Question

What mass of \(\mathrm{NaOH}\) is contained in \(250.0 \mathrm{~mL}\) of a \(0.400 \mathrm{M}\) sodium hydroxide solution?

Short answer

The mass of NaOH in the 250.0 mL of 0.400 M sodium hydroxide solution is 4.00 grams.

Step-by-step solution

Extract the given values from the problem

We have the following information: Molarity (M) = 0.400 M Volume of the solution (V) = 250.0 mL

Convert volume to liters

The volume of the solution should be in liters to use the molarity formula. We can convert the given volume from mL to L by dividing by 1000: \(V = \frac{250.0 \mathrm{~mL}}{1000\mathrm{~mL}} = 0.250 \mathrm{~L}\)

Find the moles of NaOH

We can use the molarity formula to find the moles of NaOH, rearranging the formula to solve for moles of solute: moles of solute = Molarity × Volume moles of NaOH = 0.400 M × 0.250 L = 0.100 moles

Calculate the molar mass of NaOH

To find the mass of NaOH, we need its molar mass. The molar mass of NaOH can be calculated by adding the molar masses of each of its elements: Molar mass of NaOH = (Molar mass of Na) + (Molar mass of O) + (Molar mass of H) From the periodic table: Molar mass of Na = 22.99 g/mol Molar mass of O = 16.00 g/mol Molar mass of H = 1.01 g/mol Molar mass of NaOH = 22.99 g/mol + 16.00 g/mol + 1.01 g/mol = 40.00 g/mol

Calculate the mass of NaOH using moles and molar mass

Now, we can find the mass of NaOH in the given solution using the moles of NaOH and the molar mass of NaOH: mass of NaOH = (moles of NaOH) × (molar mass of NaOH) mass of NaOH = 0.100 moles × 40.00 g/mol = 4.00 g The mass of NaOH in the 250.0 mL of 0.400 M sodium hydroxide solution is 4.00 grams.

Key concepts

Molarity

Molarity is a measure of the concentration of a solution. It tells you how many moles of a solute are present in one liter of solution. This unit is expressed as moles per liter (mol/L), or simply M.
To calculate molarity, use this formula:

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

You can think of molarity as a way to describe how concentrated or dilute a solution is.
In our example, the sodium hydroxide solution has a molarity of 0.400 M. This means there are 0.400 moles of NaOH in every liter of solution. By knowing the molarity, you can easily determine the number of moles in any given volume of the solution by rearranging the formula to solve for moles.
Understanding molarity is essential for performing calculations in chemistry because it directly relates the mass of solute to the volume of solution it is dissolved in.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is important to know the molar mass when you want to convert between the mass of a substance and the amount in moles.
To find the molar mass, you add up the atomic masses of each element present in a compound, based on the compound’s chemical formula.

• For sodium hydroxide (NaOH), the molar masses would be:
  • Sodium (Na): 22.99 g/mol
  • Oxygen (O): 16.00 g/mol
  • Hydrogen (H): 1.01 g/mol
• Adding these together gives NaOH a molar mass of 40.00 g/mol.

Knowing the molar mass helps you relate the grams of the compound you have to the moles and vice versa, enabling more accurate calculations for experiments and problem-solving.

Solution Concentration

When we talk about solution concentration, we are referring to the amount of solute that is present in a particular volume of solvent. This concentration is expressed in various ways, but molarity is one of the most common.
Concentration is crucial because it determines how the solution behaves in different reactions and processes.
To adjust or measure the concentration, you might need to:

• Add more solute to increase concentration.
• Add more solvent to decrease concentration.

In our sodium hydroxide example, the solution has a concentration of 0.400 M, meaning each liter of solution contains 0.400 moles of NaOH. Adjusting concentrations lets you prepare solutions for specific purposes and ensures that you have the right balance for chemical reactions.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows chemists to predict how much of each substance is needed or produced.
Key principles of stoichiometry involve:

• Balancing equations to ensure the same number of each type of atom on both sides of the reaction.
• Using mole ratios, derived from the coefficients in a balanced equation, to convert between moles of different substances.

In the context of our solution problem, stoichiometry can be applied to the reaction of NaOH with other chemicals, allowing for calculations on how much of each reactant is necessary to completely react without leaving any leftover reactants:

• For example, if NaOH reacts with HCl, the balanced equation is:
  \[\text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]From this equation, you know that one mole of NaOH reacts with one mole of HCl.
• This one-to-one ratio is essential for calculating amounts in reactions involving sodium hydroxide.

Mastering stoichiometry is crucial for determining the correct proportions of substances in chemical reactions, preventing waste of reactants, and ensuring safety and cost-effectiveness in chemical processes.