Question

What mass of NaOH is contained in 250.0 mL of a 0.400 M sodium hydroxide solution?

Short answer

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

Step-by-step solution

Find the number of moles of NaOH contained in the solution

To calculate the number of moles of NaOH in the solution, we can use the formula: number of moles = molarity × volume Since we know the molarity (0.400 M) and volume (250.0 mL), we can plug these values into the formula: number of moles = 0.400 mol/L × 0.250 L Note that we need to convert the volume from milliliters to liters by dividing by 1000 (1 L = 1000 mL).

Calculate the number of moles of NaOH

Now we can multiply the molarity and volume to find the number of moles of NaOH: number of moles = 0.400 mol/L × 0.250 L = 0.100 mol

Calculate the molar mass of NaOH

To convert the number of moles of NaOH to mass, we need to know the molar mass of NaOH. The molar mass can be found by adding the molar masses of each element in the compound: Molar mass of NaOH = molar mass of Na + molar mass of O + molar mass of H Using the periodic table, we can find the molar masses of each element: - Molar mass of Na = 22.99 g/mol - Molar mass of O = 16.00 g/mol - Molar mass of H = 1.01 g/mol So, the 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 in the solution

Now that we have the molar mass of NaOH and the number of moles present in the solution, we can calculate the mass of NaOH using the formula: mass = number of moles × molar mass mass of NaOH = 0.100 mol × 40.00 g/mol = 4.00 g So, there are 4.00 grams of NaOH contained in 250.0 mL of a 0.400 M sodium hydroxide solution.

Key concepts

Mass Calculation

In many chemistry problems, understanding how to calculate mass is crucial. This involves using key formulas and understanding units of measurement. To determine the mass of a substance in a solution, you first need to know the number of moles. In the example given, we were asked to find the mass of NaOH in a specific volume of solution.

We started by using the molarity and volume of the solution to find the number of moles. The formula used was:

• number of moles = molarity × volume

Here, our volume must be converted to liters if it isn't already, since molarity is expressed in moles per liter. After finding the number of moles, the next step was to use the molar mass to determine the mass. By multiplying the number of moles by the molar mass, we can find the mass in grams:

• mass = number of moles × molar mass

This process shows how interconnected these concepts are and allows you to move seamlessly from concentration to mass.

Molar Mass

Molar mass is a fundamental concept when dealing with chemical compounds. It represents the mass of one mole of a substance and is expressed in grams per mole (g/mol). Each element on the periodic table has a specific molar mass, which can be summed up to give the molar mass of a compound.

For NaOH, the molar mass is calculated by adding the molar masses of its constituent elements: sodium (Na), oxygen (O), and hydrogen (H):

• Molar mass of Na = 22.99 g/mol
• Molar mass of O = 16.00 g/mol
• Molar mass of H = 1.01 g/mol

Adding these together gives us the molar mass of NaOH:

• Molar mass of NaOH = 22.99 g/mol + 16.00 g/mol + 1.01 g/mol = 40.00 g/mol

Knowing the molar mass helps convert between moles and grams, enabling you to solve a variety of problems in chemistry involving mass, moles, and molecular composition.

Solution Concentration

Solution concentration is pivotal in chemistry as it describes how much solute is present in a given amount of solvent. The term "molarity" is frequently used to express concentration, defined as the number of moles of solute per liter of solution.

Molarity is denoted as M and is calculated using the formula:

• molarity (M) = moles of solute/volume of solution in liters

In the example with sodium hydroxide (NaOH), where the solution concentration is 0.400 M, this means there are 0.400 moles of NaOH in every 1 liter of the solution. To find how much solute is in a smaller volume, we adjust our calculations:

• number of moles = molarity × volume in liters

Understanding concentration allows for precise mixing of reactants and reagents in experiments, ensuring the correct chemical reactions and results. It also aids in calculating the needed amount of each component to achieve a desired solution concentration.