Problem 98 - General Chemistry

Question

A graduated cylinder weighed \(66.5 \mathrm{~g}\). To the cylinder was added \(58.2 \mathrm{~g}\) of water and \(5.279 \mathrm{~g}\) of sodium chloride. What was the total mass of the cylinder and the solution? Express the answer to the correct number of significant figures.

Step-by-Step Solution

Answer

The total mass of the cylinder and solution is 130 g.

Step 1: Identify the Components

We need to find the total mass by adding the mass of the graduated cylinder, the mass of the water, and the mass of the sodium chloride.

Step 2: Addition of Masses

Add the mass of the empty graduated cylinder (66.5 g), the mass of the water (58.2 g), and the mass of the sodium chloride (5.279 g). This will give us the total mass of the cylinder and its contents.

Step 3: Perform the Calculation

Calculate the total mass: \(66.5 \text{ g} + 58.2 \text{ g} + 5.279 \text{ g} = 129.979 \text{ g}\).

Step 4: Determine Significant Figures

The numbers 66.5 and 58.2 have three significant figures, while 5.279 has four significant figures. The sum should be reported to the least number of significant figures among the addends, which is three significant figures.

Step 5: Round the Result

Round 129.979 to three significant figures, resulting in 130 g.

Key Concepts

Mass Calculation

Calculating mass is essential in many scientific experiments and is especially crucial in chemistry. In this exercise, calculating the total mass involves adding up several components. Each of these components contributes a quantifiable mass, such as the mass of the graduated cylinder itself, the water, and the sodium chloride. By summing these values, we reach the total mass of the entire system or solution. This arithmetic operation allows chemists to assess the total quantity of substances involved, which is a vital part of many experimental and analytical procedures.

Graduated Cylinder

A graduated cylinder is a common piece of laboratory equipment used to measure the volume of a liquid. Though it is primarily used for measuring volumes, the graduated cylinder itself has a specific mass. In this problem, the graduated cylinder initially weighed 66.5 g. It is important to account for this mass when calculating the total mass of the mixture being analyzed, as the cylinder is the container holding the solution. Understanding the function and features of a graduated cylinder can help you accurately measure and calculate other parameters in your chemical experiments.

Addition of Masses

When dealing with mass calculation, addition of masses from various components is key. As in the original example, adding up all separate masses refines our understanding of the total mass. The mass values assigned to each element of the experiment are combined:

• The empty graduated cylinder: 66.5 g
• The water: 58.2 g
• Sodium chloride: 5.279 g

These are summed to find the complete mass in the system. Adding them straightforwardly gives us the figure: 129.979 g. This sum gives us insight into the total quantities involved in the experiment.

Rounding Numbers

Rounding numbers is crucial when applying significant figures in scientific calculations. Significant figures dictate the precision of a reported result. In the given exercise, the significant figures are driven by the values with the least digits after the decimal. Here, that is three figures, influenced by the values 66.5 and 58.2. The last step then required us to round 129.979 g to comply with this three-digit precision rule. Therefore, the total mass rounds to 130 g, accurately reflecting the precision limits implied by the input data.