Problem 45 - Chemistry: Atoms First

Question

What mass of a \(4.00 \% \mathrm{NaOH}\) solution by mass contains \(15.0 \mathrm{g}\) of \(\mathrm{NaOH}\) ?

Step-by-Step Solution

Answer

The mass of the solution containing 15.0 g of NaOH is 375 g.

Step 1: Understand the Percentage Concentration

The given solution has a concentration of 4.00%, which means that for every 100 grams of the solution, there are 4 grams of NaOH (sodium hydroxide).

Step 2: Calculate Total Mass of Solution

To find the total mass of the solution that contains 15.0 g of NaOH, set up a proportion based on the percentage concentration: \( \frac{4 g \: NaOH}{100 g \: solution} = \frac{15.0 g \: NaOH}{x g \: solution} \). Solve for x to find the total mass of the solution.

Step 3: Solve for the Total Mass

Cross-multiply and divide to find x: \( x = \frac{15.0 g \: NaOH \times 100 g \: solution}{4 g \: NaOH} = 375 g \: solution \). This is the total mass of the solution containing 15.0 g of NaOH.

Key Concepts

Concentration of Solutions

In chemistry, the concentration of a solution is a measure of how much solute is dissolved in a specified amount of solvent or solution. Concentration can be expressed in various ways, such as molarity, molality, normality, and mass percent. Mass percent, which is also known as weight percent or mass fraction, is a common way to express concentration, especially in commercial and laboratory settings. It is calculated by taking the mass of the solute and dividing it by the total mass of the solution, then multiplying by 100 to obtain a percentage.

Understanding the concentration is crucial since it directly affects the reactivity and properties of the solution. When working with a solution where the concentration is given as a mass percent, it implies that the proportion is consistent throughout the solution, allowing for straightforward calculations like the one in our exercise.

Mass Percent

Mass percent is a concept used to describe the concentration of a component in a mixture or solution. It represents the mass of the solute divided by the total mass of the solution, multiplied by 100. To clarify using a real-world example, if you have orange juice that has a mass percent of 10% orange pulp, this means that in every 100 grams of this juice, there are 10 grams of orange pulp.

To calculate the mass percent of a solute in a solution, you can use the formula:
\[\text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100\%\]
In the context of the original exercise, the mass percent of NaOH in the solution is 4.00%. This simple label tells you that for every 100 grams of this NaOH solution, there will be 4 grams of pure NaOH.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of the mole. Using stoichiometry, one can predict the amount of products produced from given reactants and vice versa.

Stoichiometric calculations often use balanced chemical equations to quantify the relationships between different substances. These calculations can be extended to include considerations of concentration, such as when dealing with solutions. In the context of our problem, stoichiometry takes the form of a simple proportion, relating the mass of solute to the mass of the solution through the given mass percent.

By understanding and applying stoichiometry, students can solve a wide range of problems, from simple dilution exercises to complex chemical syntheses, making it a fundamental tool in a chemist's skill set.