Chap 2

Quantitative Skills in Chemistry

Significant Figures

Significant figures are the digits in a measurement that are known with certainty plus one digit that is estimated. They are crucial for expressing the precision of measured quantities in chemistry.

• Definition: Significant figures reflect the accuracy of a measured or calculated value.

• Rules:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros in a decimal number are significant.

• Example: The number 0.002087 has four significant figures: 2, 0, 8, and 7.

Rounding to Significant Figures

When reporting measurements, it is important to round to the correct number of significant figures.

• Example: 10.532 g rounded to three significant figures is 10.5 g.

• Application: Use significant figures when reporting results of calculations.

Conversions and Dimensional Analysis

Dimensional analysis is a method used to convert one unit to another using conversion factors.

• Definition: A conversion factor is a ratio that expresses how many of one unit are equal to another unit.

• Example: To convert 2.54 cm to inches: $2.54 \text{ cm} \times \frac{1 \text{ in}}{2.54 \text{ cm}} = 1 \text{ in}$

• Significant Figures in Conversions: The answer should reflect the correct number of significant figures based on the original measurement.

Calculating Volume with Measured Numbers

When calculating volume, use the correct formula and pay attention to significant figures.

• Formula: $V = \frac{28.5 \text{ mL}}{3.6}$

• Application: The result should be rounded to two significant figures.

Addition and Subtraction with Significant Figures

When adding or subtracting measured values, the result should be rounded to the least number of decimal places in the original measurements.

• Example: $7.5 \text{ g} + 2.26 \text{ g} + 1.311 \text{ g} + 2 \text{ g} = 13.1 \text{ g}$

Units and Measurement

Metric Units and Abbreviations

The metric system is used in chemistry for consistency and ease of conversion.

• Common Units:

  • Milligram (mg)

  • Milliliter (mL)

  • Kilometer (km)

  • Gram (g)

• Correct Pairing Example: Microgram / mg

Comparing Metric Units

Understanding the relative sizes of metric units is important for conversions.

• Largest Unit Example: Kilometer is larger than meter, centimeter, and millimeter.

Length Conversions

Length can be converted between metric and imperial units using conversion factors.

• Example: $6.5 \text{ cm} \times \frac{1 \text{ in}}{2.54 \text{ cm}} = 2.6 \text{ in}$

Mass and Dosage Calculations

Dosage calculations are common in health-related chemistry applications.

• Formula: $\text{Dose} = \text{body weight (kg)} \times \text{dosage (mg/kg)}$

• Example: For a child weighing 8.5 lb (convert to kg: $8.5 \text{ lb} \times \frac{1 \text{ kg}}{2.2 \text{ lb}} = 3.86 \text{ kg}$), with a dosage of 5.0 mg/kg: $3.86 \text{ kg} \times 5.0 \text{ mg/kg} = 19.3 \text{ mg}$

Volume and Concentration Calculations

Calculating the required volume of a solution based on concentration is a key skill.

• Formula: $\text{Volume (mL)} = \frac{\text{Required mass (mg)}}{\text{Concentration (mg/mL)}}$

• Example: For 0.125 g (125 mg) of ampicillin in a 250 mg/5.0 mL solution: $\frac{125 \text{ mg}}{50 \text{ mg/mL}} = 2.5 \text{ mL}$

Density and Mass Calculations

Density

Density is the mass per unit volume of a substance and is used to relate mass and volume.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Units: Common units are g/mL, g/cm3, kg/L.

• Example: A solution with a density of 1.15 g/mL and a volume of 2.00 L: $2.00 \text{ L} \times \frac{1000 \text{ mL}}{1 \text{ L}} \times 1.15 \text{ g/mL} = 2300 \text{ g}$

Calculating Volume from Mass and Density

To find the volume of a substance given its mass and density, rearrange the density formula.

• Formula: $\text{Volume} = \frac{\text{Mass}}{\text{Density}}$

• Example: Diamond with a density of 3.52 g/cm3 and a mass of 15.1 g: $\frac{15.1 \text{ g}}{3.52 \text{ g/cm}^3} = 4.29 \text{ cm}^3$

Tables: Comparison of Densities

The following table compares the densities of various substances, which is useful for identifying materials and solving density problems.

Substance	Density (g/mL)
Balsa wood	0.16
Sugar	1.59
Aluminum	2.70
Mercury	13.6
Table salt	2.16

Summary

• Understanding significant figures is essential for accurate measurement and reporting in chemistry.

• Dimensional analysis allows for conversion between units and ensures correct calculation of quantities.

• Density relates mass and volume and is a key concept in identifying substances and solving practical problems.

• Metric units and their correct abbreviations are foundational for scientific communication.