Problem 45 - Chemistry and Chemical Reactivity

Question

What volume of \(0.123 \mathrm{M} \mathrm{NaOH},\) in milliliters, contains \(25.0 \mathrm{g}\) of \(\mathrm{NaOH} ?\)

Step-by-Step Solution

Answer

5081.3 mL

Step 1: Determine the Molar Mass of NaOH

The molar mass of a compound is the sum of the masses of its constituent elements. For NaOH (sodium hydroxide), the molar masses are approximately: Na = 22.99 g/mol, O = 16.00 g/mol, and H = 1.01 g/mol. Therefore, the molar mass of NaOH is: \[ 22.99 + 16.00 + 1.01 = 40.00 \text{ g/mol} \]

Step 2: Calculate the Number of Moles

To find the number of moles in 25.0 g of NaOH, use the formula:\[ \text{moles of NaOH} = \frac{\text{mass of NaOH}}{\text{molar mass of NaOH}} \]Substitute the values:\[ \text{moles of NaOH} = \frac{25.0}{40.00} = 0.625 \text{ moles} \]

Step 3: Use Molarity to Find Volume

Molarity (M) is defined as the number of moles of solute per liter of solution. The problem gives the molarity as 0.123 M, and we have 0.625 moles of NaOH. Use the formula:\[ \text{Volume (L)} = \frac{\text{moles of NaOH}}{\text{Molarity}} \]Substitute the values:\[ \text{Volume (L)} = \frac{0.625}{0.123} = 5.0813 \text{ L} \]

Step 4: Convert Volume from Liters to Milliliters

Since 1 liter equals 1000 milliliters, convert the volume from liters to milliliters:\[ \text{Volume (mL)} = 5.0813 \times 1000 = 5081.3 \text{ mL} \]

Step 5: Final Answer

Thus, the volume of 0.123 M NaOH solution that contains 25.0 g of NaOH is 5081.3 mL.

Key Concepts

Molar Mass

Understanding the molar mass is fundamental in chemistry. It tells us the mass of one mole of a given substance.
For Sodium Hydroxide (NaOH), we calculate this by adding together the atomic masses of its constituent elements.
NaOH consists of sodium (Na), oxygen (O), and hydrogen (H).

• Sodium has an atomic mass of roughly 22.99 g/mol.
• Oxygen is about 16.00 g/mol.
• Hydrogen weighs in at around 1.01 g/mol.

This makes the total molar mass of NaOH exactly 40.00 g/mol.
This value is crucial because it helps convert mass into moles, a necessary step in many chemical calculations.

Volume Conversion

Volume conversion is quite simple but incredibly important in chemistry.
In our problem, we need to convert the volume from liters to milliliters.
Remember, every 1 liter is equal to 1000 milliliters.

• If you have 5 liters, that's the same as 5000 milliliters.
• Similarly, 0.5 liters is equivalent to 500 milliliters.

This conversion is often necessary because most chemical solutions are described in liters but measured in milliliters for practical use.
By understanding this relationship, you can easily find out how much of a solution you have or need in the appropriate unit.

Sodium Hydroxide Solution

Sodium Hydroxide, often abbreviated as NaOH, is a common alkaline compound used in various industries.
It's crucial in many chemical reactions, including those involving neutralization and decomposition.
NaOH is also widely used in laboratories and industrial settings as a strong base.

• It appears as a white solid that is highly soluble in water.
• When dissolved in water, it forms a highly exothermic solution.
• Due to its reactivity, proper safety precautions should be taken during handling.

In the context of our exercise, we are working with a 0.123 M NaOH solution, meaning there are 0.123 moles of NaOH in every liter of solution.
This measurement of concentration is known as molarity, an essential aspect of chemical solution preparation.

Stoichiometry

Stoichiometry is the branch of chemistry that quantifies relationships between reactants and products in a chemical reaction.
It is crucial for predicting the amounts of substances consumed and produced.
In this exercise, stoichiometry allows us to determine how much NaOH is in a given volume of solution.

• Start by finding the number of moles of your substance, using its mass and molar mass.
• Next, use its molarity to calculate the volume necessary to achieve a reaction or concentration.
• These calculations guide chemists in preparing solutions with precise amounts of substances.

Understanding stoichiometry is key to mastering chemistry and performing accurate experimental work.
It ensures you use the correct proportions in chemical reactions, whether in the lab or industrial processes.