Question

What volume of each of the following acids will react completely with 50.00 mL of 0.200 M NaOH? a. 0.100 \({M} {HCl} \quad \)c. 0.200\(M {HC}_{2} {H}_{3} {O}_{2}$$(1 \text { acidic hydrogen })\) b. 0.150 \({M} {HNO}_{3}\)

Short answer

The volumes of each acid required to react completely with 50.00 mL of 0.200 M NaOH are: a. 100.00 mL of 0.100 M HCl b. 66.67 mL of 0.150 M HNO3 c. 50.00 mL of 0.200 M HC2H3O2

Step-by-step solution

Calculate moles of NaOH

To calculate the moles of NaOH, we'll use the formula: moles = molarity x volume (in liters). The given molarity of NaOH is 0.200 M, and its volume is 50.00 mL, which is equal to 0.050 L (since 1 L = 1000 mL). So, moles of NaOH = \(0.200 \times 0.050 = 0.010\) moles.

Write the balanced chemical equations for each reaction

We will now write the balanced chemical equations for the reactions of NaOH with each acid. a. Reaction with HCl: \(NaOH + HCl \rightarrow NaCl + H_{2}O\) b. Reaction with HNO3: \(NaOH + HNO_{3} \rightarrow NaNO_{3} + H_{2}O\) c. Reaction with HC2H3O2: (Since it has 1 acidic hydrogen) \(NaOH + HC_{2}H_{3}O_{2} \rightarrow NaC_{2}H_{3}O_{2} + H_{2}O\) All the reactions have a 1:1 stoichiometry between NaOH and the corresponding acid.

Calculate the volume of each acid

Now, we will use the moles of NaOH and the molarities of each acid to determine their respective volumes for the complete reaction. a. For 0.100 M HCl: Since the reaction has a 1:1 stoichiometry, moles of HCl = moles of NaOH = 0.010 moles. Volume (in liters) = moles / molarity = \(0.010 / 0.100 = 0.100 L\), or \(100.00\ mL\) b. For 0.150 M HNO3: Since the reaction has a 1:1 stoichiometry, moles of HNO3 = moles of NaOH = 0.010 moles. Volume (in liters) = moles / molarity = \(0.010 / 0.150 = 0.0667 L\), or \(66.67\ mL\) c. For 0.200 M HC2H3O2 (1 acidic hydrogen): Since the reaction has a 1:1 stoichiometry, moles of HC2H3O2 = moles of NaOH = 0.010 moles. Volume (in liters) = moles / molarity = \(0.010 / 0.200 = 0.050 L\), or \(50.00\ mL\)

Results:

The volumes of each acid required to react completely with 50.00 mL of 0.200 M NaOH are: a. 100.00 mL of 0.100 M HCl b. 66.67 mL of 0.150 M HNO3 c. 50.00 mL of 0.200 M HC2H3O2

Key concepts

Molarity

Molarity is a way to express the concentration of a solution. It refers to the number of moles of a solute dissolved in one liter of a solution. Understanding molarity is fundamental in stoichiometry and many areas of chemistry. With molarity, you can determine how concentrated a solution is and how much solute is in a given volume.

The formula for molarity (\( M \)) is:

• Molarity = \( \frac{\text{moles of solute}}{\text{liters of solution}} \)

In practical terms, having a solution with 1 M HCl means there is one mole of HCl in each liter of water. This measurement allows scientists or students to perform precise reactions by knowing exactly how much of each substance is present.

Balanced Chemical Equations

Balanced chemical equations are essential in chemistry to ensure that mass is conserved in a chemical reaction. A balanced equation means the number of atoms for each element is the same on both sides of the equation.

For example, in the reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl):

• Reactants: NaOH + HCl
• Products: NaCl + \( H_2O \)

To balance the equation, we ensure both the left and right sides contain equal numbers of sodium, chlorine, hydrogen, and oxygen atoms:
\[ \text{NaOH + HCl} \rightarrow \text{NaCl + } H_2O \]
This balanced equation shows a 1:1 stoichiometry, meaning one mole of NaOH reacts with one mole of HCl. This ensures all species are accounted for, and no matter is lost in the process.

Acid-Base Reaction

An acid-base reaction involves the transfer of protons (H⁺ ions) from an acid to a base. This is commonly referred to as neutralization. The outcome is usually salt and water. Such reactions are essential in various applications, from day-to-day life to complex industrial processes.

In our example, sodium hydroxide (a base) reacts with different acids:

• NaOH + HCl \( \rightarrow \text{NaCl + } H_2O \)
• NaOH + HNO_3 \( \rightarrow \text{NaNO}_3 + H_2O \)
• NaOH + HC_2H_3O_2 \( \rightarrow \text{NaC}_2H_3O_2 + H_2O \)

Each reaction maintains a 1:1 stoichiometry. The acid donates a proton to the hydroxide ion of the base to form water, while the remaining ions combine to form a salt. Acid-base reactions are integral to titrations in chemistry, which help determine unknown concentrations in solutions.

Volume Calculation

Volume calculation in stoichiometry often arises when you need to find how much of a liquid is required for a reaction. This is particularly important in acid-base reactions where precise volumes ensure complete neutralization.

In such problems, you use the relation between moles, molarity, and volume. The equation relating these is:

• Volume (L) = \( \frac{\text{moles}}{\text{molarity}} \)

Consider determining the volume of HCl needed to react with NaOH. Knowing that the moles of NaOH are 0.010 moles and the molarity of HCl is 0.100 M, the needed volume is:
\[ \text{Volume} = \frac{0.010\, \text{moles}}{0.100\, \text{M}} = 0.100 \text{ L} \]
Converting this to milliliters gives 100 mL. Understanding this relationship helps provide accurate reagents and avoid wastage in chemical reactions.