Question

How many grams of \(\mathrm{K}_{2} \mathrm{CO}_{3}\) are in \(750 \mathrm{~mL}\) of a \(3.5 \%(\mathrm{~m} / \mathrm{v})\) \(\mathrm{K}_{2} \mathrm{CO}_{3}\) solution?

Short answer

26.25 grams

Step-by-step solution

Understand the Problem

We need to find how many grams of \( \mathrm{K}_{2} \mathrm{CO}_{3} \) are in a 750 mL solution with a concentration of 3.5% (mass/volume).

Convert the Percentage to a Decimal

Convert the percentage concentration to a decimal by dividing by 100: \( 3.5 \div 100 = 0.035 \).

Calculate the Mass of \( \mathrm{K}_{2} \mathrm{CO}_{3} \)

Multiply the decimal concentration by the volume of the solution in mL: \( \text{mass} = 0.035 \times 750 \).

Perform the Multiplication

Calculate the mass: \( \text{mass} = 0.035 \times 750 = 26.25 \) grams.

Key concepts

Solution Concentration

When we talk about solution concentration, we're referring to how much solute is dissolved in a given amount of solvent. It's like mixing sugar into water. The more sugar you add, the more concentrated the solution becomes.

There are various ways to express concentration, and understanding each one helps in different problem-solving scenarios in chemistry. Some common expressions are:

• Molarity (M): Moles of solute per liter of solution
• Mass/Volume Percentage (m/v): Grams of solute per 100 mL of solution
• Mass Percentage (w/w): Grams of solute per 100 grams of solution

In this exercise, we've used a mass/volume percentage to express concentration, specifically 3.5% (m/v), meaning 3.5 grams of potassium carbonate (K₂CO₃) in every 100 mL of solution.

Mass/Volume Percentage

Mass/volume percentage is a handy way to describe the concentration of a solution. It tells us how much mass of the solute is present in a specific volume of the solution. In our example, a 3.5% (m/v) solution means:

• 3.5 grams of K₂CO₃ in every 100 mL of solution

To solve this problem, we first converted the percentage to a decimal (3.5 ÷ 100 = 0.035). This step simplifies the calculations by providing a straightforward multiplier. We then multiplied this factor by the total volume of the solution:

• 0.035 × 750 mL = 26.25 grams

This calculation gives us the mass of K₂CO₃ in 750 mL of the solution.

Molar Mass Calculations

Understanding molar mass is essential in chemistry. The molar mass of a substance is the mass of one mole of that substance (usually in grams per mole). For potassium carbonate (K₂CO₃), we calculate the molar mass by adding up the atomic masses of all the atoms in its formula:

• Potassium (K): 39.1 grams/mole × 2 = 78.2 grams/mole
• Carbon (C): 12.0 grams/mole × 1 = 12.0 grams/mole
• Oxygen (O): 16.0 grams/mole × 3 = 48.0 grams/mole

Adding these together, the molar mass of K₂CO₃ is 138.2 grams/mole (78.2 + 12.0 + 48.0). This value is useful for converting between grams and moles, especially when dealing with chemical reactions and solution preparations.

Problem-Solving in Chemistry

Problem-solving in chemistry often involves several steps. Understanding the problem is the first critical step. Here's a simple method to tackle chemistry problems:

• Read the problem carefully: Identify what is given and what needs to be found.
• Convert units if necessary: Ensure all measurements are in compatible units.
• Apply appropriate formulas: Use the correct chemical principles and formulas.
• Calculate the answer: Perform the necessary mathematical operations.
• Check your work: Review your steps and ensure the answer makes sense.

Following these steps, as we did in solving this problem, ensures accuracy and builds a deeper understanding of chemistry concepts.