Ch.2 The Metric System

specific gravity (sp gr)

the ratio of the density of a liquid compared to the density of water at 4 °C

reciprocal

the relationship between a fraction and its inverse, for example, 1 qt/946 mL and 946 mL/1 qt

cubic centimeter (cm³)

the volume occupied by a cube 1 cm on a side EQUIVALENT UNITS 1 cm³ is exactly equal to 1 mL

converting °C to °F

°C x (180 °F/100°C) + 32°F = °F SAME AS °F = (9/5 X °C) + 32 We reverse the procedure of converting °F to °C. We first multiply the Celsius temperature by the ratio 180 °F/100 °C, and then add 32 °F

temperature

(a) average energy of molecules in motion (kinetic energy); for example, the average energy of air molecules in the atmosphere (b) measure of how hot or cold a substance is relative to another

converting °F to °C

(°F-32°F) x (100°C/180°F) = °C SAME AS °C = 5/9 X (°F-32°F) Notice that 180 Fahrenheit units are equivalent to 100 Celsius units. Therefore, to convert from °F to °C, we first subtract 32 (the difference between the freezing point of water on the two scales) and then multiply by 100 °C/180 °F

VOLUME BY DISPLACEMENT

A technique for determining the volume of a solid or a gas by measuring the volume of water is displaces The volume by displacement is the difference between the initial and final readings in a calibrated container EXAMPLE What is the volume of a gold nugget if the water level in a graduated cylinder increases from 25.0 mL to 42.5 mL? 42.5 mL - 25.0 mL = 17.5 mL

unit equation

A unit equation is a simple statement of two equivalent quantities. • For example: - 1 hour = 60 minutes - 1 minute = 60 seconds • Also, we can write: - 1 minute = 1/60 of an hour - 1 second = 1/60 of a minute

THE PERCENT CONCEPT (see picture)

An expression for the amount of a SINGLE quantity compared to an entire sample; an expression of parts per hundred parts EXAMPLES (a) If a 14-karat ring contains 20.0 g gold and 14.3 g silver, what is the percent of gold? single qty./total sample (gold+silver) x 100% = 58.3% 20.0 g/(20.0 + 14.3) * 100% = 58.3% (b) 4.77% = 4.77/100

physical quantities and basic metric units

BASIC METRIC UNITS LENGTH = meter (m) MASS = gram (g) VOLUME = liter (L) TIME = second (s) TEMPERATURE = Celsius degree (°C)

specific heat equation (example)

Q = mCΔT Q = amount of heat (calorie or joules) m = mass of water (grams) C = specific heat capacity ΔT = temperature change (°C or K)

specific heat equation (heat release example)

Q = mCΔT Q = amount of heat (calorie or joules) m = mass of water (grams) C = specific heat capacity ΔT = temperature change (°C or K)

METRIC-ENGLISH CONVERSION (see picture)

STEP 1: Write down the unit asked for in the answer. STEP 2: Write down the given value related to the answer. STEP 3: Apply unit factor(s) to convert the given unit to the units desired in the answer LENGTH 1 in. = 2.54 cm MASS 1 lb. = 454 g VOLUME 1 qt. = 946 mL TIME 1 sec = 1.00 s

METRIC-TO-METRIC CONVERSION (see picture)

STEP 1: Write down the unit asked for in the answer. STEP 2: Write down the given value related to the answer. STEP 3: Apply unit factor(s) to convert the given unit to the units desired in the answer We can write unit equations for the conversion between different metric units. • The prefix kilo- means 1000 basic units, so 1 kilometer = 1000 meters • The unit equation is 1 km = 1000 m • Similarly, a millimeter is 1/1000 of a meter, so the unit equation is 1000 mm = 1 m

heat

The flow of energy from an object at a higher temperature to an object at a lower temperature. Heat is always transferred from the hot to the cold object until they reach the same temperature, called thermal equilibrium.

VOLUME BY CALCULATION (cubic units)

To calculate the volume of a RECTANGULAR solid VOLUME = length x width x thickness (a) ALL measurements must be in the SAME units (b) Volume is reported in cubic units, such as cubic centimeters 1 cm³ EXAMPLE What is the volume of a rectangular solid measuring 65 mm by 35 mm by 12 mm? 65 mm x 35 mm x 12 mm = 27,000 mm^3

converting K unit to °C

To convert from Kelvin to °C, subtract 273 units. K - 273 = °C NOTE: negative K temperatures do NOT exist; lowest K unit is 0

converting °C to K unit

To convert from °C to Kelvin, add 273 units °C + 273 = K Notice that the Kelvin scale is 273 units above the Celsius scale. Therefore, to convert from °C to K, we must add 273 units to the Celsius temperature.

International System (SI)

a comprehensive system of measurement with seven base units

metric system

a decimal system of measurment with basic units

English System

a nondecimal system of measurement without any basic units for length, mass, or volume

UNIT ANALYSIS METHOD

a procedure for solving problems that proceeds from a given value to a related answer by the conversion of units

unit factor

a ratio of two quantities that are equivalent EXAMPLES (a) 1 lb/454 g or 454 g/1 lb (b) For the unit equation 1 hour = 60 minutes, we can write two unit factors: 1 hour/60 minutes or 60 minutes/1 hour

exact equivalent

a statement of two exactly equal values, for example, 1 m = 100 cm

joule (J)

a unit of energy in the SI system 1 cal = 4.184 J

specific heat equation (see picture)

heat / mass (g) x (ΔT) = specific heat (cal)/g x °C heat = cal mass = g ΔT = T final - T initial

metric prefixes (see picture)

tera- T giga- G mega- M kilo- k BASIC UNIT: meter, gram, liter, second deci- d centi- c milli- m micro- μ nano- n pico- p

meter (m)

the BASIC unit of LENGTH in the metric system

gram (g)

the BASIC unit of MASS in the metric system

second (s)

the BASIC unit of TIME in the metric system

liter (L)

the BASIC unit of VOLUME in the metric system

Fahrenheit degree (°F)

the BASIC unit of temperature in the ENGLISH system

Celsius degree (°C)

the BASIC unit of temperature in the METRIC system

Kelvin unit (K)

the BASIC unit of temperature in the SI system

specific heat

the amount of heat required to raise 1 g of SUBSTANCE 1 °C

calorie (cal)

the amount of heat required to raise 1 g of WATER 1 °C

DENSITY CONCEPT

the amount of mass in one unit of volume density = mass/volume EXAMPLE What is the density of 10.0 mL of ether if its mass is 7.142 g? 7.142 g/10.0 mL = 0.714 g/mL

DENSITY IS EXPRESSED IN DIFFERENT UNITS (see picture)

• SOLIDS g/cm³ • LIQUIDS g/mL • GASES g/L