Measurement and Chemical Calculations

• Measurement and Chemical Calculations is the subject being studied
• Mark S. Cracolice from The University of Montana, and Edward I. Peters wrote this chapter

Textbook Learning Objectives

• Write a number in scientific notation when given ordinary decimal form
• Write a number in ordinary decimal form when given scientific notation
• Use a calculator to add, subtract, multiply, and divide numbers expressed in scientific notation
• Convert an equivalency into two conversion factors
• Apply the algorithm for using conversion factors to solve quantitative problems
• Explain why the metric system is used in sciences
• State and write with appropriate metric prefixes the relationship between any metric unit, and its corresponding kilounit, centiunit, and milliunit
• Using Table 3.1, state and write with appropriate metric prefixes the relationship between any metric unit and other larger and smaller metric units
• Distinguish between mass and weight
• Identify the metric units of mass, length, and volume
• Given a mass, length, or volume expressed in basic metric units, kilounits, centiunits, or milliunits, express that quantity in the other three units
• Given a mass, length, or volume expressed in any metric units and Table 3.1 or the equivalent, express that quantity in any other metric unit
• Given a description of a measuring instrument and an associated measurement, express the measured quantity with the uncertain digit in the correct location in the value
• State the number of significant figures in a given quantity
• Round off given values to a specified number of significant figures
• Add or subtract given measured quantities and express the result in the proper number of significant figures
• Multiply or divide given measured quantities and express the result in the proper number of significant figures
• Given a metric-USCS conversion factor and a quantity expressed in any unit in Table 3.2, express that quantity in corresponding units in the other system
• Given a temperature in either Celsius or Fahrenheit degrees, convert it to the other scale
• Given a temperature in Celsius degrees or kelvins, convert it to the other scale
• Write a mathematical expression indicating that one quantity is directly proportional to another quantity
• Use a proportionality constant to convert a proportionality to an equation
• Given the values of two quantities that are directly proportional to each other, calculate the proportionality constant, including its units
• Write the defining equation for a proportionality constant and identify units in which it might be expressed
• Given two of the following for a sample of a pure substance, calculate the third: mass, volume, and density

Course Learning Objectives

• Define the common SI units and metric prefixes (CLO 3.1)
• Use dimensional analysis to convert between units of measure (CLO 3.2)
• Use of scientific notation and significant digits (CLO 3.3)

Scientific Notation

• Scientific notation: A method of writing numbers in the form a.bcd x 10e
• Coefficient: a.bcd, which is a number equal to or greater than 1 and less than 10
• Exponential: 10e
• Exponent: Number e in 10e is a whole number, and may be positive or negative

Conversion of Decimal Number to Scientific Notation

• Rewrite the number, place the decimal after first nonzero digit and write ×10
• Count the number of places the decimal in the original number moved to its new place
• Write the number as the exponent of 10
• Compare original number with new coefficient
• If the coefficient is smaller than original number, exponent has a positive value
• If the coefficient is larger than original number, exponent has a negative value

Coefficients

• Coefficients are important in scientific notation
• For numbers less than 1, simply count the zeros; that will be the number (in negative) for the exponent
• For numbers at 1 or greater, include all numbers excluding highest priority number

Quantity

• In chemistry, quantities are expressed as the product of a value and a unit
• Value x Unit = Quantity

Equivalency and Conversion Factors

• Equivalency: Expression stating two quantities with different units, but represent the same property
• Conversion factor: Relationship between different units of measurement that express the same quantity, written as fraction
• Two conversion factors can result from each equivalency

Algorithm Steps for Solving Quantitative Chemistry Problems

• Step 1: Analyze the problem statement
• Determine the given quantity: Value x unit
• Describe the property of the given quantity
• Describe the property of the wanted quantity
• State the unit of the wanted quantity
• Step 2: Identify equivalencies or an algebraic relationship that may be needed to solve the problem
• Change the equivalencies to conversion factors or solve algebraic equation for wanted variable
• Step 3: Construct the solution setup
• Confirm that the units cancel correctly and calculate the value of the answer
• Step 4: Check the solution at two levels
• Making sense - Is the value reasonable?
• What was learned

Metric Prefixes

• 1 Gram = 100cg, 0.001kg, 1000mg
• 1 Meter = 100cm, 0.001km, 1000mm
• SI Unit of Length: Meter
• SI Unit of Mass: Kg
• SI Unit of Volume: Cubic Meter
• Conversions between Meters and Grams should be known

Table 3.1 - Metric Prefixes