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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

Expert verified
a. 22.1 mL, b. 97.8 mL

Step by step solution

01

- Write the Neutralization Reaction (Part a)

The balanced reaction for the neutralization between NaOH and HNO\textsubscript{3} is: \[ \text{NaOH} + \text{HNO}_3 \rightarrow \text{NaNO}_3 + \text{H}_2\text{O} \] This shows a 1:1 molar ratio between NaOH and HNO\textsubscript{3}.
02

- Calculate the Moles of HNO\textsubscript{3} (Part a)

First, find the moles of HNO\textsubscript{3} in the given solution using the formula: \[ \text{moles} = Molarity \times Volume \] For HNO\textsubscript{3}, the volume is 3.80 mL (or 0.00380 L) with a molarity of 1.25 M. \[ \text{moles HNO}_3 = 1.25 \text{ M} \times 0.00380 \text{ L} = 0.00475 \text{ moles} \]
03

- Calculate the Moles of NaOH Required (Part a)

Since the stoichiometry is 1:1, the moles of NaOH required are also 0.00475 moles.
04

- Calculate the Volume of NaOH Solution (Part a)

Using the molarity formula rearranged to find volume: \[ \text{Volume} = \frac{\text{moles}}{\text{Molarity}} \] For NaOH, with 0.00475 moles and a molarity of 0.215 M: \[ \text{Volume} = \frac{0.00475 \, \text{moles}}{0.215 \, \text{M}} = 0.0221 \, \text{L} = 22.1 \, \text{mL} \]
05

- Write the Neutralization Reaction (Part b)

The balanced reaction for the neutralization between NaOH and H\textsubscript{3}PO\textsubscript{4} is: \[ 3 \text{NaOH} + \text{H}_3\text{PO}_4 \rightarrow \text{Na}_3\text{PO}_4 + 3\text{H}_2\text{O} \] This shows a 3:1 molar ratio between NaOH and H\textsubscript{3}PO\textsubscript{4}.
06

- Calculate the Moles of H\textsubscript{3}PO\textsubscript{4} (Part b)

Find the moles of H\textsubscript{3}PO\textsubscript{4} in the given solution using the formula: \[ \text{moles} = Molarity \times Volume \] For H\textsubscript{3}PO\textsubscript{4}, the volume is 8.50 mL (or 0.00850 L) with a molarity of 0.825 M. \[ \text{moles H}_3\text{PO}_4 = 0.825 \text{ M} \times 0.00850 \text{ L} = 0.00701 \text{ moles} \]
07

- Calculate the Moles of NaOH Required (Part b)

Using the stoichiometry, for each mole of H\textsubscript{3}PO\textsubscript{4}, 3 moles of NaOH are required: \[ \text{moles NaOH} = 3 \times 0.00701 \text{ moles} = 0.02103 \, \text{moles} \]
08

- Calculate the Volume of NaOH Solution (Part b)

Using the molarity formula rearranged to find volume: \[ \text{Volume} = \frac{\text{moles}}{\text{Molarity}} \] For NaOH, with 0.02103 moles and a molarity of 0.215 M: \[ \text{Volume} = \frac{0.02103 \, \text{moles}}{0.215 \, \text{M}} = 0.0978 \, \text{L} = 97.8 \, \text{mL} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stoichiometry
Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows us to predict the amounts of substances consumed and produced. In a neutralization reaction, stoichiometry is essential to determine the exact amount of acid needed to neutralize a given amount of base, or vice versa.
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
Molarity (M) is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. The formula to calculate molarity is:
\( \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \)
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
Acid-Base reactions are a type of chemical reaction that occurs between an acid and a base, resulting in the formation of water and a salt. These reactions are also known as neutralization 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.

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