Question

Calculate the mass in grams for each of the following solids. (a) \(5.00 \mathrm{~cm}^{3}\) of table salt \(\left(d=2.18 \mathrm{~g} / \mathrm{cm}^{3}\right)\) (b) \(2.50 \mathrm{~cm}^{3}\) of table sugar \(\left(d=1.59 \mathrm{~g} / \mathrm{cm}^{3}\right)\)

Short answer

(a) 10.90 grams; (b) 3.98 grams

Step-by-step solution

Understand the Given Data

For part (a), the volume of table salt is given as \(5.00 \mathrm{~cm}^3\) and its density is \(2.18 \mathrm{~g/cm}^3\). For part (b), the volume of table sugar is \(2.50 \mathrm{~cm}^3\) and its density is \(1.59 \mathrm{~g/cm}^3\).

Formula for Mass Calculation

The mass of an object can be calculated using the formula: \[ \text{mass} = \text{density} \times \text{volume} \]

Calculate Mass of Table Salt

Using the formula, calculate the mass for part (a): \[ \text{mass of salt} = (2.18 \mathrm{~g/cm}^3) \times (5.00 \mathrm{~cm}^3) \] Perform the multiplication: \[ \text{mass of salt} = 10.90 \mathrm{~g} \]

Calculate Mass of Table Sugar

Using the same formula, calculate the mass for part (b): \[ \text{mass of sugar} = (1.59 \mathrm{~g/cm}^3) \times (2.50 \mathrm{~cm}^3) \] Perform the multiplication: \[ \text{mass of sugar} = 3.975 \mathrm{~g} \]

Final Results

The mass of \(5.00 \mathrm{~cm}^3\) of table salt is \(10.90\) grams, and the mass of \(2.50 \mathrm{~cm}^3\) of table sugar is approximately \(3.98\) grams when rounded to two decimal places.

Key concepts

Density

In the realm of chemistry, **density** is a crucial property that links mass and volume together. It refers to how much mass is contained within a specific volume of a substance and is often used to identify materials. Density is expressed in units such as grams per cubic centimeter (g/cm³) in the metric system. To calculate it, we use the formula: \[ \text{density} = \frac{\text{mass}}{\text{volume}} \]This formula shows that a high density means more mass in a smaller space. When dealing with solids like salts or sugars, understanding their density helps in predicting how much space they will occupy and their weight under given conditions. Remember, substances with higher densities will often weigh more than those with lower densities, given the same volume.

Volume

**Volume** is the amount of space that an object occupies. It is a three-dimensional measure and is important in chemistry when studying substances in solid, liquid, or gaseous states. In this context, volume is expressed in cubic centimeters (cm³) or liters (L). In practical situations, you might measure the volume of an irregular object by submerging it in water and measuring the displaced water, known as displacement method. In our exercise, we used the volumes directly given: - 5.00 cm³ of table salt - 2.50 cm³ of table sugar This information is vital because it allows us to calculate the mass of these solids using their respective densities. Volume is foundational in calculations, as it helps us determine how much of a substance is present and further calculate the mass or reactant needed in chemical reactions.

Chemistry Education

**Chemistry education** provides a structured understanding of the properties and behaviors of different substances. In it, we learn not only the theoretical concepts like density and volume but also practical applications such as calculating mass from these properties. Through exercises like the one we solved, students can:

• Strengthen their problem-solving skills by applying formulas in various scenarios.
• Develop their ability to analyze data and make precise calculations based on given parameters.
• Enhance their understanding of material properties and their significance in everyday life.

This comprehensive understanding enables students to grasp how materials interact in chemical processes and their application in fields ranging from engineering to environmental science.

Problem-Solving Steps

Approaching problems methodically is essential in chemistry. **Problem-solving steps** involve a structured approach to understanding and resolving questions using provided data and theoretical knowledge. Here, we followed a simple yet effective series of steps:- **Recognize the Given Information:** Identify and list all given data, such as density and volume.- **Identify the Correct Formula:** Select the appropriate formula. For mass calculation, it's \[ \text{mass} = \text{density} \times \text{volume} \].- **Perform Calculations:** Substitute the given values into the formula and compute.- **Check Results:** Review calculations for accuracy and relevance to ensure correct solutions.Following these steps helps students build a competency in handling more complex problems in chemistry, ensuring that they develop a methodical approach to learning and understanding scientific concepts.