Measurement and Problem Solving

Scientific Notation

Scientific notation is a method used in chemistry to express very large or very small numbers in a concise and manageable form. This is essential for dealing with the vast range of quantities encountered in chemical measurements.

• Definition: Scientific notation expresses numbers as a product of a coefficient (between 1 and 10) and a power of ten.

• Example:

• Application: Used for atomic and molecular scales, such as the mass of an electron or Avogadro's number.

Key Steps:

1. Move the decimal point to create a coefficient between 1 and 10.

2. Count the number of places moved; this becomes the exponent of 10.

3. If the decimal is moved to the left, the exponent is positive; if to the right, it is negative.

Example:

Standard Notation

Standard notation is the regular way of writing numbers without exponents. Converting between scientific and standard notation is a fundamental skill in chemistry calculations.

• Example:

Uncertainty in Measurement

Significant Figures

Significant figures (sig figs) reflect the precision of a measured or calculated quantity. Every measurement contains some uncertainty, and significant figures communicate this uncertainty.

• Definition: The digits in a measurement that are known with certainty plus one estimated digit.

• Example: Measuring a length as 2.35 cm means 2 and 3 are certain, 5 is estimated.

Rules for Determining Significant Figures

• Nonzero digits are always significant.

• Zeros between nonzero digits are significant.

• Leading zeros are not significant.

• Trailing zeros are significant only if there is a decimal point.

Examples:

• 0.0045 (2 sig figs)

• 100.0 (4 sig figs)

• 1200 (2 sig figs unless specified otherwise)

Rounding Calculated Answers

• Calculated answers cannot be more certain than the measurements used.

• For multiplication and division, the answer should have the same number of significant figures as the measurement with the fewest sig figs.

• For addition and subtraction, the answer should have the same number of decimal places as the measurement with the fewest decimal places.

Accuracy and Precision

Accuracy and precision are two important concepts in measurement:

• Accuracy: How close a measurement is to the true or accepted value.

• Precision: How close a series of measurements are to each other.

Example: Hitting the bullseye on a dartboard is accurate; grouping darts closely together is precise.

Quantifying Precision: Mean Absolute Deviation (MAD)

The mean absolute deviation is used to quantify the precision of a set of measurements.

• Formula:

• Where is each measurement, is the mean, and is the number of measurements.

Example Calculation: Calculate the mean, then the average of the absolute deviations from the mean.

Metric and Non-Metric Conversions

Conversion Factors

Conversion factors are ratios used to express measurements in different units. Dimensional analysis is a systematic approach to solving conversion problems using these factors.

• Example:

• Dimensional Analysis: Multiply by conversion factors so units cancel appropriately.

Metric Units and Prefixes

The metric system uses base units and prefixes to indicate multiples or fractions of these units.

SI Base Units

Temperature: Celsius and Kelvin

The Celsius and Kelvin scales are commonly used in chemistry. The size of one degree is the same, but the zero point is different.

• Conversion:

• Water freezes at: or

• Water boils at: or

Density

Definition and Calculation

Density is a physical property defined as the mass of a substance per unit volume. It is used to identify substances and predict whether they will float or sink in a fluid.

• Formula:

• Units: Commonly expressed in or

Example Calculation: If a substance has a mass of 7.9 g and a volume of 0.69 cm3, its density is:

This value is characteristic of lead.

Applications of Density

• Used to identify unknown substances.

• Determines whether an object will float or sink in water (objects with density less than water float).

Summary Table: Key Concepts

Additional info: These notes cover foundational measurement and calculation skills essential for all subsequent chemistry topics, including chemical reactions, stoichiometry, and solution preparation.