Question

\(18.72 \mathrm{~g}\) of a substance \(^{*} X\) 'occupies \(1.81 \mathrm{~cm}^{3} .\) What will be its density measured in correct significant figures? (a) \(10.3 \mathrm{~g} \mathrm{~cm}^{-3}\) (b) \(10.34 \mathrm{~g} \mathrm{~cm}^{-3}\) (c) \(10.4 \mathrm{~g} \mathrm{~cm}^{-3}\) (d) \(10.3425 \mathrm{~g} \mathrm{~cm}^{-3}\)

Short answer

The density of substance X is 10.34 g/cm^3, which corresponds to option (b).

Step-by-step solution

Identify Given Data

We are given the mass of the substance X as 18.72 g and the volume it occupies as 1.81 cm^3.

Apply Density Formula

To find the density (d), use the formula d = mass/volume, which means d = 18.72 g / 1.81 cm^3.

Calculate Density

Perform the division to obtain the density. Ensure that the answer adheres to the rule of significant figures, which is determined by the least precise measurement (in this case, to two decimal places due to the volume measurement).

Round to Correct Significant Figures

Given the significant figures in the mass and volume, the answer should also be rounded off to reflect the same level of precision. The result from the calculation is thus rounded to two decimal places.

Key concepts

Density Calculation

Understanding how to calculate density is an important skill in chemistry, as it helps to identify substances and understand their properties. Density is defined as mass per unit volume and is calculated using the formula:

\( density (d) = \frac{mass (m)}{volume (v)} \).

In the context of the provided exercise, the mass of the substance X is given as 18.72 g, and the volume is given as 1.81 cm³. By applying the formula, we perform the division of the given mass by the volume to find the density. It's essential to take into account the units of measure, which in this example are grams (g) for mass and cubic centimeters (cm³) for volume, leading to a density expressed in g/cm³. An accurate density calculation is the foundation for correct problem-solving and comprehending material characteristics in chemistry.

Here are a few pointers to ensure your density calculations are precise:

• Ensure that you are using the correct units for mass and volume.
• Be consistent with units throughout the calculation to avoid unit conversion errors.
• When measuring substances, use devices that provide the most accurate and precise measurements possible to ensure the reliability of your results.

Significant Figures Rules

The rules governing significant figures are critical in chemistry to accurately report measurements and calculated results. Significant figures are the digits in a number that carry meaning contributing to its precision. When performing calculations like density, these rules help maintain the precision of the measurements involved.

For the exercise, the significant figures rule dictates that the final answer should be reported with the same number of decimal places as the least precise measurement. Since the volume (1.81 cm³) is measured to two decimal places, the final density should also be reported to two decimal places.

Here's a quick summary of key significant figures rules:

• All non-zero digits are considered significant.
• Zeros between non-zero digits are significant (e.g., 1003 has four significant figures).
• Leading zeros are not significant (e.g., 0.052 has two significant figures).
• Trailing zeros in a number with a decimal point are significant (e.g., 2.0 has two significant figures).
• When multiplying or dividing, the result must have the same number of significant figures as the measurement with the fewest significant figures.
• When adding or subtracting, the result should have the same number of decimal places as the measurement with the least precision.

It is crucial to apply these rules consistently to ensure the credibility of your work in chemistry.

Chemistry Problem Solving

Effective problem-solving in chemistry involves a systematic approach to analyze and solve questions, which typically includes understanding concepts, identifying the problem, and applying scientific principles. In our textbook exercise, the problem-solving process requires calculating the density of substance X given its mass and volume.

The step-by-step technique is a reliable way to address chemistry problems:

• Identify the problem: Determine what you are being asked to find - in this case, the density of a substance.
• Gather information: Collect the data provided or necessary for calculating the answer, such as mass and volume in this exercise.
• Choose the appropriate formula
• Plug in the values and calculate: Insert the known values into the formula and perform the calculation, being sure to follow the rules for significant figures as they apply.
• Review and check: Always double-check your calculations and the application of significant figures to ensure the answer is accurate and precise.

In the example problem, after performing the division and applying the significant figures rules, we get a density of 10.34 g/cm³, rounded to two decimal places as required. By following a clear and structured problem-solving approach, students can minimize errors and build confidence in their chemistry capabilities.