Question

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

Short answer

To react completely with 50.00 mL of 0.200 M NaOH, the required volumes of each acid are as follows: 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

Determine the moles of NaOH given

To find the moles of NaOH, we'll use the given volume and concentration of NaOH: Moles of NaOH = (Concentration of NaOH) × (Volume of NaOH) Moles of NaOH = \(0.200 M \times 50.00 mL = 0.200 M \times 50.00 \times 10^{-3} L = 0.0100 mol\)

Calculate the moles of required acid

All the reactions given are 1:1 acid-base reactions: One mole of the acid reacts with one mole of the hydroxide ion. Therefore, the moles of the acid required for each reaction are the same as the moles of NaOH. Moles of required acid = Moles of NaOH = 0.0100 mol

Calculate volumes of each acid

Now, we'll use the concentrations of the acids and the moles of the acids required for the reaction to calculate the volume of each acid: a. For 0.100 M HCl: Volume = (Moles of HCl) / (Concentration of HCl) Volume = \(0.0100 mol / 0.100 M = 0.100 L = 100.00 mL\) b. For 0.150 M HNO₃: Volume = (Moles of HNO₃) / (Concentration of HNO₃) Volume = \(0.0100 mol / 0.150 M = 0.0667 L = 66.67 mL\) c. For 0.200 M HC₂H₃O₂: Volume = (Moles of HC₂H₃O₂) / (Concentration of HC₂H₃O₂) Volume = \(0.0100 mol / 0.200 M = 0.0500 L = 50.00 mL\)

Final answer

To react completely with 50.00 mL of 0.200 M NaOH, the required volumes of each acid are as follows: 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

Mole Concept

The mole concept is a cornerstone of chemistry and helps us count atoms, molecules, or ions in a substance. It's especially useful when dealing with chemical reactions. The mole is a unit used to measure the amount of a substance, and it is denoted by the symbol "mol".
The reason the mole is so useful is because it represents a specific number, known as Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities per mole. This large number allows chemists to count and quantify particles that are way too small to be counted individually.

In this exercise, you need to calculate the moles of the base \(\mathrm{NaOH}\) and the acids involved. By knowing the volume and concentration, you can convert these into moles using the formula:

• Moles = Concentration \( \times \) Volume

This helps to determine the exact amount of reactants that will completely react with each other. Understanding this concept is key to comprehending any stoichiometric calculation. To recap, always ensure that your measurements of volume are in liters for the calculations to work correctly.

Stoichiometry

Stoichiometry revolves around the quantitative relationships between reactants and products in a chemical reaction. In simpler terms, it tells us how much of each substance is involved, which is essential for predicting the outcomes of reactions.
In this case, the acid-base reactions given are all 1:1. This means that one mole of the acid reacts with one mole of \(\mathrm{NaOH}\). Knowing this simple ratio makes it straightforward to determine how much of one reactant is needed to completely react with another.

If you have the moles of \(\mathrm{NaOH}\), you have the moles needed for each acid since they match the 1:1 ratio. Understanding stoichiometry allows for accurate predictions and calculations of needed quantities, ensuring there's no wastage or excess in reactions. When the ratios are different, stoichiometry becomes a bit more complex, but the principle remains the same: use the coefficients from the balanced chemical equation to find the proportions.

Solution Concentration

Solution concentration is a measure of how much solute is dissolved in a specific volume of solvent. It is expressed in molarity \( (M) \), which is moles of solute per liter of solution. For instance, a \(0.200 \mathrm{M}\) solution means that there are 0.200 moles of the solute present in one liter of solution.
This concept lets chemists know exactly how strong or weak a solution is, which can be crucial when conducting experiments and reactions. Knowing the concentration of your solutions helps effectively utilize stoichiometry in your calculations.

For example, with the given \(\mathrm{NaOH}\) concentration and volume, you calculate how many moles are present. Following that, you use the concentration of each of the acids to calculate the required volume to react with the \(\mathrm{NaOH}\). Accurate concentration data is vital because even a small miscalculation can lead to significant differences in the final volumes calculated for reacting solutions.

Volume Calculation

Volume calculation in chemistry involves converting between the moles of a substance and the volume of solution it is dissolved in, using its concentration. This exercise demonstrates this as you calculate how much of each acid is needed to react completely with the given amount of \(\mathrm{NaOH}\).
The formula for this is:

• Volume \( (\text{L}) \) = Moles \(/ \) Concentration \( (\text{M}) \)

This formula helps you determine how many liters, and subsequently how many milliliters, of a solution you need, based on the moles calculated in previous steps. Whether you're working with acids, bases, or any other solutions, this concept ensures that you can accurately determine the volumes needed for a reaction.

Remember, when the concentration is known, you can always solve for volume if you know the moles needed. Proper understanding and application of this concept prevent errors in laboratory settings and allow for precise chemical experimentation.