3}. In other words:
• 1 mole of NaOH reacts with 1 mole of HNO\textsubscript{3}.
A different ratio appears in the reaction between NaOH and H\textsubscript{3}PO\textsubscript{4}:
\( 3 \text{NaOH} + \text{H}_3\text{PO}_4 \rightarrow \text{Na}_3\text{PO}_4 + 3\text{H}_2\text{O} \)
Here, the ratio is 3:1:
• 3 moles of NaOH react with 1 mole of H\textsubscript{3}PO\textsubscript{4}.
** Understanding these ratios guides the calculation of needed reactants or products. By practicing stoichiometry, students can efficiently determine the quantities required for any chemical reaction.
Molarity Calculations
\( \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \)
For neutralization reactions, we use molarity to find out how much of an acid or base is needed to neutralize the other.
In the given example:
• For HNO\textsubscript{3}, the moles are calculated as:
\(. 1.25 \text{ M} \times 0.00380 \text{ L} = 0.00475 \text{ moles HNO}_3 \)
With a 1:1 ratio, the same number of moles of NaOH is required. Using the molarity of NaOH:
\( \text{Volume} = \frac{0.00475 \text{ moles}}{0.215 \text{ M}} = 0.0221 \text{ L} = 22.1 \text{ mL} \)
• Similarly, for H\textsubscript{3}PO\textsubscript{4}, the moles are calculated as:
\( 0.825 \text{ M} \times 0.00850 \text{ L} = 0.00701 \text{ moles H}_3\text{PO}_4 \)
With a 3:1 ratio, NaOH moles required are:
\(. 3 \times 0.00701 \text{ moles} = 0.02103 \text{ moles NaOH}\ \) Utilizing the molarity of NaOH:
\( \text{Volume} = \frac{0.02103 \text{ moles}}{0.215 \text{ M}} = 0.0978 \text{ L} = 97.8 \text{ mL} \)
Mastery of molarity calculations ensures accurate and efficient preparation for laboratory and real-world applications.
Acid-Base Reactions
For instance, when NaOH (a base) reacts with HNO\textsubscript{3} (an acid), sodium nitrate (a salt) and water are formed:
\( \text{NaOH} + \text{HNO}_3 \rightarrow \text{NaNO}_3 + \text{H}_2\text{O} \)
Similarly, in the reaction between NaOH and H\textsubscript{3}PO\textsubscript{4} (phosphoric acid), the products are sodium phosphate and water:
\( 3 \text{NaOH} + \text{H}_3\text{PO}_4 \rightarrow \text{Na}_3\text{PO}_4 + 3 \text{H}_2\text{O} \)
Neutralization reactions are crucial in various applications:
• They help in controlling pH levels in different environments, like in agriculture.
• They are used in antacid medications to neutralize stomach acid.
• Water treatment plants utilize these reactions to balance chemicals in water supplies.
Understand the fundamentals of acid-base reactions to apply them effectively in both controlled settings and everyday life. Being able to predict the outcome of these reactions empowers students to handle a wide range of practical and theoretical chemistry challenges.